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MCNP User Manual, Version 5

1. 43000 01p moplib 1982 461 51 0 1 B IV B IV E amp C n a 43000 02p mcplib02 1993 695 90 100 89 B IV E amp C n a 43000 03p 03 2002 2180 90 100 B IV 89 B IV E amp C BM amp M 43000 04p mcplib04 2002 7946 1051 100 B VL8 B VL8 B VI8 BM amp M Z 44 Ruthenium se oi oko OR SR OR k kk 44000 01p moplib 1982 461 51 0 1 B IV B IV E amp C n a 44000 02p mcplib02 1993 695 90 100 89 B IV E amp C n a 44000 03p mcplib03 2002 2180 90 100 89 B IV E amp C BM amp M 44000 04p mcplib04 2002 7988 1058 100 B VL8 B VL8 B VI8 BM amp M Z 45 modium 25 he k k kkk kk kkk kkk kkk k he kk kk k 45000 01 mcplib 1982 461 51 0 1 B IV B IV E amp C n a 45000 02p mcplib02 1993 695 90 100 B IV 89 B IV E amp C n a 45000 03p mcplib03 2002 2180 90 100 89 B IV E amp C BM amp M 45000 04p mcplib04 2002 7856 1036 100 B VL8 B VL8 B VI8 BM amp M 7 46 ak koko E282 Palladium 7 k k a k k ak a he he 46000 01p mcplib 1982 461 51 0 1 B IV B IV E amp C n a 46000 02p mcplib02 1993 695 90 100 89 B IV E amp C n a 46000 03p mcplib03 2002 2081 90 100 89 B IV E amp C BM amp M 46000 04p mcplib04 2002 7595 1009 100 B VL8 B VL8 B VI8 BM amp M 7 47 k k 47000
2. 100000 04p mcplib04 2002 10916 1348 100 B VL8 8 B VI8 BM amp M 10 3 05 G 57 APPENDIX MCNP DATA LIBRARIES PHOTONUCLEAR DATA VI PHOTONUCLEAR DATA 1500 is the only photonuclear data library supported by X 5 It is derived from work done at Los Alamos National Laboratory in the Nuclear Physics Group LANL T 16 The entries in each of the columns of Table G 5 are described as follows ZAID Atomic Weight Ratio Library Evaluation Date Source Length Number of Energies max CP G 58 The nuclide identification number with the form ZZZAAA nnX where ZZZ is the atomic number AAA is the mass number 000 for elements nn is the unique table identification number X U for continuous energy photonuclear tables The atomic weight ratio AWR is the ratio of the atomic mass of the nuclide to a neutron as contained in the original evaluation and used in the NJOY processing of the evaluation Name of the library that contains the data file for that ZAID The date the evaluation was officially released The source from which the evaluated data was obtained The abbreviation LANL T 16 indicates that the data were produced by the Nuclear Physics Group T 16 at Los Alamos National Laboratory The total length of a particular photonuclear table in words The number of energy points NE on the grid used for the photonuclear cross sections for that data table In general a f
3. tuba uud tesi au Eds 41 FSn Examples e 42 laf bris TS 44 Repeated Str cture Lattice Tally Example 1 1 5 rrt Iano earns notare as etta 45 TALLYX Subroutine EXAamples tit e 49 SOURCE 53 SOURCE SUBROUTINE 60 SRCDX SUBROUTINE 3 752250 9548999 42 due Ra Di MORAN 62 CHAPTERS OUTPUT 1 DEMO PROBLEM AND OUTPUT 1 TESTI PROBLEM AND OUTPUT 8 Hrs epa indidit eigo 49 63 EVENT LOG AND GEOMETRY ERRORS 110 ls obl FP H P EY 110 Debus Print for a Lost Particle oil od 113 REFERENCES T 114 APPENDIX SUMMARY OF MCNP COMMANDS 1 GENERAL INFO FILE NAMES EXECUTION LINE UNITS 1 Form of Input INP File Required to Initiate and Run a Problem 1 Form of CONTINUE Input File Requires a RUNTPE file 2 MCNP File Names aud Contents
4. 5 Ex N Or 4 3 2 2 2 4 3 2 2 Xx AXExXx N 8Xx Exj N 4 Xx N Xx N VOV t cA UI 2 2 2 27 Ex Ex P N Now consider the truncated Cauchy formula for the following analysis The truncated Cauchy is similar in shape to some difficult Monte Carlo tallies After numerous statistical experiments on sampling a truncated positive Cauchy distribution Cauchy f x 2 n 1 x 0 lt x lt CES 2 28 it is concluded that the VOV should be below 0 1 to improve the probability of forming a reliable confidence interval The quantity 0 1 is a convenient value and is why the VOV is used for the statistical check and not the square root of the VOV R of the R Multiplying numerator and denominator of Eq 2 24 by 1 N converts the terms into averages and shows that the VOV is expected to decrease as 1 N It is interesting to examine the VOV for the n identical history scores x n N that were used to analyze in Table 2 4 page 2 114 The VOV behaves as 1 n in this limit Therefore ten identical history scores would be enough to satisfy the VOV criterion a factor of at least ten less than the R criterion There are two reasons for this phenomenon 1 it is more important to know R well than the VOV in forming confidence intervals and 2 the history scores will ordinarily not be identical and thus the fourth moment terms in the VOV will increase rapidly over the second moment terms in R The behavior of
5. Volume I LA UR 03 1987 provides an overview of the capabilities of MCNPS and a detailed discussion of the theoretical basis for the code The first chapter provides introductory information about MCNPS5 The second chapter describes the mathematics data physics and Monte Carlo simulation techniques which form the basis for 5 This discussion is not meant to be exhaustive details of some techniques and of the Monte Carlo method itself are covered by references to the literature Volume II LA CP 03 0245 provides detailed specifications for MCNP5 input and options numerous example problems and a discussion of the output generated by MCNP5S The first chapter is a primer on basic MCNPS use The third chapter shows the user how to prepare input for the code The fourth chapter contains several examples and the fifth chapter explains the output The appendices provide information on the available data libraries for MCNP the format for several input output files and plotting the geometry tallies and cross sections Volume III LA CP 03 0284 provides details on how to install MCNP on various computer systems how to modify the code the meaning of some of the code variables and data layouts for certain arrays The Monte Carlo method for solving transport problems emerged from work done at Los Alamos during World War II The method is generally attributed to Fermi von Neumann Ulam Metropolis and Richtmyer MCNP fir
6. when the two fission neutron source distributions are nearly the same The average value of v in a problem can be calculated by dividing the fission neutrons gained by the fission neutrons lost as given in the totals of the neutron weight balance for physical events Note however that the above estimate is subject to the same limitations as described in Eq 2 26 2 182 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CRITICALITY CALCULATIONS C Recommendations for Making a Good Criticality Calculation l Problem Set Up As with any calculation the geometry must be adequately and correctly specified to represent the true physical situation Plot the geometry and check cells materials and masses for correctness Specify the appropriate nuclear data including S a B thermal data at the correct material temperatures Do as good a job as possible to put initial fission source points in every cell with fissionable material Try running short problems with both analog and implicit capture see the PHYS N card to improve the figure of merit for the combined k and any tallies being made Follow the tips for good calculations listed at the end of Chapter 1 2 Number of Neutrons per Cycle and Number of Cycles Criticality calculations can suffer from two potential problems The first is the failure to sufficiently converge the spatial distribution of the fission source from its initial guess to a distribution flu
7. 17 BTU ANUS 17 REFERENCES p 18 CHAPTER 3 DESCRIPTION OF MCNP INPUT 2 0 0 0 0 00 000 2 1 INP EE e E 1 Message des quc 1 rir RUN 2 CMU uela aa 2 Card Format 4 MN TI TT 7 Default rd 7 Input Error Messages D 7 Geometry t us Mu 8 gt ip c 9 Shorthand Cell Specification 11 SURFACE CARDS 14 2 2 08 QA Dua Meu a EUROCOPA A RE QA REM TU Fu RD RAE 11 Surfaces Defined by Equations ita RN E M 11 Axisymmetric Surfaces Defined by Points I5 General Plane Defined by Three Points 17 Surfaces Defined by Macrobodies Lea etae Drac 18 DATA SE ib 23 10 3 05 3 Table of Contents Prob
8. K K K K K K K K K K Fe 56 26056 24u 55 454 la150u 1998 LANL T 16 64043 50 150 Yes Z 29 K K KK K K K K Cu 63 29063 24u 62 389 la150u 1999 LANL T 16 73548 57 150 Yes Z 73 Tantalum Ta 18 73181 24u 179 4 lal50u 1999 LANL T 16 85094 50 150 Yes Z 74 Tungsten ok ok K K W 184 74184 24u 182 3707 lal50u 1998 LANL T 16 78439 51 150 Yes Z 82 Lead K K K K KK K P 206 82206 24u 204 2 lal50u 1998 LANL T 16 78186 49 150 Yes pp 207 82207 24u 205 2 lal50u 1998 LANL T 16 178259 52 150 Pb 208 82208 24u 206 19 la150u 1998 LANL T 16 77099 51 150 Yes 10 3 05 G 59 APPENDIX G MCNP DATA LIBRARIES DOSIMETRY DATA VII DOSIMETRY DATA The tally multiplier FM feature in MCNP allows users to calculate quantities of the form c E R E dE where is a constant is the fluence n cm and R E is a response function If R E is a cross section and with the appropriate choice of units for C atom b cm the quantity calculated becomes the total number of some type of reaction per unit volume If the tally is made over a finite time interval it becomes a reaction rate per unit volume In addition to using the standard reaction cross section information available in our neutron transport libraries dosimetry or activation reaction data can also be used as a res
9. X s e For one dimensional deep penetration through highly absorbing media the variance typically will decrease as p goes from zero to some and then increase as p goes from p to one For p p the solution is underbiased and for p gt the solution is overbiased Choosing p is usually a matter of experience although some insight may be gleaned by understanding what happens in severely underbiased and severely overbiased calculations For illustration apply the variance analysis of page 2 118 to a deep penetration problem when the exponential transform is the only nonanalog technique used In a severely underbiased calculation p gt 0 very few particles will score but those that do will all contribute unity Thus the variance in an underbiased system is caused by a low scoring efficiency rather than a large dispersion in the weights of the penetrating particles In a severely overbiased system p 1 particles will score but there will be a large dispersion in the weights of the penetrating particles with a resulting increase in variance Comments MCNP gives a warning message if the exponential transform is used without a weight window There are numerous examples where an exponential transform without a weight window gives unreliable means and error estimates However with a good weight window both the means and errors are well behaved The exponential transform works best on highly absorbing medi
10. he he he oe he oe he he oe 50112 30y 111 90500 LLNL ACTL 1983 789 50114 30y 113 90300 LLNL ACTL 1983 435 50115 30y 114 90300 LLNL ACTL 1983 389 50116 30y 115 90200 LLNL ACTL 1983 603 50117 30y 116 90300 LLNL ACTL 1983 313 50118 30y 117 90200 LLNL ACTL 1983 745 50119 30y 118 90300 Illdos LLNL ACTL 1983 311 50120 26y 118 87200 532dos ENDF B V 1974 12881 50120 30y 119 90200 LLNL ACTL 1983 309 50122 26y 120 85600 532dos ENDF B V 1974 1891 50122 30y 121 90300 LLNL ACTL 1983 275 50124 26y 122 84100 532dos ENDF B V 1974 1693 50124 30y 123 90500 LLNL ACTL 1983 485 7 51 ARR PR ae Antimony 51121 30 120 90400 LLNL ACTL 1983 811 51123 30y 122 90400 LLNL ACTL 1983 1013 53127 24 125 81400 531405 ENDF B V 1972 115 53127 26y 125 81400 532dos ENDF B V 1980 14145 53127 30y 126 90400 LLNL ACTL 1983 221 Z 55 Cesium 55133 30 132 90500 LLNL ACTL 1983 215 7 57 T anthanum eesetesesee esee k k k kk kkk 57139 26y 137 71300 532dos ENDF B V 1980 15475 Z258 Cerium 58140 30 139 90500 LLNL ACTL 1983 427 58142 30y 141 90900 LLNL ACTL 1983 265 Z 2590 Praseodymium 59141 30 140 90800 LLNL ACTL 1983 215 G 68 10 3 05 APPEND
11. Bromine 35000 01 1982 457 51 0 1 B IV B IV E amp C n a 35000 02p meplib02 1993 691 90 100 89 B IV E amp C n a 35000 03p mcplib03 2002 1483 90 100 89 B IV E amp C BM amp M 35000 04p meplib04 2002 6853 985 100 B VL8 8 B VI8 BM amp M 7 36 Krypton 36000 01p meplib 1982 457 51 0 1 B IV B IV E amp C n a 36000 02p mcplib02 1993 691 90 100 89 B IV E amp C n a 36000 03p meplib03 2002 1879 90 100 B IV 89 B IV E amp C BM amp M 36000 04p meplib04 2002 7177 973 100 B VL8 8 B VI8 BM amp M 37000 01p mcplib 1982 461 51 0 1 B IV B IV E amp C n a 37000 02p meplib02 1993 695 90 100 89 B IV E amp C n a 37000 03p mcplib03 2002 1982 90 100 B IV 89 B IV E amp C BM amp M 37000 04p mcplib04 2002 7364 987 100 B VL8 8 B VI8 BM amp M Z 38 Strontium he he 2 2 ee 2 oe 38000 01p 1982 461 51 0 1 B IV B IV E amp C n a 38000 02p meplib02 1993 695 90 100 89 B IV E amp C n a 38000 03p meplib03 2002 1982 90 100 89 B IV E amp C BM amp M 38000 04p meplib04 2002 7256 969 100 B VL8 8 B VI8 BM amp M Z 39 Yttrium kkk k he oe k k kak aak ak ak akak ak ak ak akak k ak ak k 39000 01 mcplib 1982 461 51 0 1 B IV B IV E amp C n a 39000 02p mcplib02 1993 695 90 100 89 B IV E amp C n a 39000 03p mcplib03 2002 2081 90 10
12. k ak ak ak ak 3k gt K K 30064 30 30066 30 30067 30 30068 30 30070 30 Z23 Gallium kk kk kk k kk kkk k kk 31069 30y 31071 30y 7 22 Germanium 39 xk xk x ak ak sk kak ak ak ak ak sk ak ak ak sk ak K ak 3K 32070 30y 32072 30y 32073 30y 32074 30y 32076 30y APPENDIX G MCNP DATA LIBRARIES Table G 6 Cont Dosimetry Data Libraries for MCNP Tallies AWR Library 63 93580 56 93980 57 43760 531405 57 43760 532405 57 93530 58 93430 59 41590 531405 59 41590 532405 59 93080 60 93110 61 39630 532405 61 92830 62 92970 63 92800 64 93010 61 93260 62 93000 531405 62 93000 532405 62 92960 63 92980 64 92800 531405 64 92800 532405 64 92780 65 92890 63 92910 65 92600 66 92710 67 92480 69 92530 68 92560 70 92470 69 92420 71 92210 72 92350 73 92120 75 92140 10 3 05 Source LLNL ACTL LLNL ACTL ENDF B V ENDF B V LLNL ACTL LLNL ACTL ENDF B V ENDF B V LLNL ACTL LLNL ACTL ENDF B V LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL ENDF B V ENDF B V LLNL ACTL LLNL ACTL ENDF B V ENDF B V LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL
13. kk k Beryllium FK K K K K K K K K K KK K K K K K K K K K K K KK K K K K K K K K K K 4007 30y 7 01693 LLNL ACTL 1983 253 4009 30y 9 01218 LLNL ACTL 1983 335 Z2 5 2 oron he he 28 2 2 5010 24y 9 92690 531405 ENDF B V 1979 769 5010 26y 9 92690 532dos ENDF B V 1976 589 5010 30y 10 01290 LLNL ACTL 1983 381 5011 30y 11 00930 Illdos LLNL ACTL 1983 119 G 60 10 3 05 APPENDIX G MCNP DATA LIBRARIES DOSIMETRY DATA Table 6 Cont Dosimetry Data Libraries for MCNP Tallies ZAID AWR Library Source Date Length 6 KK K K K K K K K Carbon 6012 30 12 00000 LLNL ACTL 1983 97 6013 30y 13 00340 LLNL ACTL 1983 479 6014 30y 14 00320 LLNL ACTL 1983 63 Z 7 KKK ee K K KK K K K K K K K K Nitrogen 7014 26 13 88300 53205 ENDF B V 1973 1013 7014 30y 14 00310 LLNL ACTL 1983 915 Z 8 KKK KK K K K K KK K K K K K K K Oxygen 8016 26 15 85800 53205 ENDF B V 1973 95 8016 30y 15 99490 LLNL ACTL 1983 215 8017 30y 16 99910 LLNL ACTL 1983 239 Z 9 KKK KKK K K K KK K K K Fluorine 9019 26 18 83500 532408 ENDF B V 1979 31 9019 30y 18 99840 LLNL ACTL 1983 517 Z 11 K K K K K Sodium 11023 30 22 98980 LLNL ACTL 1983 621 Z 12 Magnesium LELLLLLLLLLLLLLLELLLLLLLLLLLLLLELLLLLLI 12023 3
14. where o 15 the elastic scattering cross section 15 the inelastic cross section includes any neutron out process 7 n nf n np etc is the absorption cross section Xo n x where x n that is all neutron disappearing reactions is the total cross section Gg Both and opare adjusted for the free gas thermal treatment at thermal energies 10 3 05 2 35 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS The selection of an inelastic collision is made with the remaining probability Oin 0 If the collision is determined to be inelastic the type of inelastic reaction n is sampled from 1 n z N ois 6 i l i l where 6 is a random number on the interval 0 1 N is the number of inelastic reactions and o is the inelastic reaction cross section at the incident neutron energy Directions and energies of all outgoing particles from neutron collisions are determined by sampling data from the appropriate cross section table Angular distributions are provided and sampled for scattered neutrons resulting from either elastic or discrete level inelastic events the scattered neutron energy is then calculated from two body kinematics For other reaction types a variety of data representations is possible These representations may be divided into two types a the outgoing energy and outgoing angle are sampled independently of each
15. 10 Locating Data Tables in MONP 11 igilur 11 DATA BLOCKS FOR CONTINUOUS DISCRETE NEUTRON TRANSPORT TABLES 11 DATA BLOCKS FOR DOSIMETRY TABLES 34 DATA BLOCKS FOR THERMAL S o p TABLES enne 35 DATA BLOCKS FOR PHOTOATOMIC TRANSPORT TABLES 38 FORMAT FOR MULTIGROUP TRANSPORT TABLES 41 FORMAT FOR ELECTRON TRANSPORT TABLES 53 FORMAT FOR PHOTONUCLEAR TRANSPORT TABLES 53 Data Blocks for Photonuclear Transport Tables see 54 REFERENCES M 69 1 10 3 05 7 Table of Con TOC 8 10 3 05 CHAPTER 1 MCNP OVERVIEW MCNP AND THE MONTE CARLO METHOD CHAPTER 1 MCNP OVERVIEW WHAT IS COVERED IN CHAPTER 1 Brief explanation of the Monte Carlo method Summary of MCNP features Introduction to geometry Chapter 1 provides an overview of the MCNP Monte Carlo code with brief summaries of the material covered in depth in later chapters It begins with a short discussion of the Monte Carlo method Five features of MCNP ar
16. 14000 01p meplib 1982 409 45 0 1 B IV B IV E amp C n a 14000 02p meplib02 1993 643 84 100 B IV 89 E amp C n a 14000 03p mcplib03 2002 1138 84 100 B IV 89 E amp C BM amp M 14000 04p mcplib04 2002 4792 693 100 B VL8 B VL8 B VI8 BM amp M Z 15 Phosphorus 15000 01p mcplib 1982 409 45 0 1 B IV B IV E amp C n a 15000 02p meplib02 1993 643 84 100 B IV 89 E amp C n a 15000 03p meplib03 2002 1138 84 100 B IV 89 E amp C BM amp M 15000 04p mcplib04 2002 4498 644 100 B VL8 B VL8 8 BM amp M Z 16 eee Sulfur 16000 01p meplib 1982 409 45 0 1 B IV B IV E amp C n a 16000 02p mcplib02 1993 643 84 100 B IV 89 E amp C n a 16000 03p meplib03 2002 1138 84 100 B IV 89 B IV E amp C BM amp M 16000 04p mcplib04 2002 4654 670 100 B VL8 B VL8 8 amp G 46 10 3 05 APPENDIX G MCNP DATA LIBRARIES PHOTOATOMIC DATA Table G 4 Cont Continuous Energy Photoatomic Data Libraries Maintained by X 5 CS FF Source Source B IV B IV 89 B IV 89 B VI 8 B IV B IV B IV B VI 8 B IV B IV 89 B IV 89 B VI 8 B IV B IV B IV B VI 8 B IV B IV 89 B IV B IV 89 B IV 8 8 B IV B IV B IV 89 B IV B IV 89 B IV B IV 8 8 B IV 89 B IV 89 B VI 8 B IV B IV B IV B VI 8 B IV B IV 89 B IV 89 B VI 8 B IV B IV B IV B VI 8 B IV B IV 89 B IV 89 B V
17. 6 TE 7 REFERENCES 9 APPENDIX E GLOBAL CONSTANTS VARIABLES AND ARRAYS 1 DICTIONARY OE SYMBOLIC NAMES prb YER SANE epi 1 SOME IMPORTANT COMPLICATED ARRAYS 27 US AITAVS ERE 27 Transport LAGS NE EP 28 Tally Arrays e 30 TOC 6 10 3 05 Table of Contents Accounting ATTaAYS RP ncm 35 KRCODE rco 40 Universe Map Lattice Activity Arrays for Table 128 42 Weight Window Mesh Parameters 2255 ede vir tendo Quan eR VN ee Eti 42 Perturbation Liu d o ec despir 43 Macrobody and Identical Surface Arrays esee 44 DERIVED STRUCTURES d RUM AUR 45 APPENDIX DATA TABLE FORMATS eerie eene eee een seen aeos atas tasa tastes atta 1 DATA TYPESAND CLASSES E side 1 ASDIR DATA DIRECTORY FILE 2 DATA TABLES 4 Loeating Data Type 1 Table 4 Locating Data on Type 2 Vale
18. 74 APPENDIX H FISSION SPECTRA CONSTANTS AND ELUX TO DOSE FACTORS lt cccssecesiceastcsnsdeaccsncdsdaccnssedenieassecationnsenetecicacensseduasesneetactenss 1 CONSTANTS FOR FISSION SPECTRA Sd itr 1 Constants for the Maxwell Fission Spectrum Neutron induced 1 Constants for the Watt Fission Spectrum 3 TOC 2 10 3 05 Table of Contents FLUX TO DOSE CONVERSION FACTORS 2 2 3 Biological Dose Equivalent Rate Factors Leute rase 4 Silicon Displacement Kerma Factors 1 etit tree dena dad 5 REFERENCES dw 7 Volume II User s Guide CHAPTER 1 PRIMER ape 1 MCNP INPUT FOR SAMPLE PROBLEM ritate raritate pee etnies 1 INP File A 3 Cell MAPS 4 Surface IS 5 Data Coats M 6 HOW TO RUN MONP am 11 Execution Line 12 NES T H 15 c 15 TIPS FOR CORRECT AND EFFICIENT PROBLEMS eee 16 Problemi Heo 16 PTS OC UC 16 E
19. Idos Idos LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL 1983 1983 1983 1983 1983 1983 1983 1983 1983 7 74 EER k k k kkk kk Tungsten KKK K K K K K K K K K K K K K K K K KK K K K K KK K K K K K K K K K K 74179 30y 74180 30y 74181 30y 74182 30y 74183 30y 74184 30y 74185 30y 74186 30y 74187 30 74188 30 178 94700 179 94700 180 94800 181 94800 182 95000 183 95100 184 95300 185 95400 186 95700 187 95800 Idos LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL 1983 1983 1983 1983 1983 1983 1983 1983 1983 1983 7 75 Phenium k kkk k k k k 75184 30y 75184 31y 75185 30y 75186 30y 75187 30y 75188 30y 75188 31y 183 95300 183 95300 184 95300 185 95500 186 95600 187 95800 187 95800 Idos LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL 1983 1983 1983 1983 1983 1983 1983 7 77 Iridium 77191 30 77193 30 77194 30 G 70 190 96100 192 96300 193 96500 10 3 05 LLNL ACTL LLNL ACTL LLNL ACTL 1983 1983
20. 1 1 if gt v Ej I where 6 is a random number If more microscopically correct fission neutron multiplicities are desired for fixed source problems the fifth entry on the PHYS N card can be used to select which set of Gaussian widths are used to sample the actual number of neutrons from fission that typically range from 0 to 7 or 8 49 For a given fission event there is a probability that neutrons are emitted This distribution is generally called the neutron multiplicity distribution Fission neutron multiplicity distributions are known to be well reproduced by simple Gaussian distributions 1 2 2 Py 2 2 2 2 2 2 9 00 2 50 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS and 1 n 1 2 Heztea P exp 2o i where v is the mean multiplicity b is a small adjustment to make the mean equal to v and is the Gaussian width For the range of realistic widths the adjustment b can be accurately expressed as a single smooth function of v 0 5 o gt To determine the value of from experimental data many authors have minimized the chi squared P o l x 0 zx 2 3 TL AB where Ap is the uncertainty in the experimentally measured multiplicity distribution p The factorial moments of the neutron multiplicity distribution v XP n n
21. we sample distance to scatter rather than distance to collision It is preferable to sample distance to scatter in highly absorbing media in fact this is the standard procedure for astrophysics problems Sampling distance to scatter is also equivalent to implicit capture along a flight path see page 2 34 However in such highly absorbing media there is usually a more optimal choice of transform parameter p and it is usually preferable to take advantage of the directional component by not fixing 1 8 Implicit Capture 99 Implicit capture survival biasing and absorption by weight reduction are synonymous Implicit capture is a variance reduction technique applied in MCNP after the collision nuclide has been selected Let total microscopic cross section for nuclide i and microscopic absorption cross section for nuclide 7 When implicit capture is used rather than sampling for absorption with probability the particle always survives the collision and is followed with new weight W 1 Implicit capture is a splitting process where the particle is split into absorbed weight which need not be followed further and surviving weight Implicit capture can also be done along a flight path rather than at collisions when a special form of the exponential transform is used See page 2 34 for details Two advantages of implicit capture are a particle that has fina
22. HR 7 ODSDIIOP dte debts Due em cn E 8 Repeated Structure Geometry EUH ERE 9 cessa tentare rv EP E NARNIA RE DIU A 9 CROSS SECTIONS MH 14 Neutron Interaction Data Continuous Energy and Discrete Reaction 16 ce MP re 20 Electron Interaction Data enar od bru PAR PE PIE 23 Neutron Dosimetry Cross Sections qe 23 Neutron Thermal Tabl s 24 Multigroup dr Mc O OO 24 PHYSICS T M 23 T CETTE 25 Particle Bere MENOR RR RT QE IP ERROR 27 Neutron Interactions Oeo er dime 27 Photon Interactions 57 Electron Interactions 67 TALLIES 80 Current Tally RP 84 Fiuk Tallies emt 85 Track Length Cell Energy Deposition Tallies 42 5 2 oet rni rta tace 87 Pulse Height Tallies EM 89 10 3 05 TOC 1 Table of Content
23. Los Alamos National Laboratory report LA 12740 1994 available URL http t2 lanl gov codes codes html C Little New Photon Library from ENDF Data Los Alamos National Laboratory internal memorandum to Buck Thompson February 26 1982 available URL http www xdiv lanl gov PROJECTS DATA nuclear pdf la ur 03 0164 pdf E Storm I Israel Photon Cross Sections from 1 keV to 100 MeV for Elements Z 1 to Z 100 Nuclear Data Tables Volume A7 pp 565 681 1970 10 3 05 G 75 APPENDIX MCNP DATA LIBRARIES REFERENCES 27 28 29 30 31 32 33 34 G 76 C J Everett and E D Cashwell Code Fluorescence Routine Discussion Los Alamos National Laboratory report LA 5240 MS 1973 Hughes Information on the Photon Library MCPLIBO2 Los Alamos National Laboratory internal memorandum X 6 HGH 93 77 revised 1996 available URL http www xdiv lanl gov PROJECTS DATA nuclear pdf mcplib02 pdf D E Cullen M H Chen J H Hubbell S T Perkins E F Plechaty J A Rathkopf and J H Scofield Tables and Graphs of Photon Interaction Cross Sections from 10 eV to 100 GeV Derived from the LLNL Evaluated Photon Data Library EPDL Lawrence Livermore National Laboratory report UCRL 50400 Volume 6 Rev 4 Part A Z 1 to 50 and Part B Z 51 to 100 1989 M C White Photoatomic Data Library MCPLIBO3 An Update to MCPLIBO2 Containing
24. Thallium 81000 01p 1982 521 61 0 1 B IV B IV E amp C n a 81000 02p mcplib02 1993 755 100 100 B IV 89 E amp C n a 81000 03p mcplib03 2002 3032 100 100 B IV 89 B IV E amp C BM amp M 81000 04p mcplib04 2002 10142 1285 100 B VL8 8 8 amp Z 82 Lead 82000 01 mcplib 1982 521 61 0 1 B IV B IV E amp C n a 82000 02p mcplib02 1993 755 100 100 B IV 89 E amp C n a 82000 03p mcplib03 2002 3032 100 100 B IV 89 B IV E amp C BM amp M 82000 04p mcplib04 2002 10010 1263 100 B VL8 8 B VI8 BM amp M Z 83 Bismuth 83000 01 meplib 1982 521 61 0 1 B IV B IV E amp C n a 83000 02p meplib02 1993 755 100 100 B IV 89 E amp C n a 83000 03p mcplib03 2002 3131 100 100 B IV 89 B IV E amp C BM amp M 83000 04p mcplib04 2002 10373 1307 100 B VL8 8 B VI8 BM amp M Z 84 Polonium 84000 01p mcplib 1982 467 52 0 015 DLC 15 Unknown E amp C n a 84000 02p meplib02 1993 749 99 100 S amp I 89 Unknown E amp C n a 84000 03p mcplib03 2002 3125 99 100 581 89 Unknown E amp C BM amp M 84000 04p mcplib04 2002 10247 1286 100 B VL8 8 B VI8 BM amp M Z 85 Astatine 85000 01p meplib 1982 479 54 0 015 DLC 15 Unknown E amp C n a 85000 02p meplib02 1993 761 101 100 541 89 Unknown E amp C n a 85000 03p mcplib03 2002 3137 101 100 S amp I 89 Unknown E amp C BM amp M 85000 04p
25. pd 105 46105 50c 104 0040 kidman B V 0 1980 293 6 4647 505 200 no 46105 66c 104 0039 endf66b B VL5 1996 293 6 634077 13480 30 0 yes Pd 106 46106 66c 104 9937 endf66b B VI 5 1996 293 6 150930 1154 30 0 yes Pd 108 46108 50c 106 9770 kidman B V 0 1980 293 6 4549 555 20 0 no 46108 66c 106 9769 endf66b B VI 5 1996 293 6 1068900 1981 30 0 yes 110 46110 66c 108 9610 endf66b B VL5 1996 203 6 127359 862 30 0 yes 2546 Average fission product from Plutonium 239 Pu 239fp 46119 90d 117 5255 drmccs LANL T 1982 293 6 9542 263 200 yes 46119 90c 117 5255 rmccs LANL T 1982 293 6 10444 407 200 yes 7 47 Silyep Ag nat 47000 55c 106 9420 rmccsa LANL T 1984 293 6 29092 2350 200 yes 47000 55d 106 9420 drmccs LANL T 1984 293 6 12409 263 20 0 yes Ag 107 47107 42c 105 9867 endl92 LLNL lt 1992 300 0 27108 2885 30 0 yes 47107 50c 105 9870 rmccsa B V 0 1978 293 6 12111 1669 20 0 no 47107 50d 105 9870 B V 0 1978 293 6 4083 263 20 0 no 47107 60c 105 9870 endf60 0 1983 293 6 64008 10101 20 0 no 47107 66c 105 9870 endf66b 0 1983 293 6 104321 13835 20 0 10 3 05 no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no yes yes no
26. both no both no both no both no both no both no both no yes both no yes both no yes both no both no both no both no no both no no both no both no both no yes both no yes both no yes both no no tot no no tot no tot no no tot no no tot no no tot no no both no tot no no tot no no tot no no tot no no both no both no yes both no yes both no yes both no yes both no yes no no no no yes yes yes yes yes yes no yes no no no no yes yes no yes no no no no no no yes yes no yes no no no no no no yes yes no no yes yes no yes yes no no no no no no no yes yes yes yes ZAID AWR Am 242metastable 95242 42c 239 9801 95242 50c 239 9800 95242 50d 239 9800 95242 51d 239 9800 95242 51c 239 9800 95242 65c 239 9800 95242 66c 239 9800 Am 243 95243 42c 240 9733 95243 50c 240 9730 95243 50d 240 9730 95243 51d 240 9730 95243 51c 240 9730 95243 60c 240 9730 95243 61c 240 9730 95243 65c 240 9734 95243 66c 240 9734 95243 68c 240 9734 95243 69 240 9734 7 96 Cm 241 96241 60c 238 9870 96241 66c 238 9870 Cm 242 96242 42c 239 9794 96242 50c 239 9790 96242 50d 239 9790 96242 51d 239 9790 96242 51c 239 9790 96242 60c 239 9790 96242 61c 239 9790 96242 65c 239 9790 96242 66c 239 9790 Cm 243 96243 42c 240 9733 96243 60c 240 9730
27. mcplib04 2002 9560 1221 100 B VL8 8 8 BM amp M 10 3 05 APPENDIX G MCNP DATA LIBRARIES PHOTOATOMIC DATA Table G 4 Cont Continuous Energy Photoatomic Data Libraries Maintained by X 5 Library Release Length Emax CS FF Fluor ZAID Name Date Words NE GeV Source Source Source Z 65 Terbium 65000 01p meplib 1982 521 61 0 1 B IV B IV E amp C 65000 02p meplib02 1993 755 100 100 B IV 89 E amp C 65000 03p mcplib03 2002 2735 100 100 B IV 89 E amp C 65000 04p mcplib04 2002 9143 1168 100 B VL8 8 8 Z 66 Dysprosium 66000 01p mcplib 1982 521 61 0 1 B IV B IV E amp C 66000 02p meplib02 1993 755 100 100 B IV 89 E amp C 66000 03p mcplib03 2002 2735 100 100 B IV 89 B IV E amp C 66000 04p mcplib04 2002 9479 1224 100 B VL8 8 8 Z 67 Holmium 67000 01p meplib 1982 521 61 0 1 B IV B IV E amp C 67000 02p mcplib02 1993 755 100 100 B IV 89 B IV E amp C 67000 03p mcplib03 2002 2735 100 100 B IV 89 B IV E amp C 67000 04p mcplib04 2002 9419 1214 100 B VL8 8 8 Z 68 Erbium 68000 01p meplib 1982 521 61 0 1 B IV B IV E amp C 68000 02p mcplib02 1993 755 100 100 B IV 89 E amp C 68000 03p meplib03 2002 2735 100 100 B IV 89 B IV E amp C 68000 04p mcplib04 2002 9233 1183 100 B VL8 8 8 7 69 Thulium 69000 01p
28. Germanium 32000 01p meplib 1982 457 51 0 1 B IV B IV E amp C 32000 02p meplib02 1993 691 90 100 B IV 89 E amp C 32000 03p meplib03 2002 1483 90 100 B IV 89 B IV E amp C 32000 04p mcplib04 2002 7027 1014 100 B VL8 8 8 G 48 10 3 05 CDBD Source n a n a BM amp M BM amp M n a n a BM amp M BM amp M n a n a BM amp M BM amp M n a n a BM amp M BM amp M n a n a BM amp M BM amp M n a n a BM amp M BM amp M n a n a BM amp M BM amp M n a n a BM amp M BM amp M APPENDIX G MCNP DATA LIBRARIES PHOTOATOMIC DATA Table G 4 Cont Continuous Energy Photoatomic Data Libraries Maintained by X 5 Library Release Length Emax CS FF Fluor CDBD ZAID Name Date Words GeV Source Source Source Source Z 33 KK KK KKK K Arsenic 33000 01 1982 457 51 0 1 B IV B IV E amp C n a 33000 02p meplib02 1993 691 90 100 89 B IV E amp C n a 33000 03p mcplib03 2002 1483 90 100 89 B IV E amp C BM amp M 33000 04p meplib04 2002 6595 942 100 B VL8 8 B VI8 BM amp M Z 34 Selenium 34000 01 mcplib 1982 457 51 0 1 B IV B IV E amp C n a 34000 02p meplib02 1993 691 90 100 89 B IV E amp C n a 34000 03p mcplib03 2002 1483 90 100 B IV 89 B IV E amp C BM amp M 34000 04p meplib04 2002 6655 952 100 B VL8 8 B VI8 BM amp M Z 35
29. yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no APPENDIX G MCNP DATA LIBRARIES NEUTRON CROSS SECTION LIBRARIES Table G 2 Cont Continuous Energy and Discrete Neutron Data Libraries Maintained by X 5 Library Eval Temp Length E max ZAID AWR Name Source Date words NE MeV GPD 7 15 Phosphorus oir 15031 24 30 7080 la150n 6 1997 293 6 71942 990 150 0 15031 42c 30 7077 end192 LLNL lt 1992 300 0 6805 224 30 0 15031 50c 30 7080 endf5u 0 1977 293 6 5733 326 20 0 15031 504 30 7080 dre5 0 1977 293 6 5761 263 20 0 15031 514 30 7080 drmccs B V 0 1977 293 6 5761 263 20 0 15031 51 30 7080 rmccs B V 0 1977 293 6 5732 326 20 0 15031 60c 30 7080 endf60 B VLO 1977 293 6 6715 297 200 15031 66c 30 7080 endf66a 6 1997 293 6 71942 990 150 0 7 16 Sulfgp k S nat 16000 60 31 7882 endf60 B VLO 1979 293 6 108683 8382 20 0 16000 61 31 7888 actib B VL8 2000 77 0 162749 10
30. 4 The sides of the cone in the figure become parallel and the cone resembles a cylinder near the shrinking sphere Thus the tally becomes 1 Z s ds R 74 f GE y 5 P Q dQ e wp Q or p Q X 5 5 In all the scattering distributions and in the standard sources MCNP assumes azimuthal symmetry This provides some simplification The angle Q can be expressed in polar coordinates with the incoming particle direction being the polar axis The azimuthal angle is and the cosine of the polar angle is The probability density of scattering into dQ can then be written in terms of a probability density in That is dQ p w 9 du Defining the PDF for scattering at as ph f pu 9 d 2 92 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS TALLIES and recalling that p u is independent of 4 yields ph 9 On Substituting this into the last expression for the F5 tally yields 5 4 5 wP e 27R A point detector tally is known as a next event estimator because it is a tally of the flux at a point as if the next event were a particle trajectory directly to the detector point without further collision A contribution to the point detector is made at every source or collision event The e term accounts for attenuation between the present event and the detector point The 1 27 R term
31. 4 Energy Straggling Because an energy step represents the cumulative effect of many individual random collisions fluctuations in the energy loss rate will occur Thus the energy loss will not be a simple average A rather there will be a probability distribution f s A dA from which the energy loss A for the step of length s be sampled Landau studied this situation under the simplifying assumptions that the mean energy loss for a step is small compared with the electron s energy that the energy parameter amp defined below is large compared with the mean excitation energy of the medium that the energy loss can be adequately computed from the Rutherford cross section and that the formal upper limit of energy loss can be extended to infinity With these simplifications Landau found that the energy loss distribution can be expressed as f s 4 in terms of A a universal function of a single scaled variable 2 eoe 2 72 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS Here and v are the mass and speed of the electron 6 is the density effect correction is vc Iis the mean excitation energy of the medium and is Euler s constant y 0 5772157 The parameter amp is defined by 2ne NZ 2 5 5 where e is the charge of the electron and N Z is the number density of atomic electrons and the universal function is ioo
32. F4 to V o F4 dt ws Remember to multiply by volume either by setting the FM card constant to the volume or overriding the F4 volume divide by using segment divisors of unity on the SD card W should be unity for KCODE calculations The only difference between dr and the modified F4 tally will be 2 174 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CRITICALITY CALCULATIONS any variations from unity in W and the error estimation which will be batch averaged for dr and history averaged for the F4 tally Lifetimes for all other processes also can be estimated by using the FM multiplier to calculate reaction rates as well the numerator and denominator are separate tallies that must be divided by the user see the examples in Chapters 4 and 5 Savar git 1 v multiplier 0 x 7 reaction rate multiplier f f o DdVdt V 0 Note that the lifetimes are inversely additive 5 Combined Estimators MCNP provides a number of combined kep and estimators that are combinations of the three individual estimators using two at a time or all three The combined k and values are computed by using a maximum likelihood estimate as outlined by Halperin and discussed further by Urbatsch 4 This technique which is a generalization of the inverse variance weighting for uncorrelated estimators produces the maximum likelihood estimate for t
33. Figure 2 7 Diagram for description of the surface current tally 2 84 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS TALLIES Note that the MCNP current J of Table 2 2 is the total current not the net current It is the total number of particles crossing a surface Frequently the net current rather than the total current is desired Defining the partial currents crossing in the positive and negative directions right and left or up and down as 15 4 dala E n n gt lt the net current across the surfaceis J J J_ The total current of Table 2 2 is J J J_ The partial currents J across a surface can be calculated in MCNP using an F1 tally with two cosine bins one each for 1 lt 0 lt p lt 1 The units of the F1 tally are those of the source If the source has units of particles per unit time the tally has units of particles per unit time When the source has units of particles the tally has units of particles The SD card can be used to input a constant that divides the tally In other words if xis input on the SD card the tally will be divided by x B Flux Tallies gt gt gt Defining the scalar flux 1 E t r E t d rdE is the total scalar flux in volume element dr about and energy element dE about and introducing energy and time bins the integrals of Table 2 2
34. Number of Angles Number of Energies Elastic Scattering Data The table identification to be specified on MTn cards The portion of the ZAID before the decimal point provides a shorthand alphanumeric description of the material The two digits after the decimal point differentiate among different tables for the same material The final character in the ZAID is a t which indicates a thermal 5 table There are currently three evaluated sources of MCNP S o p tables 1 ENDF5 Indicates that the data were processed from evaluations distributed by the National Nuclear Data Center at Brookhaven National Laboratory as part of ENDF B V Note ru these evaluations were carried over from ENDF 2 LANL89 Initial work on cold moderator scattering data performed at Los Alamos National Laboratory 3 ENDF6 3 Indicates that the data were processed from evaluations distributed by the National Nuclear Data Center at Brookhaven National Laboratory as part of ENDF B VI Release 3 Name of the library that contains the data table for this ZAID Date that the data table was processed by the NJOY code The temperature of the data in degrees Kelvin The number of equally likely discrete secondary cosines provided at each combination of incident and secondary energy for inelastic scattering and for each incident energy for incoherent elastic scattering The number of secondary energies provided for each incident energy for inelast
35. Table 6 Cont Dosimetry Data Libraries for MCNP Tallies Library 10 3 05 Idos APPENDIX MCNP DATA LIBRARIES Source LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL DOSIMETRY DATA Date Length 1983 673 1983 473 1983 431 1983 467 1983 465 1983 483 1983 465 1983 491 1983 491 1983 495 1983 545 1983 491 1983 335 1983 485 1983 467 APPENDIX MCNP DATA LIBRARIES REFERENCES VIII REFERENCES 10 11 G 74 McLane L Dunford and Rose ed ENDF 102 Data Formats and Procedures for the Evaluated Nuclear Data File ENDF 6 Brookhaven National Laboratory report BNL NCS 44945 revised 1995 available URL http www nndc bnl gov S C Frankle and C Little Cross section and Reaction Nomenclature for MCNP Continuous energy Libraries and DANTSYS Multigroup Libraries Los Alamos National Laboratory internal memorandum XTM 96 313 July 15 1996 available URL http www xdiv lanl gov PROJECTS DATA nuclear pdf scf 96 313 pdf J A Halbleib Kensek D Valdez T A Mehlhorn S M Seltzer and M J Berger ITS The Integrated TIGER Series of Coupled Electron Photon Monte
36. Young B Smith and C A Philis New Tungsten Isotope Evaluations for Neutron Energies Between 0 1 and 20 MeV Trans Am Nucl Soc 39 793 1981 M Asprey B Lazarus and E Seamon EVXS A Code to Generate Multigroup Cross Sections from the Los Alamos Master Data File Los Alamos Scientific Laboratory report LA 4855 June 1974 E MacFarlane W Muir and M Boicourt The NJOY Nuclear Data Processing System Volume I User s Manual Los Alamos National Laboratory report LA 9303 M Vol ENDF 324 May 1982 E MacFarlane W Muir and M Boicourt NJOY Nuclear Data Processing System Volume II The NJOY RECONR BROADR HEATR and THERMR Modules Los Alamos National Laboratory report LA 9303 M Vol II ENDF 324 May 1982 R J Howerton R E Dye P C Giles J R Kimlinger S T Perkins and E F Plechaty Omega Documentation Lawrence Livermore National Laboratory report UCRL 50400 Vol 25 August 1983 E Storm and I Israel Photon Cross Sections from 0 001 to 100 Mev for Elements 1 through 100 Los Alamos Scientific Laboratory report LA 3753 November 1967 J H Hubbell W J Veigele E A Briggs R T Brown D T Cromer and R J Howerton Atomic Form Factors Incoherent Scattering Functions and Photon Scattering Cross Sections J Phys Chem Ref Data 4 471 1975 J Everett and E D Cashwell Code Fluorescence Routine
37. ZAID AWR Name Source Date words NE MeV GPD 0 CP DN UR 39089 60c 88 1420 endf60 B VLO 1986 293 6 86556 9567 20 0 yes no no no 39089 66c 88 1420 endf66b 4 1986 293 6 144304 13207 20 0 yes no no no no Zr nat 40000 42c 90 4364 endl92 LLNL 1992 300 0 131855 17909 30 0 yes no no no no 40000 56d 90 4360 misc5xs 7 11 B V X 1976 300 0 5400 263 20 0 no no no no no 40000 56c 90 4360 misc5xs 7 11 B V X 1976 300 0 52064 7944 20 0 no no no no no 40000 57d 90 4360 misc5xs 7 11 B V X 1976 300 0 5400 263 20 0 no no no no no 40000 57c 90 4360 misc5xs 7 11 B V X 1976 300 0 16816 2116 20 0 no no no no no 40000 58c 90 4360 misc5xs 7 11 B V X 1976 587 2 57528 8777 20 0 no no no no 40000 60c 90 4360 endf60 1 1976 11 293 6 66035 10298 20 0 no no no no no 40000 66c 90 4360 endf66b B VI 1 1976 293 6 165542 22226 20 0 no no no no no 71 90 40090 66c 89 1320 endf66b B VL0O X 1976 293 6 51841 6243 20 0 no no no no no Zr 91 40091 65c 90 1220 endf66e 0 1976 3000 1 86834 10971 20 0 40091 66 90 1220 endf66b 0 1976 293 6 106833 13828 200 no no no no yes 7 92 40092 66c 91 1120 endf66b 0 1976 293 6 82986 10664 20 0 no no no no no 71 93 40093 50 92 1083 kidman B V 0 1974 293 6 2579 236 200 no no no no no Zr 94 40094 66c 93 0960 endf66b B VI 0 X 1976 293 6 86543 11144 20 0 no no no no Zr 96 40096 66c 95 0810 en
38. lt 1983 lt 1983 lt 1983 lt 1983 lt 1983 lt 1983 lt 1983 lt 1983 lt 1983 lt 1983 1979 lt 1983 lt 1983 lt 1983 lt 1983 lt 1983 lt 1983 lt 1983 1979 lt 1983 lt 1983 lt 1983 lt 1983 lt 1983 lt 1983 Length 65 263 393 145 417 435 437 339 293 279 401 459 563 407 33 309 311 311 337 3861 317 291 295 603 405 675 33 369 343 275 283 283 APPENDIX G MCNP DATA LIBRARIES DOSIMETRY DATA Table 6 Cont Dosimetry Data Libraries for MCNP Tallies ZAID AWR Library Source Date Length Z 20 Calcium 20039 30 38 97070 LLNL ACTL 1983 601 20040 30y 39 96260 LLNL ACTL 1983 309 20041 30y 40 96230 LLNL ACTL 1983 313 20042 30y 41 95860 LLNL ACTL 1983 285 20043 30y 42 95880 LLNL ACTL 1983 295 20044 30y 43 95550 LLNL ACTL 1983 269 20045 30y 44 95620 LLNL ACTL 1983 271 20046 30y 45 95370 LLNL ACTL 1983 255 20047 30y 46 95450 LLNL ACTL 1983 243 20048 30y 47 95250 LLNL ACTL 1983 239 20049 30y 48 95570 LLNL ACTL 1983 229 Z 21 K K K K Scandium 21044 30 43 95940 LLNL ACTL 1983 313 21044 31y 43 95940 LLNL ACTL 1983 311 21045 24y 44 56790 531dos ENDF B V 1979 20179 21045 26y 44 56790 532dos ENDF B V 1979 20211 21045 30y 44 95590 LLNL ACTL 1983 547 21046 30y 45 95520 LLNL ACTL 1983
39. mcplib04 2002 10463 1322 100 B VL8 8 B VI8 amp Z 86 Radon 86000 01p 1982 533 63 0 1 B IV B IV E amp C n a 86000 02p mcplib02 1993 767 102 100 B IV 89 E amp C n a 86000 03p mcplib03 2002 3143 102 100 B IV 89 B IV E amp C BM amp M 86000 04p mcplib04 2002 10325 1299 100 B VL8 8 B VI8 BM amp M Z 87 Hee Francium 87000 01 mcplib 1982 479 54 0 015 S amp I Unknown E amp C n a 87000 02p mcplib02 1993 761 101 100 S amp I 89 Unknown E amp C n a 87000 03p mcplib03 2002 3236 101 100 S amp I 89 Unknown E amp C BM amp M 87000 04p mcplib04 2002 10532 1317 100 B VL8 8 8 BM amp M Z 88 Radium 88000 01p mcplib 1982 479 54 0 015 S amp I Unknown E amp C n a 88000 02p mcplib02 1993 761 101 100 S amp I 89 Unknown E amp C n a 88000 03p mcplib03 2002 3236 101 100 541 89 Unknown E amp C BM amp M 88000 04p mcplib04 2002 10346 1286 100 B VL8 8 8 BM amp M 10 3 05 APPENDIX G MCNP DATA LIBRARIES PHOTOATOMIC DATA Table G 4 Cont Continuous Energy Photoatomic Data Libraries Maintained by X 5 Library Release Length Emax CS FF Fluor CDBD ZAID Name Date Words GeV Source Source Source Source Z 89 Actinium 89000 01 mcplib 1982 479 54 0 015 S amp I Unknown E amp C n a 89000 02p meplib02 1993 761 101 100 S amp I 89 Unknown E amp C n a 89000 03p mcplib0
40. moplib 1982 389 43 0 1 B IV B IV E amp C n a 9000 02p moplib02 1993 623 82 100 B IV 89 E amp C n a 9000 03p mcplib03 2002 920 82 100 B IV 89 E amp C BM amp M 9000 04p moplib04 2002 3206 463 100 B VL8 B VL8 B VI8 BM amp M Z 10 10000 01p mcplib 1982 389 43 0 1 B IV B IV E amp C n a 10000 02p meplib02 1993 623 82 100 B IV 89 E amp C n a 10000 03p mcplib03 2002 920 82 100 B IV 89 E amp C BM amp M 10000 04p mcplib04 2002 3278 475 100 B VL8 B VL8 B VI8 BM amp M Z 11 eee Sodium 11000 01p meplib 1982 401 45 0 1 B IV B IV E amp C n a 11000 02p mcplib02 1993 635 84 100 B IV 89 B IV E amp C n a 11000 03p mcplib03 2002 1031 84 100 B IV 89 B IV E amp C BM amp M 11000 04p meplib04 2002 3995 578 100 B VL8 B VL8 B VI8 BM amp M Z 12 Magnesium 12000 01p meplib 1982 409 45 0 1 B IV B IV E amp C n a 12000 02p meplib02 1993 643 84 100 B IV 89 B IV E amp C n a 12000 03p mcplib03 2002 1039 84 100 B IV 89 B IV E amp C BM amp M 12000 04p mcplib04 2002 3781 541 100 B VL8 B VL8 B VI8 BM amp M Z 13 Aluminum 13000 01p meplib 1982 409 45 0 1 B IV B IV E amp C n a 13000 02p mcplib02 1993 643 84 100 B IV 89 E amp C n a 13000 03p mcplib03 2002 1138 84 100 B IV 89 E amp C BM amp M 13000 04p mcplib04 2002 4846 702 100 B VL8 B VL8 B VI8 BM amp M Z 14 Silicon
41. neutron moving with a scalar velocity and a target nucleus moving with a scalar velocity V and p is the cosine of the angle between the neutron and the target direction of flight vectors The equation for is 1 2 2 2 Vael v 20 Vut The scattering cross section at the relative velocity is denoted by o v and p V is the probability density function for the Maxwellian distribution of target velocities 4 43 2 pv p V 5B Ve with defined as 1 e 2kT where A is the mass of a target nucleus in units of the neutron mass M is the neutron mass in MeV sh cm and KT is the equilibrium temperature of the target nuclei in MeV The most probable scalar velocity V of the target nuclei is 1 B which corresponds to a kinetic energy of KT for the target nuclei This is not the average kinetic energy of the nuclei which is 3kT 2 The quantity that MCNP expects on the TMPn input card is KT and not just T see page 3 132 Note that kT is not a function of the particle mass and is therefore the kinetic energy at the most probable velocity for particles of any mass Equation 2 1 implies that the probability distribution for a target velocity V and cosine y is o v PC 25 r rel 26 E v It is assumed that the variation of with target velocity can be ignored The justification for this approximation is that 1 for light nuclei 6 v is slowly varying with velocity and 2
42. rules when running a Monte Carlo calculation They will be more meaningful as you read this manual and gain experience with MCNP but no matter how sophisticated a user you may become never forget the following five points Define and sample the geometry and source well You cannot recover lost information Question the stability and reliability of results Be conservative and cautious with variance reduction biasing des po poc The number of histories run is not indicative of the quality of the answer 10 3 05 1 1 CHAPTER 1 MCNP OVERVIEW MCNP AND THE MONTE CARLO METHOD The following sections compare Monte Carlo and deterministic methods and provide a simple description of the Monte Carlo method A Monte Carlo Method vs Deterministic Method Monte Carlo methods are very different from deterministic transport methods Deterministic methods the most common of which is the discrete ordinates method solve the transport equation for the average particle behavior By contrast Monte Carlo obtains answers by simulating individual particles and recording some aspects tallies of their average behavior The average behavior of particles in the physical system is then inferred using the central limit theorem from the average behavior of the simulated particles Not only are Monte Carlo and deterministic methods very different ways of solving a problem even what constitutes a solution is different Deterministic methods typic
43. t Analog Monte Carlo simply samples the events according to their natural physical probabilities In this way an analog Monte Carlo calculation estimates the number of physical particles executing any given random walk Nonanalog techniques do not directly simulate nature Instead nonanalog techniques are free to do anything if hence lt gt is preserved This preservation is accomplished by adjusting the weight of the particles The weight can be thought of as the number of physical particles represented by the MCNP particle see page 2 25 Every time a decision is made the nonanalog techniques require that the expected weight associated with each outcome be the same as in the analog game In this way the expected number of physical particles executing any given random walk is the same as in the analog game For example if an outcome A is made q times as likely as in the analog game when a particle chooses outcome A its weight must be multiplied by to preserve the expected weight for outcome A Let p be the analog probability for outcome A then pq is the nonanalog probability for outcome If wo is the current weight of the particle then the expected weight for outcome in the analog game is wo p and the expected weight for outcome A in the nonanalog game is wo q pq MCNP uses three basic types of nonanalog games 1 splitting 2 Russian roulette and 3 sampling from nonana
44. 09 14 99 09 17 99 09 08 86 09 08 86 09 08 86 09 08 86 09 08 86 09 14 99 09 14 99 09 14 99 09 14 99 09 08 86 09 08 86 09 08 86 09 08 86 09 14 99 09 14 99 09 14 99 09 14 99 09 14 99 09 14 99 05 30 89 09 16 99 05 30 89 09 16 99 10 3 05 Temp CK 300 600 800 1200 294 400 600 800 1000 1200 77 300 400 500 600 800 294 400 600 800 300 600 800 1200 294 400 600 800 1000 1200 20 19 20 19 Numof Num of Elastic Angles Energies Data coh coh coh coh coh coh coh coh coh coh coh none none none none none none none none none coh coh coh coh coh coh coh coh coh coh none none none none Library ZAID Source Name Graphite 6000 6012 grph 0lt endf5 tmccs grph 04t endf5 tmccs grph O5t endf5 tmccs grph 06t endf5 tmccs grph 07t endf5 tmccs grph 08t endf5 tmccs grph 60t endf6 3 sab2002 grph 61t endf6 3 sab2002 grph 62t endf6 3 sab2002 grph 63t endf6 3 sab2002 grph 64t endf6 3 sab2002 grph 65t endf6 3 sab2002 Hydrogen in Zirconium Hydride 1001 h zr 01t endf5 tmccs h zr 02t endf5 tmccs h zr 04t endf5 tmccs h zr 05t endf5 tmccs h zr 06t endf5 tmccs h zr 60t endf6 3 sab2002 h zr 61t endf6 3 sab2002 h zr 62t endf6 3 sab2002 h zr 63t endf6 3 sab2002 h zr 64t endf6 3 sab2002 h zr 65t endf6 3 sab2002 Ortho Hydrogen 1001 hortho O1t lanl89 therxs hortho 60t endf6 3 sab2002 hortho 61t endf6 3 sab2002 hortho 62t endf6 3 sab2002 hortho
45. 175 errata in 26 1981 477 H K Tseng and R H Pratt Exact Screened Calculations of Atomic Field Bremsstrahlung Phys Rev A3 1971 100 H K Tseng and R H Pratt Electron Bremsstrahlung from Neutral Atoms Phys Rev Lett 33 1974 516 H Davies H A Bethe and L C Maximom Theory of Bremsstrahlung and Pair Production II Integral Cross Section for Pair Production Phys Rev 93 1954 788 and H Olsen Outgoing and Ingoing Waves in Final States and Bremsstrahlung Phys Rev 99 1955 1335 G Elwert Verscharte Berechnung von Intensitat und Polarisation im Kontinuierlichen Rontgenspektrum Ann Physick 34 1939 178 R J Jabbur and R H Pratt High Frequency Region of the Spectrum of Electron and Positron Bremsstrahlung Phys Rev 129 1963 184 and High Frequency Region of the Spectrum of Electron and Positron Bremsstrahlung IL Phys Rev 133 1964 1090 J Hubbell W J Veigele E A Briggs T Brown D T Cromer and R J Howerton Atomic Form Factors Incoherent Scattering Functions and Photon Scattering Cross Sections J Phys Chem Ref Data 4 1975 471 and J H Hubbell and I Overbo Relativistic Atomic Form Factors and Photon Coherent Scattering Cross sections J Phys Chem Ref Data 8 1979 69 H K Tseng and R H Pratt Electron Bremsstrahlung Energy Spectra Above 2 MeV Phys Rev A19 1979 1525 E Haug Bremsstrahlung and Pai
46. 24051 30y 24052 26y 24052 30y 24053 30y 24054 30y 24055 30y 24056 30y 48 95130 49 51650 49 94600 50 94480 51 49380 51 94050 52 94060 53 93890 54 94080 55 94070 532405 53240 Idos LLNL ACTL ENDF B V LLNL ACTL LLNL ACTL ENDF B V LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL lt 1983 1979 lt 1983 lt 1983 1979 lt 1983 lt 1983 lt 1983 lt 1983 lt 1983 7 25 Manganese 25051 30y 25052 30y 25053 30y 25054 30y 25055 24y 25055 30y 25056 30y 25057 30y 25058 30y 50 94820 51 94560 52 94130 53 94040 54 46610 54 93800 55 93890 56 93830 57 93970 531405 Idos LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL ENDF B V LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL 1983 1983 1983 1983 1977 1983 1983 1983 1983 7 26 26053 30 26054 24y 26054 26y 26054 30y 26055 30y 26056 24y 26056 26y 26056 30y 26057 30y 26058 24y 26058 26y 26058 30y 26059 30y 26060 30y 52 94530 53 47620 53 47600 53 93960 54 93830 55 45400 55 45400 55 93490 56 93540 57 43560 57 43560 57 93330 58 93490 59 93400 531405 532405 531405 53240 531405 532405 LLNL ACTL ENDF B
47. 47108 30 47108 31y 47109 30y 47110 30y 47110 31y 105 90700 105 90700 106 90500 107 90600 107 90600 108 90500 109 90600 109 90600 LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL 7 48 Cadmium 48106 30 48111 30y 48112 30y 48116 30y 105 90600 110 90400 111 90300 115 90500 10 3 05 LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL DOSIMETRY DATA Date Length 1983 335 1983 339 1983 341 1983 349 1983 261 1983 281 1980 7815 1983 537 1983 420 1983 461 1983 443 1983 523 1983 501 1983 427 1980 6489 1983 421 1983 445 1980 4971 1983 427 1983 447 1983 469 1983 469 1983 275 1983 417 1983 263 1983 265 1983 517 1983 275 1983 275 1983 583 1983 277 1983 281 1983 177 1983 317 1983 221 1983 231 APPENDIX G MCNP DATA LIBRARIES DOSIMETRY DATA Table 6 Cont Dosimetry Data Libraries for MCNP Tallies ZAID AWR Library Source Date Length 7 49 Indum eee he e k ak ak ak ak k ak 49113 30y 112 90400 LLNL ACTL 1983 861 49115 24y 113 92000 531dos ENDF B V 1978 26009 49115 26y 113 92000 532dos ENDF B V 1978 26009 49115 30y 114 90400 LLNL ACTL 1983 1265 2 50
48. 92238 15c 236 0060 endf62mt 2 1993 800 0 386305 45096 20 0 yes both no no 92238 16c 236 0060 endf62mt 2 1993 900 0 372625 43386 200 yes both no no no 92238 17c 236 0060 endf62mt 2 1993 1200 0 348137 40325 20 0 yes both no no 92238 21c 236 0060 100xs3 LANL T X 1993 300 0 279245 30911 100 0 yes both no no no 92238 42c 236 0058 endl92 LLNL 1992 300 0 107739 7477 30 0 yes both no no no 92238 48c 236 0060 uresa 16 2 1993 300 0 705623 85021 20 0 no both no no yes 92238 50c 236 0060 rmccs B V 0 1979 293 6 88998 9285 200 yes both no no 92238 50d 236 0060 drmecs B V 0 1979 293 6 16815 263 200 yes both no no 92238 52c 236 0060 endf5mt 1 B V 0 1979 587 2 123199 8454 20 0 yes both no no no 92238 53c 236 0060 endf5mt 1 B V 0 1979 587 2 160107 17876 20 0 yes both no no 92238 54c 236 0060 endf5mt 1 B V 0 1979 880 8 160971 17984 20 0 yes both no no no 92238 60c 236 0060 endf60 2 1993 293 6 206322 22600 20 0 yes both 92238 61c 236 0060 2 1993 293 6 211310 22600 20 0 yes both yes 92238 64c 236 0060 endf66d 5 1993 770 976500 103602 20 0 yes both no yes yes 92238 65c 236 0060 endf66e 5 1993 3000 1 425088 42334 200 yes both yes yes 92238 66c 236 0060 endf66c B VL5 1993 293 6 751905 78647 20 0 yes both no yes yes 92238 67c 236 0058 t16 2003 LANL T16 2003 77 0 1099087 103664 30 0 yes both no yes yes 92238 68c 236 0058 t16 2003 LANL T16 2003 3000 0 5
49. 94238 61c 94238 65c 94238 66c Pu 239 94239 11c 94239 12c 94239 13 94239 14 94239 15 94239 16 94239 17 94239 42 94239 49 94239 50d 94239 50c AWR 233 0249 234 0188 235 0118 235 0120 235 0120 235 0120 235 0120 235 0118 235 0118 235 0118 235 0118 236 0060 236 9990 236 9990 234 0180 234 0180 235 0120 235 0120 235 0120 236 0046 236 0045 236 1670 236 1670 236 1670 236 1670 236 0045 236 0045 236 0045 236 0045 236 9986 236 9986 236 9986 236 9986 236 9986 236 9986 236 9986 236 9986 236 9986 236 9990 236 9990 Library Name Source endl92 LLNL endl92 LLNL endl92 LLNL endf5p B V 0 dre5 B V 0 drmccs LANL T rmccsa LANL T endf60 endf6dn B VI 1 endf66c B VI 1 t16 2003 LANL TI6 endl92 LLNL endf60 0 endf66c 0 endf60 endf66c endl92 endf60 endf66c endl92 uresa dre5 endf5p rmccs drmccs endf60 endf6dn endf66e endf66c endf62mt endf62mt endf62mt endf62mt endf62mt endf62mt endf62mt endl92 uresa dre5 endfSp 0 4 LLNL 0 B VLO LLNL 0 0 B V 0 B V 0 B V 0 0 0 0 0 2 2 2 2 2 2 2 LLNL 2 0 0 APPENDIX MCNP DATA LIBRARIES NEUTRON CROSS SECTION LIBRARIES Table G 2 Cont Continuous Energy and Discrete Neutron Data Libraries
50. 98249 65c 246 9400 endf66e 0 1989 3000 1 62455 4376 20 0 no both no yes yes 98249 66c 246 9400 endf66c 0 1989 293 6 78679 6404 20 0 both no yes yes Cf250 98250 42c 247 9281 92 LLNL 1992 300 0 17659 574 30 0 yes both no no no 98250 60c 247 9280 endf60 2 1976 293 6 47758 5554 20 0 yes tot no no no 98250 65c 247 9280 endf66e B VI2 1976 3000 1 66024 6701 200 yes tot no no yes 98250 66c 247 9280 endf66c B VI2 1976 293 6 71434 8132 20 0 yes tot no no yes Cf25 98251 42c 248 9227 endl92 LLNL lt 1992 300 0 17673 545 300 yes both no no no 98251 60c 248 9230 endf60 B VI 2 1976 293 6 42817 4226 20 0 yes both no no no 98251 61c 248 9230 B VI2 1976 293 6 47715 4226 200 yes both no yes 98251 65c 248 9230 endf66e B VI2 1976 3000 1 64568 5257 200 yes both no yes yes 98251 66c 248 9230 endf66c B VI2 1976 293 6 73253 6222 20 0 yes both no yes yes 252 98252 42c 249 9161 endl92 LLNL 1992 300 0 21027 1210 30 0 yes both no no 98252 60c 249 9160 endf60 B VI2 1976 293 6 49204 5250 20 0 yes both no no 98252 65c 249 9160 endf66e 2 1976 3000 1 66642 6250 20 0 tot no no yes 98252 66c 249 9160 endf66c 2 1976 293 6 78378 7554 20 0 tot no no yes G 38 10 3 05 Notes 10 11 12 13 14 15 APPENDIX G MCNP DATA LIBRARIES NEUTRON CROSS SECTION LIBRARIES The data libraries previously known as EPRIXS and U600K are now a part of the data
51. Estimators 2 171 Neutron 2 34 2 171 Accounting Arrays E 35 Accuracy 2 110 Accuracy Factors Affecting 2 111 ACE format 2 17 2 18 G 75 Adjoint option 2 24 3 125 Ambiguity Cell 2 10 Surfaces 2 7 2 9 2 10 Analog Capture 2 34 3 127 Angular Bins 3 93 Angular Distribution Functions for point detectors 2 104 Sampling of 2 36 Area calculation 2 8 2 187 AREA card 3 25 Arrays 3 26 Asterisk 3 11 3 12 3 31 3 80 3 86 Tally 3 80 Atomic Density 3 9 Fraction 3 118 Mass 3 118 Number 3 118 Weight AWTAB card 3 123 Auger Electrons 2 63 2 78 Axisymmetric Surfaces Defined by Points 3 15 B BBREM card 3 52 Biasing Cone 2 153 Continuous 2 153 Direction 2 153 Energy 3 52 Source 2 152 3 61 Bin limit control 2 105 Binning 10 3 05 MCNP MANUAL INDEX Cards By detector cell 2 107 By multigroup particle type 2 107 By particle charge 2 107 By source distribution 2 107 By the number of collisions 2 107 Bins Angular 3 93 Cell 3 81 Energy 3 80 Multiplier 3 80 Surface 3 81 Tally 3 80 Blank Line delimiter 3 2 BOX 3 18 3 21 Bremsstrahlung 2 77 Biasing BBREM 3 52 Model 2 57 C Capture Analog 2 34 3 127 Implicit 2 34 Neutron 2 28 2 34 Card Format 3 4 Horizontal Input Format 3 4 Vertical Input Format 3 5 Cards AREA 3 25 Atomic Weight AWTAB 3 123 Bremsstrahlung Biasing BBREM 3 52 Cell 3 2 3 9 to 3 11 Cell Importance IMP 3 34 Cell Trans
52. Figure 2 11 Diagram of an FIR Flux Image Radiograph tally for a source external to the object 10 3 05 2 97 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS TALLIES S Axis FS Card Oylinder Axis T Axis C Card X4 Y4Z for Polar Bins Cylinder Center Source Reference Object Point Particle Boundary Scatter X Yo Zo Point Detector Counterclockwise d from T Axis FIC Oylindrical Image Surface Polar Bins Figure 2 12 Diagram of an FIC Flux Image on a Cylinder tally for a source internal to the object In both cases a ray trace point detector flux contribution is made to every image grid bin pixel from each source and scatter event Allowing each event to contribute to all pixels reduces statistical fluctuations across the grid that would occur if the grid location for the contribution were selected randomly For each source and scatter event the direction cosines to a pixel detector point are determined The option exists to select a random position in the pixel The same relative random offset is used for all pixels for a source or scatter event The random detector location in a pixel changes from event to event The option also exists to select the point detector location at the center of each pixel when the center flux is desired A standard point detector attenuated ray trace flux contribution to the image pixel is then made A new direction cosine is determined for each pixel followed by the
53. In subroutine SRCDX the variable PSC must be set for each detector and DXTRAN sphere An example of how this is done and also a description of several other source angular distribution functions is in Chapter 4 g Detectors and the 5 0 thermal treatment The S o p thermal treatment poses special challenges to next event estimators because the probability density function for angle has discrete lines to model Bragg scattering and other molecular effects Therefore MCNP has an approximate model that for the PSC calculation not the transport calculation replaces the discrete lines with finite histograms of width lt 1 This approximation has been demonstrated to accurately model the discrete line S o p data In cases where continuous data is approximated with discrete lines the approximate scheme cancels the errors and models the scattering better than the random walk Thus the S a B thermal treatment can be used with confidence with next event estimators like detectors and DXTRAN F Additional Tally Features The standard MCNP tally types can be controlled modified and beautified by other tally cards These cards are described in detail in Chapter 3 an overview 15 given here 2 104 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS TALLIES 1 Bin Limit Control The integration limits of the various tally types can be controlled by E T C and FS cards The E card establishes energy bin ranges the
54. LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL DOSIMETRY DATA Date Length 1983 323 1983 441 1977 411 1978 4079 1983 509 1983 513 1977 435 1978 479 1983 503 1983 489 1978 3847 1983 459 1983 375 1983 397 1983 345 1983 507 1978 3375 1978 3615 1983 513 1983 437 1978 40 1978 49 1983 563 1983 397 1983 555 1983 561 1983 411 1983 643 1983 619 1983 197 1983 419 1983 405 1983 423 1983 431 1983 629 1983 623 APPENDIX G MCNP DATA LIBRARIES DOSIMETRY DATA Table 6 Cont Dosimetry Data Libraries for MCNP Tallies ZAID AWR Library Source Date Length Z 2398 Arsenic 7 2 2 ak tek sek sss ee a ok f lt 33075 30y 74 92160 LLNL ACTL 1983 987 Z 234 Selenium k kk kkk k k k 34074 30 73 92250 LLNL ACTL 1983 159 34076 30y 75 91920 LLNL ACTL 1983 177 34080 30y 79 91650 LLNL ACTL 1983 205 34082 30y 81 91670 LLNL ACTL 1983 223 Z 359 Bromine 8 k k k k k xk ak kak ak ak ak ak ak ak ak ak sk kak ak ak ak ak k ak sk ak K k 35079 30y 78 91830 LLNL ACTL lt 1983 263 35081 30y 80 91630 LLNL ACTL 1983 695 7 37 Rubidium 37085 30 84 91180 LLNL ACTL 1983 193
55. Law 61 Tabular Distribution ENDF Law 1 Lang 0 12 or 14 correlated energy angle scattering Law 61 is an extension of Law 4 For each incident energy there is a pointer to a table of secondary energies E probability density functions p cumulative density functions c and pointers to tabulated angular distributions L The secondary emission 2 46 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS energy is found exactly as stated in the Law 4 description on page 2 42 Unlike Law 4 Law 61 includes a correlated angular distribution associated with each incident energy E as given by the tabular angular distribution located using the pointers L Thus the sampled emission angle is dependent on the sampled emission energy If the secondary distribution is given using histogram interpolation the angular distribution located at L is used to sample the emission angle If the secondary distribution is specified as linear interpolation between energy points L is chosen by selecting the bin closest to the randomly sampled cumulative distribution function CDF point If the value of L is zero the angle is sampled from an isotropic distribution as described on page 2 37 If the value of L is positive it points to a tabular angular distribution which is then sampled as described on page 2 37 As with Law 4 the emission energy and angle are transformed from the center of mass to the laboratory syst
56. Library Source Date Z 2898 Bismuth kkkeskek 24 obese ok te 83208 30y 83209 30y 83210 30y 83210 31y 207 98000 208 98000 209 98400 209 98400 LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL 1983 1983 1983 1983 Z284 Polonium 7 7 HE A ae eH 2 x xk k k kk ak k k k he reete 84210 30y 209 98300 LLNL ACTL 1983 72 090 Thorium 5 8 k k k k ak ak ak k k sk ak k k ak ak ak sk k k ak ak ak ak k 90230 30y 90231 30y 90232 30y 90233 30y 90234 30y 230 03300 231 03600 232 03800 233 04200 234 04400 LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL 1983 1983 1983 1983 1983 7 91 Protactinium LELLLLLLLLLLLLLLLLLELLLLLLLLLLLLLELI 91231 26y 91233 26y 91233 30y 229 05000 231 03800 233 04000 532dos 532dos ENDF B V ENDF B V LLNL ACTL 1978 1978 lt 1983 7 092 k kk kk k kk k 92233 26y 92233 30y 92234 30y 92235 30y 92236 30y 92237 30y 92238 30y 92239 30y 92240 30y 231 04300 233 04000 234 04100 235 04400 236 04600 237 04900 238 05 100 239 05400 240 05700 532dos ENDF B V LLNL
57. M Rotenberg Academic Press New York 1963 135 Stephen M Seltzer Overview of ETRAN Monte Carlo Methods in Monte Carlo Transport of Electrons and Photons edited by Theodore M Jenkins Walter R Nelson and Alessandro Rindi Plenum Press New York 1988 153 J Halbleib Structure and Operation of the ITS Code System in Monte Carlo Transport of Electrons and Photons edited by Theodore M Jenkins Walter R Nelson and Alessandro Rindi Plenum Press New York 1988 249 M Sternheimer M J Berger and S M Seltzer Density Effect for the Ionization Loss of Charged Particles in Various Substances Phys Rev B26 1982 6067 M Sternheimer and Peierls General Expression for the Density Effect for the Ionization Loss of Charged Particles Phys Rev 1971 3681 T A Carlson Photoelectron and Auger Spectroscopy Plenum Press New York N Y 1975 Stephen M Seltzer Cross Sections for Bremsstrahlung Production and Electron Impact Ionization in Monte Carlo Transport of Electrons and Photons edited by Theodore M Jenkins Walter R Nelson and Alessandro Rindi Plenum Press New York 1988 81 S M Seltzer and J Berger Bremsstrahlung Spectra from Electron Interactions with Screened atomic Nuclei and Orbital Electrons Nucl Instr Meth B12 1985 95 5 M Seltzer and M J Berger Bremsstrahlung Energy Spectra from Electrons with Kinetic Energy 1 keV 10 GeV Incident on S
58. The monoenergetic isotropic point source always will make the same contribution to the point detector so the variance of that contribution will be zero If no particles have yet collided in the scattering region the detector tally will be converged to the source contribution which is wrong and misleading But as soon as a particle collides in the scattering region the detector tally and its variance will jump Then the detector tally and variance will steadily decrease until the next particle collides in the scattering region at which time there will be another jump These jumps in the detector score and variance are characteristic of undersampling important regions Next event estimators are prone to undersampling as already described on page 2 64 for the p w term of photon coherent scattering The jump discussed here is from the sudden change in the and possibly terms Jumps in the tally caused by undersampling can be eliminated only by better sampling of the undersampled scattering region that caused them Biasing Monte Carlo particles toward the tally region would cause the scattering region to be sampled better thus eliminating the jump problem It is recommended that detectors be used with caution and with a complete understanding of the nature of next event estimators When detectors are used the tally fluctuation charts printed in the output file should be examined closely to see the degree of the fluctuations Also the detector diag
59. accounts for the solid angle effect The term accounts for the probability of scattering toward the detector instead of the direction selected in the random walk For an isotropic source or scatter p w 0 5 and the solid angle terms reduce to the expected 1 42 R Note that p u can be larger than unity because it is the value of a density function and not a probability Each contribution to the detector can be thought of as the transport of a pseudoparticle to the detector The R term in the denominator of the point detector causes a singularity that makes the theoretical variance of this estimator infinite That is if a source or collision event occurs near the detector point R approaches zero and the flux approaches infinity The technique is still valid and unbiased but convergence is slower and often impractical If the detector is not in a source or scattering medium a source or collision close to the detector is impossible For problems where there are many scattering events near the detector a cell or surface estimator should be used instead of a point detector tally If there are so few scattering events near the detector that cell and surface tallies are impossible a point detector can still be used with a specified average flux region close to the detector This region is defined by a fictitious sphere of radius R surrounding the point detector R can be specified either in centimeters or in mean free paths If R is specifie
60. and a variety of unphysical artifacts are eliminated The new logic is selected by setting the 18th entry of the DBCN card to 2 for example with the card DBCN 17J 2 6 Angular Deflections The ETRAN codes and MCNP rely on the Goudsmit Saunderson theory for the probability distribution of angular deflections The angular deflection of the electron is sampled once per substep according to the distribution FG Y r 3 ewcscppi 120 where s is the length of the substep cos is the angular deflection from the direction at the beginning of the substep is the Legendre polynomial and is 1 d G 2 ES 1 in terms of the microscopic cross section do 4 and the atom density of the medium For electrons with energies below 0 256 MeV the microscopic cross section is taken from numerical tabulations developed from the work of Riley For higher energy electrons the microscopic cross section is approximated as a combination of the Mott and Rutherford cross sections with a screening correction Seltzer presents this factored cross section in the form 2 76 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS Ze 00 4 mon pv u 24 do dQ Rutherford where e p and v are the charge momentum and speed of the electron respectively The screening correction was originally given by Moli re as _ 273 2 n 4 0
61. c Variance reduction schemes for detectors Pseudoparticles of point detectors are not subject to the variance reduction schemes applied to particles of the random walk They do not split according to importances weight windows etc although they are terminated by entering zero importance cells However two Russian roulette games are available specifically for detector pseudoparticles The PD card can be used to specify the pseudoparticle generation probability for each cell The entry for each cell i is p where 0 p 1 Pseudoparticles are created with probability p and weight 1 p If p 1 which is the default every source or collision event produces a pseudoparticle If p 0 no pseudoparticle is produced Setting p 0 in a cell that can actually contribute to a detector erroneously biases the detector tally by eliminating such contributions Thus p 0 should be used only if the true probability of scoring is zero or if the score from cell i is unwanted for some legitimate reason such as problem diagnostics Fractional entries of p should be used with caution because the PD card applies equally to all pseudoparticles The DD card can be used to Russian roulette just the unimportant pseudoparticles However the DD card roulette game often requires particles to travel some distance along their trajectory before being killed When cells are many mean free paths from the detector the PD card may be preferable The DD card controls
62. collides before reaching the DXTRAN sphere and b the weight that enters the DXTRAN sphere on the next flight Let wo be the weight of the particle before exiting the collision let p be the analog probability that the particle does not enter the DXTRAN sphere on its next flight and let p be the analog probability that the particle does enter the DXTRAN sphere on its next flight The particle must undergo one of these mutually exclusive events thus p p 1 The expected weight not entering the DXTRAN sphere is w p1 and the expected weight entering the DXTRAN sphere is Wop Think of DXTRAN as deterministically splitting the original particle with weight w into two particles a non DXTRAN particle 1 particle of weight w and a DXTRAN particle 2 particle of weight Unfortunately things are not quite that simple Recall that the non DXTRAN particle is followed with unreduced weight wo rather than weight The reason for this apparent discrepancy is that the non DXTRAN particle particle 1 plays a Russian roulette game Particle 1 s weight is increased from w to w by playing a Russian roulette game with survival probability p w Avo The reason for playing this Russian roulette game is simply that p is not known so assigning weight w p4wy to particle 1 is impossible However it is possible to play the Russian roulette game without explicitly knowing It is not magic just slightly subtl
63. for heavy nuclei where o v can vary rapidly the moderating effect of scattering is small so that 2 30 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS the consequences of the approximation will be negligible As a result of the approximation the probability distribution actually used is 2 22 uoo v2 V 2 Vv n P V Note that the above expression can be written as 2 n 2Vv u pv py e v V P V V v V e As a consequence the following algorithm is used to sample the target velocity 1 With probability 1 1 Inv 2 the target velocity V is sampled from the 2 72 distribution P V 26V eP Y The transformation reduces this distribution to the sampling distribution for MCNP actually codes 1 2 With probability the target velocity is sampled from the distribution 212 4B Jv e d Substituting y B reduces the distribution to the 2 sampling distribution for y P y 4 Any e 3 cosine of angle between the neutron velocity and the target velocity is sampled uniformly on the interval 1 lt 1 4 The rejection function A V is computed using fv 2 R V u lt l With probability the sampling is accepted otherwise the sampling is rejected and the procedure is repeated The minimum efficiency of this reje
64. for example Law 2 The conversion from center of mass to target at rest laboratory coordinate systems is given in the above equations Law1 ENDF law 1 Equiprobable energy bins The index and the interpolation fraction are found on the incident energy grid for the incident energy such that lt lt and E Ej r Ej E itl A random number on the unit interval is used to select an equiprobable energy bin k from the equiprobable outgoing energies E 5 1 Then scaled interpolation is used with random numbers and 6 on the unit interval Let Ei Ej 1 E E and Ex Ej gt r Eji and l iif 4 r or l i clif 4 r and Ej Sx Ej p41 then E g Ej Law2 Discrete photon energy The value provided in the library is The secondary photon energy Eou is either E for non primary photons or E AXA 1 E for primary photons out where A is the atomic weight to neutron weight ratio of the target and E is the incident neutron energy 10 3 05 2 41 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS Law3 ENDF law 3 Inelastic scattering 7 7 from nuclear levels The value provided in the library is Q 2 Q A 1 Eu E Fin A Law 4 Tabular distribution ENDF law 4 For each incident neutron energy there is a pointer to a table of secondary energies E probabilit
65. mcplib 1982 521 61 0 1 B IV B IV E amp C 69000 02p mcplib02 1993 755 100 100 B IV 89 E amp C 69000 03p meplib03 2002 2735 100 100 B IV 89 B IV E amp C 69000 04p mcplib04 2002 9473 1223 100 B VL8 8 8 Z 70 Ytterbium 70000 01 mcplib 1982 521 61 0 1 B IV B IV E amp C 70000 02 meplib02 1993 755 100 100 B IV 89 E amp C 70000 03 mcplib03 2002 2735 100 100 B IV 89 B IV E amp C 70000 04 mcplib04 2002 9539 1234 100 B VL8 8 8 Z 71 Hee Lutetium 71000 01 mcplib 1982 521 61 0 1 B IV B IV E amp C 71000 02 mcplib02 1993 755 100 100 B IV 89 E amp C 71000 03 mcplib03 2002 2834 100 100 B IV 89 E amp C 71000 04 mcplib04 2002 9914 1280 100 B VL8 8 8 Z 72 Hafnium K K K K K K K KK K 72000 01 mcplib 1982 521 61 0 1 B IV B IV E amp C 72000 02 meplib02 1993 755 100 100 B IV 89 E amp C 72000 03 mcplib03 2002 2834 100 100 B IV 89 B IV E amp C 72000 04 mcplib04 2002 9932 1283 100 B VL8 8 8 10 3 05 CDBD Source n a n a BM amp M BM amp M n a n a BM amp M BM amp M n a n a BM amp M BM amp M n a n a BM amp M BM amp M n a n a BM amp M BM amp M n a n a BM amp M BM amp M n a n a BM amp M BM amp M n a n a BM amp M BM amp M APPENDIX G MCNP DATA LIBRARIES PHOTOATOMIC DATA Table G 4 Cont Conti
66. no no no no no no no no no no no no no no no no no no no U CP DN UR no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no ZAID AWR Library Name Source APPENDIX G MCNP DATA LIBRARIES NEUTRON CROSS SECTION LIBRARIES Table G 2 Cont Continuous Energy and Discrete Neutron Data Libraries Maintained by X 5 Eval Date Temp Length words CK 7 4007 42 9 4009 21 4009 24 4009 50 4009 50 4009 60 4009 62 4009 66 72 5 Boron ACA AS A a A 5010 42c 5010 50d 5010 50c 5010 53c 5010 60c 5010 66c 5011 42c 5011 50d 5011 50c 5011 55d 5011 55c 5011 56d 5011 56c 5011 60c 5011 66c Z 26 Carbon ASAI A A 6000 24 6000 504 6000 50 6000 60c 6000 66c 7 12 6012 21 6012 42 6012 50 6012 50 7212 6013 42 6 9567 8 9348 8 9347 8 9348 8 9348 8 9348 8 9348 8 9348 9 9269 9 9269 9 9269 9 9269 9 9269 9 9269 10 9147 10 9150 10 9150 10 9150 10 9150 10 9147 10 9147 10 9147 10 9147 11 8980 11 8969 11 8969 11 8980 11 8980 11 8969 11 8969 11 8969 11 8969 12 8916 endl92 100xs 3 lal50n rmccs drmc
67. no yes yes yes yes yes yes yes yes yes yes yes no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no yes no no no no no no yes yes yes yes yes yes no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no yes yes yes yes yes yes yes yes yes yes yes yes no no no no no no no no yes no yes yes yes no no no yes yes no no no no no yes yes yes yes yes yes G 29 APPENDIX G MCNP DATA LIBRARIES NEUTRON CROSS SECTION LIBRARIES ZAID W 183 74183 24c 74183 48 74183 50 74183 50 74183 55 74183 55 74183 60 74183 61c 74183 62c 74183 63c 74183 64c 74183 65c 74183 66c W 184 74184 24c 74184 48c 74184 50 74184 50 74184 55 74184 55 74184 60 74184 61 74184 62 74184 63 74184 64 74184 65 74184 66 W 186 74186 24 74186 48 74186 50 74186 50 74186 55 74186 55 74186 60 74186 61 74186 62 74186 63 74186 64 74186 65 74186 66 72 175
68. that is collision to boundary boundary to collision and boundary to boundary derivatives of r can be taken leading to one or more of these four terms for The second term of is x h TE arm JRO i beB heH where the tally response is a linear function of some combination of reaction cross sections or ty X ceC 10 3 05 2 195 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PERTURBATIONS where c is an element of the tally cross sections c eC and may be an element of the perturbed cross sections c B Then R X h h pm Ox h 2 9400 beB heH X ceB EcH Y is the fraction of the reaction rate tally involved in the perturbation If none of the nuclides participating in the tally is involved in the perturbation then 0 which is always the case for F1 F2 and F4 tallies without FM cards For F4 tallies with an FM card if the FM card multiplicative constant is positive no flag to multiply by atom density it is assumed that the FM tally cross sections are unaffected by the perturbation and 0 For KCODE k track length estimates F6 and F7 heating tallies and F4 tallies with FM cards with negative multipliers multiply by atom density to get macroscopic cross sections if the tally cross section is affected by the perturbation then gt 0 For k and and F7 tallies in perturbed cells where
69. www nndc bnl gov In addition to the ENDF B library many other data centers provide libraries of evaluated data These include the Japanese Atomic Energy Research Institute s JAERI JENDL library the European JEFF library maintained by the Nuclear Energy Agency NEA the Chinese Nuclear Data Center s CNDC CENDL library and the Russian BOFOD library Other libraries also exist These centers may provide processed versions of their library in MCNP ACE format Contact the appropriate center for more information In recent years the primary evaluated source of neutron interaction data provided as part of the MCNP code package has been the ENDF B library i e ENDF B V and ENDF B VI However these have been supplemented with evaluated neutron interaction data tables from other sources in particular data from Lawrence Livermore National Laboratory s Evaluated Nuclear Data Library ENDL library and supplemental evaluations performed in the Nuclear Physics Group in the Theoretical Division at Los Alamos 9 725 The package also includes older evaluations from previous versions of ENDF B ENDL the Los Alamos Master Data File and the Atomic Weapons Research Establishment in Great Britain MCNP does not access evaluated data directly from the ENDF format these data must first be processed into ACE format ACE is an acronym for A Compact A better description of is that it is the processed data for use in MCNP as these files ar
70. 0 293 6 9288 14070 56334 48917 14070 55776 69108 68746 67880 67511 35022 214549 32388 41947 54162 55427 220073 220418 213659 214004 220104 220449 76399 16696 98609 69498 88129 69498 104198 264892 264592 263728 264592 263728 252663 252671 252591 252791 252615 195933 196252 195852 196252 195852 E max NE MeV GPD 468 263 2430 1928 263 2525 3213 3172 3213 3172 1473 3148 1645 263 2028 2241 3038 3081 3037 3036 3038 3081 2883 855 2440 263 1887 263 2824 7417 7472 7364 7472 7364 4878 4879 4869 4894 4872 5791 5831 5781 5831 5781 30 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 100 0 150 0 30 0 20 0 20 0 20 0 150 0 150 0 150 0 150 0 150 0 150 0 100 0 30 0 20 0 20 0 20 0 20 0 20 0 150 0 150 0 150 0 150 0 150 0 150 0 150 0 150 0 150 0 150 0 150 0 150 0 150 0 150 0 150 0 yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no yes no no no no yes yes yes yes yes yes no no no no no no no
71. 0 49885 6154 39089 42c 88 1421 endl92 LLNL 1992 300 0 69315 8771 39089 50d 88 1421 dre5 B V 0 10 1985 293 6 2311 263 39089 50c 88 1421 endfSu B V 0 10 1985 293 6 18631 3029 10 3 05 20 0 20 0 30 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 30 0 20 0 30 0 20 0 20 0 yes yes yes no no no no no no no no no no yes no no no yes no no no yes no no no yes no no no no no yes yes yes no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no G 21 APPENDIX G MCNP DATA LIBRARIES NEUTRON CROSS SECTION LIBRARIES Table G 2 Cont Continuous Energy and Discrete Neutron Data Libraries Maintained by X 5 Library Eval Temp Length Emax _
72. 01 moplib 1982 461 51 0 1 B IV B IV E amp C n a 47000 02p meplib02 1993 695 90 100 89 B IV E amp C n a 47000 03p mcplib03 2002 2180 90 100 B IV 89 B IV E amp C BM amp M 47000 04p meplib04 2002 7772 1022 100 B VL8 B VL8 B VI8 BM amp M Z 48 999 Cadmium kk k kkk k kk k 48000 01p 1982 461 51 0 1 amp 48000 02p mcplib02 1993 695 90 100 89 B IV E amp C n a 48000 03p mcplib03 2002 2180 90 100 B IV 89 B IV E amp C BM amp M 48000 04p mcplib04 2002 7700 1010 100 B VL8 B VL8 B VI8 BM amp M G 50 10 3 05 APPENDIX G MCNP DATA LIBRARIES PHOTOATOMIC DATA Table G 4 Cont Continuous Energy Photoatomic Data Libraries Maintained by X 5 Library Release Length Emax CS FF Fluor CDBD ZAID Name Date Words GeV Source Source Source Source Z 49 Indium 49000 01p mcplib 1982 461 51 0 1 B IV B IV E amp C n a 49000 02p mcplib02 1993 695 90 100 B IV 89 E amp C n a 49000 03p mceplib03 2002 2279 90 100 B IV 89 B IV E amp C BM amp M 49000 04p meplib04 2002 8291 1092 100 B VL8 8 B VI8 BM amp M 7 50 50000 01p meplib 1982 461 51 0 1 B IV B IV E amp C n a 50000 02p meplib02 1993 695 90 100 B IV 89 E amp C n a 50000 03p mcplib03 2002 2279 90 100 B IV 89 B IV E amp C BM amp M 50000 04p mcplib04 2002 8039 1050 100 B VL8 8 B VI8 BM amp M Z 51 A
73. 1 63 64 2 5 B 64 Inp and 63 3 X x y then 2 48 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS The cosine of the scattering angle is always sampled isotropically in the center of mass system using another random number on the unit interval u 22 1 Law 67 Correlated energy angle scattering ENDF law 7 For each incident neutron energy first the exiting particle direction is sampled as described on page 2 36 In other Law data first the exiting particle energy is sampled and then the angle is sampled The index i and the interpolation fraction r are found on the incident energy grid for the incident energy E such that E lt E Ej Eitr E 4 Ej For each incident energy there is a table of exiting particle direction cosines and locators L j This table is searched to find which ones bracket u namely Hig MS Then the secondary energy tables at L and L are sampled for the outgoing particle energy The secondary energy tables consist of a secondary energy grid E jx probability density functions p x and cumulative density functions c A random number 5 on the unit interval is used to pick between incident energy indices if 6 lt r then i 1 otherwise i Two more random numbers and 5 on the unit interval are used to determine interpolation energies If 5 lt Qs pjek and 1
74. 133785 153808 101915 130334 97047 83882 102222 55903 66642 65498 93662 269821 12755 9142 8366 8963 300 0 248212 300 0 248212 10 3 05 E max NE MeV GPD 3796 2120 263 11903 16086 29369 263 2981 818 263 10194 12949 11496 14744 10737 13902 16016 11153 14515 9799 10534 13154 6607 8141 7870 10116 30337 164 119 232 263 34612 34612 30 0 20 0 20 0 20 0 20 0 30 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 30 0 20 0 20 0 30 0 30 0 20 0 20 0 30 0 30 0 yes no no no no yes no no no no no no no no no no no no no no no no no no yes yes yes yes yes yes yes yes yes no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no 0 CP DN UR no no no no no no no no no no yes yes yes yes yes yes no yes yes no yes yes yes yes no no no no no no no no no APPENDIX G
75. 146 6460 kidman B V 0 1980 293 6 10867 1054 20 0 no no no no no Z26 Promethium Pm 147 61147 50c 145 6530 kidman B V 0 1980 293 6 9152 825 20 0 no no no no no Pm 148 61148 50c 146 6470 kidman 0 1979 293 6 1643 257 20 0 Pm 149 61149 50c 147 6390 kidman B V 0 1979 293 6 2069 238 20 0 no no no no no Z 262 Samarium SR a a ok ao a Sm 147 62147 50c 145 6530 kidman B V 0 1980 293 6 33773 2885 200 no no no no no 62147 65c 145 6530 endf66e B VLO 1980 3000 1 186194 15025 20 0 no no no no yes 62147 66c 145 6530 endf66b 0 1980 293 6 315674 25815 20 0 Sm 149 62149 49c 147 6380 uresa 0 1978 300 0 57787 7392 20 0 62149 50 147 6380 endf5u B V 0 1978 293 6 15662 2008 200 no no no no 62149 50d 147 6380 dre5 B V 0 1978 293 6 4429 263 20 0 no no no no no 62149 65c 147 6380 endf66e 0 1978 3000 1 47902 5399 20 0 62149 66c 147 6380 endf66b 0 1978 293 6 64240 7733 20 0 Sm 150 62150 49c 148 6290 uresa 2 1992 300 0 60992 8183 20 0 62150 50 148 6290 kidman B V 0 1974 293 6 9345 1329 200 no no no no Sm I51 62151 50c 149 6230 kidman B V 0 1980 293 6 7303 605 20 0 no no no no no Sm 152 62152 49c 150
76. 1983 Length 147 121 153 157 153 433 409 365 373 629 523 435 715 435 447 425 371 377 263 397 263 415 499 443 267 413 279 271 331 335 373 381 547 339 341 237 243 421 ZAID AWR Table 6 Cont Dosimetry Data Libraries for MCNP Tallies Library APPENDIX G MCNP DATA LIBRARIES Source DOSIMETRY DATA Date Length 78 Platinum 4 2 a kk 78190 30y 78192 30y 78193 30y 78193 31y 78194 30y 78195 30y 78196 30y 78197 30y 78197 31y 78198 30y 78199 30y 78199 31y 189 96000 191 96100 192 96300 192 96300 193 96300 194 96500 195 96500 196 96700 196 96700 197 96800 198 97100 198 97100 LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL 1983 1983 1983 1983 1983 1983 1983 1983 1983 1983 1983 1983 7 79 79193 30 79194 30y 79195 30y 79196 30y 79196 31y 79197 30y 79198 30y 79199 30y 79200 30y 192 96400 193 96500 194 96500 195 96700 195 96700 196 96700 197 96800 198 96900 199 97100 LLNL ACTL LLNL AC
77. 2 B V 2 B VLO B VL8 B VL8 8 6 6 6 6 0 B V 0 0 B V 2 B V 2 B VLO 8 B VL8 B VL8 6 6 6 LLNL LLNL B V 0 B V 0 0 0 B VLO LLNL LLNL B V 0 B V 0 0 0 B VLO Table G 2 Cont Eval Date 1996 1980 1973 1973 1980 1980 1980 2000 2000 2000 1996 1996 1996 1996 1980 1973 1973 1980 1980 1980 2000 2000 2000 1996 1996 1996 1996 1980 1973 1973 1980 1980 1980 2000 2000 2000 1996 1996 1996 1985 1992 1968 1968 1990 1990 1990 1985 1992 1968 1968 1990 1990 1990 Temp Length words 293 6 217095 300 0 119637 293 6 58799 293 6 19443 293 6 26320 293 6 79534 293 6 89350 77 0 235761 0 293 6 224856 0 3000 1 198226 0 77 0 228392 3000 1 190833 293 6 217447 293 6 192693 300 0 97118 293 6 58870 293 6 17032 293 6 26110 293 6 80006 293 6 78809 77 0 200883 0 293 6 194523 0 3000 1 181213 0 77 0 198499 3000 1 178773 293 6 192123 293 6 187863 300 0 102199 293 6 17018 293 6 63701 293 6 26281 293 6 83618 293 6 82010 77 0 207824 0 293 6 202211 0 3000 1 190276 0 77 0 193372 3000 1 175817 293 6 187731 13650 300 0 23715 293 6 9190 293 6 4252 293 6 102775 3000 1 179325 293 6 397396 12318 300 0 20969 293 6 8262 293 6 4675 293 6 96989 3000 1 180705 293 6 358295 10 3 05 NE MeV GPD 13034 12616 584
78. 2 The reason for the 1 2 1s the indistinguishability of the two outgoing electrons The electron with the larger energy is by definition the primary Therefore only the range lt 1 2 is of interest With 1 2 Eq 2 6 becomes 1 Fuge Bea n2 m2 y On the right side of Eq 2 5 we can express both and in units of the electron rest mass Then E can be replaced by on the right side of the equation We also introduce supplementary constants C2 nQ 1 12 2 12 c4 lima 8 so that Eq 2 5 becomes d 2 2 2 2 2296 mp ve2 C24 C3 p 4 ca 8 2 13 ds nv t 1 This is the collisional energy loss rate in MeV cm in a particular medium In MCNP we are actually interested in the energy loss rate in units of MeV barns so that different cells containing the same material need not have the same density Therefore we divide Eq 2 10 by N and multiply by the conversion factor 1024 barns cm We also use the definition of the fine structure constant 2 _ 2 hc where h is Planck s constant to eliminate the electronic charge e from Eq 2 10 The result is as follows 24 2 2 2 2 4 2 2 2 C3 g ca JE 2 14 ds 2nmc gd p 10 3 05 2 71 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS This is the form actually used in MCNP to preset the collisional stopping powers at the energy boundar
79. 2 41 The expanded photon production method has clear advantages over the original 30 x 20 matrix method described below In coupled neutron photon problems users should attempt to specify data sets that contain photon production data in expanded format Such data sets are identified by entries in the GPD column in Table G 2 in Appendix G However it should be noted that the evaluations from which these data are processed may not include all discrete lines of interest evaluators may have binned sets of photons into average spectra that simply preserve the energy distribution b 30x20 Photon Production Method For lack of better terminology we will refer to the photon production data contained in older libraries as 30 x 20 photon production data In contrast to expanded photon production data there is no information about individual photon production reactions in the 30 x 20 data method is not used in modern tables and is only included to maintain backwards compatibility for very old data libraries 10 3 05 2 33 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS The only secondary photon data are a 30 x 20 matrix of photon energies that is for each of 30 incident neutron energy groups there are 20 equally probable exiting photon energies There is no information regarding secondary photon angular distributions therefore all photons are taken to be produced isotropically in the laboratory system T
80. 27 3 79 3 85 3 111 3 128 Repeat nR 3 4 Repeated Structures Tally 3 85 Repeated structures 3 10 3 11 3 88 3 89 3 90 3 105 3 143 3 146 Cards 3 25 to 3 32 Geometry 2 9 Source 3 59 Tally 3 88 Response function 3 85 3 96 3 99 3 100 10 3 05 RHP 3 19 3 22 RHP 3 19 3 22 Ring detectors 2 94 3 82 Cautions 2 64 Ring detector card 3 82 RPP 3 18 3 21 Russian roulette 2 6 2 32 2 140 3 109 D 8 Russian roulette also see Energy roulette 2 142 S Sampling Angular Distributions 2 36 SBn card 3 61 Scattering Elastic 2 35 2 39 Inelastic 2 35 2 39 Photon 2 33 S a p 2 29 S a B Treatment 2 28 SCn card 3 66 SDEF card 3 53 SDn card 3 104 Segment Divisor SDn card 3 104 Segmenting card 3 102 Sense 2 7 3 12 3 94 5 114 E 44 SFn surface flagging card 3 102 Simple physics treatment 2 7 2 57 D 8 SIn card 3 61 Source Bias SBn card 3 61 Comment SCn card 3 66 Dependent source distribution DSn card 3 65 Direction Biasing 2 153 Energy biasing 3 52 Fission 3 64 Fusion 3 64 Information SIn card 3 61 Probability SPn Card 3 61 SDEF General Source card 3 53 SOURCE subroutine 3 78 Specification 3 52 Spectra 3 64 subroutine 3 78 SSR card 3 71 SSW card 3 60 Surface 3 26 3 31 3 50 3 52 3 57 3 69 10 3 05 MCNP MANUAL INDEX Surface Source Read SSR card 3 71 3 71 weight minimum cutoff 3 136 Source Biasing 2 152 Space energy
81. 323 21046 31y 45 95520 LLNL ACTL 1983 323 21047 30y 46 95240 LLNL ACTL 1983 331 21048 30y 47 95220 LLNL ACTL 1983 325 Z 22 Titanium 22045 30 44 95810 LLNL ACTL 1983 449 22046 24y 45 55780 531dos ENDF B V 1977 53 22046 26y 45 55780 532dos ENDF B V 1977 53 22046 30y 45 95260 LLNL ACTL 1983 391 22047 24 46 54800 531405 ENDF B V 1977 209 22047 26y 46 54800 532dos ENDF B V 1977 209 22047 30y 46 95180 LLNL ACTL 1983 419 22048 24y 47 53600 531dos ENDF B V 1977 145 22048 26y 47 53600 532dos ENDF B V 1977 177 22048 30y 47 94790 LLNL ACTL 1983 415 22049 30y 48 94790 LLNL ACTL 1983 409 22050 26y 49 577000 532dos ENDF B V 1979 33 22050 30y 49 94480 LLNL ACTL 1983 345 22051 30y 50 94660 LLNL ACTL 1983 389 Z 23 Vanadium 23047 30 46 95490 LLNL ACTL 1983 209 23048 30y 47 95230 LLNL ACTL 1983 399 23049 30y 48 94850 LLNL ACTL 1983 423 23050 30y 49 94720 LLNL ACTL 1983 407 23051 30y 50 94400 LLNL ACTL 1983 357 23052 30y 51 94480 LLNL ACTL 1983 401 10 3 05 G 63 APPENDIX G MCNP DATA LIBRARIES DOSIMETRY DATA ZAID Dosimetry Data Libraries for MCNP Tallies AWR Table 6 Cont Library Source Date Z224 Chromium ak ak sk ak he k 2 ak ak ak k kak ak 24049 30y 24050 26y 24050 30y
82. 37087 30y 86 90920 LLNL ACTL 1983 199 Z 38 Strontium 38084 30 83 91340 LLNL ACTL 1983 163 38086 30y 85 90930 LLNL ACTL 1983 33 7 39 Y teigpm k k kk 39089 30 88 90590 LLNL ACTL 1983 419 7 40 Zirconium ak ak sk kak ak ak sk ak 40089 30y 88 90890 LLNL ACTL 1983 321 40090 26y 89 13200 532dos ENDF B V 1976 37 40090 30y 89 90470 LLNL ACTL 1983 385 40091 30y 90 90560 LLNL ACTL 1983 407 40092 26y 91 11200 532dos ENDF B V 1976 3821 40092 30y 91 90500 LLNL ACTL 1983 431 40093 30y 92 90650 LLNL ACTL 1983 371 40094 26y 93 09600 532dos ENDF B V 1976 5255 40094 30y 93 90630 LLNL ACTL 1983 417 40095 30y 94 90800 LLNL ACTL 1983 375 40096 30y 95 90830 LLNL ACTL 1983 57 40097 30y 96 91090 LLNL ACTL 1983 339 7 41 aR ra oi Niobium 41091 30 90 90700 LLNL ACTL 1983 49 41091 31y 90 90700 LLNL ACTL 1983 49 41092 30y 91 90720 LLNL ACTL 1983 285 41092 31y 91 90720 LLNL ACTL 1983 285 41093 30y 92 90640 LLNL ACTL 1983 493 41094 30y 93 90730 LLNL ACTL 1983 331 41095 30y 94 90680 LLNL ACTL 1983 333 G 66 10 3 05 ZAID 41096 30y 41097 30y 41098 30y 41100 30
83. 5000 01p 5000 02p 5000 03p 5000 04p 7 6 6000 01 6000 02 6000 03 6000 04 Z 7 7000 01 7000 02 7000 03 7000 04 Z 8 8000 01 8000 02p 8000 03p 8000 04p APPENDIX G MCNP DATA LIBRARIES Table G 4 PHOTOATOMIC DATA Continuous Energy Photoatomic Data Libraries Maintained by X 5 CS FF Source Source Library Name Release Length E Date Words NE max GeV Hydrogen meplib 1982 389 43 0 1 B IV B IV meplib02 1993 623 82 100 B IV 89 B IV meplib03 2002 722 82 100 B IV 89 B IV meplib04 2002 1898 278 100 B VI 8 8 oe ob ok os 2 7 A a k a a a a a aa oe meplib 1982 389 43 0 1 B IV B IV meplib02 1993 623 82 100 B IV 89 B IV meplib03 2002 722 82 100 B IV 89 B IV meplib04 2002 1970 290 100 B VI 8 8 meplib 1982 389 43 0 1 B IV B IV meplib02 1993 623 82 100 B IV 89 B IV meplib03 2002 821 82 100 B IV 89 B IV meplib04 2002 2339 335 100 B VI 8 8 Beryllium meplib 1982 389 43 0 1 B IV B IV meplib02 1993 623 82 100 B IV 89 meplib03 2002 821 82 100 B IV 89 B IV meplib04 2002 2363 339 100 B VI 8 8 Boron OK OROR k kK kk GR e kk k K k kk SK OR k meplib 1982 389 43 0 1 B IV B IV mcplib02 1993 623 82 100 B IV 89 B IV meplib03 2002 920 82 100 B IV 89 B IV meplib04 2002 3116 448 100 B VI 8 8 Carbon 8 k k k
84. 54488 293 6 90407 yes 54279 yes 7019 300 0 103467 293 6 56605 293 6 42266 293 6 75307 293 6 101124 300 0 3000 1 293 6 3000 1 293 6 10 3 05 47941 T utetjum A 34931 42687 37422 48096 E max NE MeV GPD 6314 263 6314 9052 6748 13011 3964 263 3964 5281 7354 263 5370 5370 8368 8101 12007 263 15000 15000 8909 19903 263 8229 8229 8304 11183 7075 263 13884 2426 263 4688 6648 4738 3631 4739 3903 5428 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 30 0 30 0 20 0 30 0 30 0 20 0 20 0 20 0 20 0 20 0 no no yes no no no no no yes no no no no yes no no no no no yes no no no no yes no no yes yes yes yes yes yes yes no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no
85. 6150 uresa 2 1992 300 0 203407 19737 20 0 62152 50 150 6150 kidman B V 0 1980 293 6 41252 4298 200 no no no no no G 26 10 3 05 ZAID kokk Eu nat 63000 35c 63000 35d 63000 42c Eu 151 63151 49c 63151 50c 63151 50d 63151 55d 63151 55c 63151 60c 63151 65c 63151 66c Eu 152 63152 49c 63152 50d 63152 50c 63152 65c 63152 66c Eu 153 63153 49c 63153 50d 63153 50c 63153 55d 63153 55c 63153 60c 63153 65c 63153 66c 154 63154 49c 63154 50c 63154 50d 63154 65c 63154 66c 155 63155 50c 63155 66c 7 64 Gadolinium AWR 150 6546 150 6546 150 6546 149 6230 149 6230 149 6230 149 6230 149 6230 149 6230 149 6230 149 6230 150 6200 150 6200 150 6200 150 6200 150 6200 151 6080 151 6070 151 6070 151 6080 151 6080 151 6080 151 6080 151 6080 152 6000 152 6000 152 6000 152 6000 152 6000 153 5920 153 5920 Gd nat 64000 35 64000 35d Gd 152 64152 50c 64152 50d 64152 55c 64152 60c 64152 65c 64152 66c 54 154 64154 50d 64154 50c 64154 55c 64154 60c 64154 65c 64154 66c 155 8991 155 8991 150 6150 150 6150 150 6150 150 6150 150 6150 150 6150 152 5990 152 5990 152 5990 152 5990 152 5990 152 5990 Library Name rmccsa drmccs endl92 uresa rmccs drmccs newxsd newxs endf60 endf66e endf66b uresa dre5 end
86. 8 B VI8 BM amp M Z 60 Neodymium 60000 01p mcplib 1982 509 59 0 1 B IV B IV E amp C n a 60000 02p mcplib02 1993 743 98 100 B IV 89 B IV E amp C n a 60000 03p meplib03 2002 2624 98 100 B IV 89 E amp C BM amp M 60000 04p mcplib04 2002 9362 1221 100 B VL8 8 B VI8 BM amp M Z 61 eee Promethium 61000 01p meplib 1982 521 61 0 1 B IV B IV E amp C n a 61000 02p meplib02 1993 755 100 100 B IV 89 E amp C n a 61000 03p mcplib03 2002 2636 100 100 B IV 89 B IV E amp C BM amp M 61000 04p mcplib04 2002 9350 1219 100 B VL8 8 B VI8 BM amp M Z 62 eee Samarium 62000 01p meplib 1982 521 61 0 1 B IV B IV E amp C n a 62000 02p meplib02 1993 755 100 100 B IV 89 E amp C n a 62000 03p meplib03 2002 2636 100 100 B IV 89 B IV E amp C BM amp M 62000 04p mcplib04 2002 9374 1223 100 B VL8 8 B VI8 Z 63 Europium K K K KK K K K K K K K 63000 01p mcplib 1982 521 61 0 1 B IV B IV E amp C n a 63000 02p meplib02 1993 755 100 100 B IV 89 E amp C n a 63000 03p mcplib03 2002 2735 100 100 B IV 89 E amp C BM amp M 63000 04p mcplib04 2002 9323 1198 100 B VL8 B VI8 B VI8 BM amp M Z 64 Gadolinium 64000 01p mcplib 1982 521 61 0 1 B IV B IV E amp C n a 64000 02p meplib02 1993 755 100 100 B IV 89 E amp C n a 64000 03p meplib03 2002 2834 100 100 B IV 89 B IV E amp C BM amp M 64000 04p
87. 94242 60c 94242 61c 94242 65c 94242 66c Pu 243 94243 42c 94243 60c 94243 65c 94243 66c Pu 244 94244 60c 94244 65c 94244 66c 7 95 241 95241 42 95241 50 95241 50d 95241 51c 95241 51d 95241 60c 95241 61c 95241 65c 95241 66c 95241 68c 95241 69c G 36 AWR 236 9990 236 9990 236 9986 236 9986 236 9986 236 9986 236 9986 236 9986 236 9986 236 9986 237 9916 237 9920 237 9920 237 9920 237 9920 237 9920 237 9920 237 9920 238 9860 238 9780 238 9780 238 9780 238 9780 238 9780 238 9780 238 9780 238 9780 238 9780 239 9793 239 9790 239 9790 239 9790 239 9790 239 9790 239 9790 239 9790 239 9790 239 9790 240 9740 240 9740 240 9740 240 9740 241 9680 241 9680 241 9680 238 9860 238 9860 238 9860 238 9860 238 9860 238 9860 238 9860 238 9860 238 9860 238 9860 238 9860 Library Name drmccs rmccs endf60 endf6dn endf66d endf66e endf66c t16 2003 t16 2003 t16 2003 endl92 uresa drmccs rmccs endf60 endf6dn endf66e endf66c 192 uresa endf5p dre5 rmccs drmccs endf60 endf6dn endf66e endf66c endl92 uresa endf5p dre5 rmccs drmccs endf60 endf6dn endf66e endf66c endl92 endf60 endf66e endf66c endf60 endf66e endf66c Americium endl92 endf5u dre5 rmccs drmccs endf60 endf6dn endf66e endf66c t16_2003 t16_2003 Source B V 2 B V 2 B VI2 2 5 5 5 L
88. AND AREAS The particle flux in Monte Carlo transport problems often is estimated as the track length per unit volume or the number of particles crossing a surface per unit area Therefore knowing the volumes and surface areas of the geometric regions in a Monte Carlo problem is essential Knowing volumes is useful in calculating the masses and densities of cells and thus in calculating volumetric or mass heating Furthermore calculation of the mass of a geometry is frequently a good check on the accuracy of the geometry setup when the mass is known by other means Calculating volumes and surface areas in modern Monte Carlo transport codes is nontrivial MCNP allows the construction of cells from unions and or intersections of regions defined by an arbitrary combination of second degree surfaces toroidal fourth degree surfaces or both These surfaces can have different orientations or be segmented for tallying purposes The cells they form can even consist of several disjoint subcells Cells can be constructed from quadralateral or hexagonal lattices or can be embedded in repeated structures universes Although such generality greatly increases the flexibility of MCNP computing cell volumes and surface areas understandably requires increasingly elaborate computational methods 10 3 05 2 185 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VOLUMES AND AREAS MCNP automatically calculates volumes and areas of polyhedral cells and of cells o
89. Data Libraries Maintained by X 5 Library Eval Temp Length Emax ZAID AWR Name Source Date words NE MeV GPD 28061 24c 60 4080 la150n 6 1997 2936 244768 7384 150 0 yes 28061 60c 60 4080 endf60 B VI 1 1989 293 6 93801 5882 20 0 yes 28061 61c 60 4080 actib B VL8 2000 77 0 247660 7438 150 0 yes 28061 62c 60 4080 actia B VI 8 2000 2936 247188 7379 150 0 yes 28061 64c 60 4080 endf66d 6 1997 77 0 245215 7440 150 0 yes 28061 66c 60 4080 endf66a B VI 6 1997 2903 6 244743 7381 150 0 yes 28062 24c 61 3960 lal50n 6 1997 2936 232065 9219 150 0 yes 28062 60c 61 3960 endf60 1989 293 6 82085 7230 20 0 28062 61c 61 3960 8 2000 77 0 234983 9227 150 0 yes 28062 62c 61 3960 actia B VI 8 2000 293 6 234511 9168 150 0 yes 28062 64c 61 3960 endf66d 6 1997 77 0 232193 9235 150 0 28062 66c 61 3960 endf66a 6 1997 2936 231705 9174 150 0 yes 28064 24c 63 3790 lal50n 6 1997 2936 197799 7958 150 0 yes 28064 60c 63 3790 endf60 B VI 1 1989 293 6 66656 6144 200 yes 28064 61c 63 3790 actib 8 2000 77 0 199097 7992 150 0 yes 28064 62c 63 3790 actia B VL8 2000 293 6 198313 7894 150 0 yes 28064 64c 63 3790 endf66d 6 1997 77 0 198112 7997 150 0 yes 28064 66c 63 3790 endf66a 6 1997 293 6 197296 7895 150 0 yes Cu nat 29000 50d 63 5460 drmccs B V 0 1978 293 6 12777 263 20 0 yes 29000 50c 63 5460 rmccs B V 0 1978 293 6 51850 3435 20 0 yes 63 29063 24c 6
90. ENDL85 and ENDL92 Los Alamos National Laboratory internal memorandum XTM 95 254 1995 S C Frankle Summary Documentation for the ENDL92 Continuous Energy Neutron Data Library Release 1 Los Alamos National Laboratory internal memorandum XTM 96 05 and report LA UR 96 327 1996 available URL http www xdiv lanl gov PROJECTS DATA nuclear doc textend192 html R Little and R Seamon ENDEF B V 0 Gd Cross Sections with Photon Production Los Alamos National Laboratory internal memorandum X 6 RCL 87 132 1986 R C Little Neutron and Photon Multigroup Data Tables for MCNP3B Los Alamos National Laboratory internal memorandum X 6 RCL 87 225 1987 available URL http www xdiv lanl gov PROJECTS DATA nuclear doc mgxsnp html R C Little and R E Seamon New MENDF5 and MENDF5G Los Alamos National Laboratory internal memorandum X 6 RCL 86 412 1986 J C Wagner et al MCNP Multigroup Adjoint Capabilities Los Alamos National Laboratory report LA 12704 1994 available URL http www xdiv lanl gov PROJECTS DATA nuclear pdf la ur 03 0164 pdf E Seamon Weight Functions for the Isotopes on Permfile THIRTY2 Los Alamos National Laboratory internal memorandum TD 6 July 23 1976 E Seamon Plots of the TD Weight Function Los Alamos National Laboratory internal memorandum X 6 RES 91 80 1980 E MacFarlane and D W Muir The NJOY Nuclear Data Processing System
91. Energy and Discrete Neutron Data Libraries Maintained by X 5 Library Eval Temp Length Emax ZAID AWR Name Source Date K words NE MeV GPD K nat 19000 42c 38 7624 192 LLNL 1992 300 0 11060 544 30 0 yes 19000 50c 38 7660 endf5u B V 0 1974 293 6 22051 1243 200 yes 19000 50d 38 7660 dre5 0 1974 293 6 23137 263 20 0 yes 19000 51d 38 7660 B V 0 1974 293 6 23137 263 20 0 yes 19000 51 38 7660 rmccs 0 1974 293 6 18798 1046 20 0 19000 60 38 7660 endf60 B VLO 1974 293 6 24482 1767 20 0 yes 19000 62c 38 7660 actia B VI 8 2000 293 6 52304 2734 20 0 yes 19000 66c 38 7660 endf66a B VLO 1974 293 6 51384 2734 200 yes Ca nat 20000 24c 39 7360 la150n 6 1997 293 6 187818 4470 150 0 20000 42c 39 7357 endl92 LLNL 1992 300 0 13946 1002 30 0 yes 20000 50c 39 7360 endfSu 0 1976 293 6 62624 2394 20 0 20000 50d 39 7360 dre5 B V 0 1976 293 6 29033 263 20 0 yes 20000 51d 39 7360 drmccs 0 1976 293 6 29033 263 20 0 20000 51 39 7360 rmccs B V 0 1976 293 6 53372 1796 20 0 yes 20000 60c 39 7360 endf60 B VLO 1980 293 6 76468 2704 20 0 yes 20000 61c 39 7360 actib B VL8 2000 77 0 185636 4178 150 0 yes 20000 62c 39 7360 actia B VL8 2000 293 6 187296 4344 150 0 yes 20000 64c 39 7360 endf66d 6 1997 77 0 184909 4179 150 0 20000 66c 39 7360 endf66a 6 1997 293 6 186569 4345 150 0 yes 40 20040 21c 39 6193 100xs3 LANL T X 1989 300 0 53013 2718 100 0
92. Figure 2 18 represents the MCNP process of calculating the first and second moments of each tally bin and relevant totals using three tally storage blocks of equal length for each tally bin The hypothetical grid of tally bins in the bottom half of Figure 2 18 has 24 tally bins including the time and energy totals During the course of the history sums are performed in the first MCNP tally storage block Some of the tally bins receive no contributions and others receive one or more contributions At the conclusion of the history the sums are added to the second MCNP tally storage block The sums in the first MCNP tally storage block are squared and added to the third tally storage block The first tally storage block is then filled with zeros and history i 1 begins After the last history N the estimated tally means are computed using the second MCNP tally storage block and Eq 2 15 The estimated relative errors are calculated using the second and third MCNP tally storage blocks and Eq 2 19b This method of estimating the statistical uncertainty of the result produces the best estimate because the batch size is one which minimizes the variance of the variance 122123 Note that there is no guarantee that the estimated relative error will decrease inversely proportional to the as required by the Central Limit Theorem because of the statistical nature of the tallies Early in the problem will generally have large statistical fluctua
93. GUARANTEE however The possibility always exists that some as yet unsampled portion of the problem may change the confidence interval if more histories were calculated Chapter 2 contains more information about estimation of Monte Carlo precision E Variance Reduction As noted in the previous section the estimated relative error is proportional to 1 JN where N is the number of histories For a given MCNP run the computer time T consumed is proportional to N Thus R where Cisa positive constant There are two ways to reduce R 1 increase T and or 2 decrease C Computer budgets often limit the utility of the first approach For example if it has taken 2 hours to obtain 0 10 then 200 hours will be required to obtain 0 01 For this reason MCNP has special variance reduction techniques for decreasing C Variance is the square of the standard deviation The constant C depends on the tally choice and or the sampling choices l Tally Choice As an example of the tally choice note that the fluence in a cell can be estimated either by a collision estimate or a track length estimate The collision estimate is obtained by tallying 1 2 Z macroscopic total cross section at each collision in the cell and the track length estimate is obtained by tallying the distance the particle moves while inside the cell Note that as gets very small very few particles collide but give enormous tallies when they do producing
94. K K K K K K K 69169 30y 168 93400 LLNL ACTL 1983 453 Z 71 Lutetium 71173 30 172 93900 LLNL ACTL 1983 587 71174 30y 173 94000 LLNL ACTL 1983 417 71174 31y 173 94000 LLNL ACTL 1983 465 71175 30y 174 94100 LLNL ACTL 1983 559 71176 30y 175 94300 LLNL ACTL 1983 621 71176 31y 175 94300 LLNL ACTL 1983 637 71177 30y 176 94400 LLNL ACTL 1983 573 71177 31y 176 94400 LLNL ACTL 1983 573 10 3 05 G 69 APPENDIX G MCNP DATA LIBRARIES DOSIMETRY DATA ZAID AWR Table 6 Cont Dosimetry Data Libraries for MCNP Tallies Library Source Date Z 72 BR aR a a oe k kk 7 72174 30y 72175 30y 72176 30y 72171 30y 72178 30y 72179 30y 72180 30y 72181 30y 72183 30y 173 94000 174 94100 175 94100 176 94300 177 94400 178 94600 179 94700 180 94900 182 95400 LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL 1983 1983 1983 1983 1983 1983 1983 1983 1983 7 73 Tantalum 9 HE 7 R he he 2 k k k kk kk 73179 30y 73180 30y 73180 31y 73181 30y 73182 30y 73182 31y 73183 30y 73184 30y 73186 30y 178 94600 179 94700 179 94700 180 94800 181 95000 181 95000 182 95100 183 95400 185 95900
95. MCNP DATA LIBRARIES NEUTRON CROSS SECTION LIBRARIES Table G 2 Cont Continuous Energy and Discrete Neutron Data Libraries Maintained by X 5 Library Eval Temp Length ZAID AWR Name Source Date words Sb nat 51000 42c 120 7041 endl92 LLNL lt 1992 300 0 95953 10721 53127 42c 125 8143 endl92 LLNL lt 1992 300 0 76321 10 53127 55c 125 8140 misc5xs 7 9 LANL T 1982 293 6 59725 9423 53127 60c 125 8143 endf60 13 LANL T 1991 293 6 399760 7888 53127 66c 125 8143 endf66b B VI 2 1991 293 6 373991 11519 53129 60c 127 7980 endf60 0 1980 293 6 8792 1237 53135 50 133 7510 kidman 0 1974 293 6 1232 194 Xe nat 54000 42c 130 1721 endl92 LLNL 1992 300 0 43411 5173 124 54124 66c 122 8420 endf66b 0 1978 293 6 21034 1979 Xe 126 54126 66c 124 8230 endf66b 0 1978 293 6 21388 2133 Xe 128 54128 66c 126 8050 endf66b 0 1978 293 6 32739 3817 129 54129 66c 127 7970 endf66b 0 1978 293 6 118721 15971 130 5 54130 66c 128 7880 endf66b 0 1978 293 6 34346 3984 Xe 131 54131 50 129 7810 B V 0 1978 293 6 22572 3376 54131 66c 129 7810 endf66b 0 1978 293 6 79510 10434 132 54132 66c 130 7710 endf66b 0 1978 293 6 17947 1709 Xe 134 54134 42c 132 7551 endl92 LLNL 1992 300 0 8033 192 54134 66c 132 7550 endf66b 0 1978 293 6 15028 1349 Xe 135 54135 50c 133 7480 endfSmt
96. New Compton Doppler Broadening Data Los Alamos National Laboratory internal memorandum X 5 MCW 02 110 2002 available URL http www xdiv lanl gov PROJECTS DATA nuclear pdf mcw 02 110 pdf F Biggs L B Mendelsohn and J B Mann Hartree Fock Compton Profiles for the Elements Atomic Data and Nuclear Data Tables Volume 16 pp 201 309 1975 M C White Photoatomic Data Library MCPLIB04 A New Photoatomic Library Based on Data from ENDF B VI Release 8 Los Alamos National Laboratory internal memorandum X 5 MCW 02 111 2002 available URL http www xdiv lanl gov PROJECTS DATA nuclear pdf mcw 02 111 pdf D E Cullen J Hubbel and L D Kissel EPDL97 The Evaluated Photon Data Library 97 Version Lawrence Livermore National Laboratory report UCRL 50400 Volume 6 Rev 5 1997 C Little and E Seamon Dosimetry Activation Cross Sections for MCNP Los Alamos National Laboratory internal memorandum March 13 1984 available URL http www xdiv lanl gov PROJECTS DATA nuclear pdf dosimetry pdf 10 3 05 APPENDIX H FISSION SPECTRA CONSTANTS AND FLUX TO DOSE FACTORS CONSTANTS FOR FISSION SPECTRA APPENDIX H FISSION SPECTRA CONSTANTS AND FLUX TO DOSE FACTORS Appendix H is divided into two sections fission spectra constants to be used with the SP input card and ANSI standard flux to dose conversion factors to be used with the DE and DF input cards Il CONSTANTS FOR FISSION S
97. P E the electron and positron are created and banked and the photon track terminates 2 For Mode P problems with the TTB approximation both an electron and positron are produced but not transported Both particles can make TTB approximation photons The positron is then considered to be annihilated locally and a photon pair is created as in case 3 3 For Mode P problems when positrons are not created by the TTB approximation the incident photon of energy E vanishes The kinetic energy of the created positron electron pair assumed to be E 2mc is deposited locally at the collision point The positron is considered to be annihilated with an electron at the point of collision resulting in a pair of photons each with the incoming photon weight and each with an energy of mc 0 511 MeV The first photon is emitted isotropically and the second is emitted in the opposite direction The very rare single annihilation photon of 1 022 MeV is ignored e Caution for detectors and coherent scattering The use of the detailed photon physics treatment is not recommended for photon next event estimators such as point detectors and ring detectors nor for DXTRAN unless coherent scatter is turned off with the NOCOH 1 option on the PHYS P card Alternatively the simple physics treatment EMCPF 001 on the PHYS P card can be used Turning off coherent scattering can improve the figure of merit see page 2 116 by more than a factor of 10 for
98. PLOTTING COMMANDS 50 Tally and Cross Section Plotting Command Formats eene 50 Tally and Cross Section Plotting Commands 50 Tally and Cross Section Plotting Commands By Function 52 Concise Tally and Cross Section Plotting Command Descriptions 54 APPENDIX B MCNP GEOMETRY AND TALLY PLOTTING 1 SYSTEM GRAPHICS INFORMATION tumba anh been 1 X dun o 1 THE GEOMETRY PLOTTER 2 Geometry PLOT Input and Execute Line Options 2 Geometry Plot Commands Grouped by Function 4 Geometry Debugging and Plot Orientation sess 9 Interactive Geometry Plotting 10 THE MCPLOT TALLY AND CROSS SECTION PLOTTER 14 Input for MCPLOT and Execution Line Options 15 Plot Conventions and Command Syntax e 17 Plot Commands Grouped by 17 MCOCTAL LII C EN
99. R 1 0 0 32 0 10 0 032 0 010 Another interpretation for the FOM involves defining the problem s particle computation rate f as t 2 24c where is the number of particles per minute for a problem on a specific computer and is the number of particles run in the problem Substituting Eq 2 21c into Eq 2 21a and using Eqs 2 162 2 17 and 2 192 the becomes FOM 1 2 5 2 240 where S is the estimated standard deviation of the sampled population not the mean The squared quantity is a ratio of the desired result divided by a measure of the spread in the sampled values This ratio is called the tally signal to noise ratio signal to noise ratio x S 2 24e 10 3 05 2 117 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS ESTIMATION OF THE MONTE CARLO PRECISION The quantity 5 approaches the expected value of the signal to noise ratio for a problem tally bin as N becomes large Using Eq 2 21e the FOM becomes FOM t signal to noise ratio 2 24f The FOM is directly proportional to the particles per minute 7 as would be expected and the tally bin signal to noise ratio squared The tally bin signal to noise ratio is dependent on the shape of the underlying history score probability density function f x for the tally bin see page 2 122 To increase the FOM t and or the signal to noise ratio can be increased Since x should be the same for the problems with different variance reduction
100. Revision Los Alamos Scientific Laboratory report LA 5240 MS May 1973 Grady Hughes Information on the MCPLIBO2 Photon Library Los Alamos National Laboratory report LA UR 08 539 January 23 1993 D E Cullen M H Chen J H Hubbell S T Perkins E F Plechaty J A Rathkopf and J Scofield Tables and Graphs of Photon Interaction Cross Sections from 10 eV to 100 GeV Derived from the LLNL Evaluated Photon Data Library EPDL Lawrence Livermore National Laboratory report UCRL 50400 Vol 6 October 31 1989 10 3 05 37 38 29 40 41 42 43 44 45 46 47 48 49 50 51 32 53 54 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS REFERENCES F Biggs L B Mendelsohn and J B Mann Hartree Fock Compton Profiles for the Elements Atomic Data and Nuclear Data Tables Vol 16 No 3 201 309 1975 D E Cullen J Hubbell and L D Kissel EPDL97 The Evaluated Photon Data Library 97 Version UCRL 50400 Vol 6 Rev 5 Lawrence Livermore National Laboratory 1997 P Oblozinsky ed Handbook on Photonuclear Data for Applications Cross Sections and Spectra IAEA TECDOC 1178 International Atomic Energy Agency Vienna Austria 2000 7 Halbleib R P Kensek T A Mehlhorn D Valdez S M Seltzer and 7 Berger ITS Version 3 0 Integrated TIGER Series of Coupled Electron Photon Monte Carlo Transpor
101. T card establishes time bin ranges the C card establishes cosine bin ranges and the FS card segments the surface or cell of a tally into subsurface or subcell bins 2 Flagging Cell and surface flagging cards CF and SF determine where the different portions of a tally originate Example F4 1 CF4 234 The flux tally for cell 1 is output twice first the total flux in cell 1 and second the flagged tally or that portion of the flux caused by particles having passed through cells 2 3 or 4 3 Multipliers and Modification MCNP tallies can be modified in many different ways The EM TM and CM cards multiply the quantities in each energy time or cosine bin by a different constant This capability is useful for modeling response functions or changing units For example a surface current tally can have its units changed to per steradian by entering the inverse steradian bin sizes on the CM card The DE and DF cards allow modeling of an energy dependent dose function that is a continuous function of energy from a table whose data points need not coincide with the tally energy bin structure E card An example of such a dose function is the flux to radiation dose conversion factor given in Appendix H The FM card multiplies the F1 F2 F4 and F5 tallies by any continuous energy quantity available in the data libraries For example average heating numbers avg E total cross section are stored on the MCNP data lib
102. TFC summary table for the user to consider This check is not a pass or no pass test because a hole in the tail may be appropriate for a discrete 2 130 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS ESTIMATION OF THE MONTE CARLO PRECISION f x or an exceptional sample occurred with so little impact that none of the ten checks was affected The empirical f x should be examined to assess the likelihood of complete sampling d Forming Valid TFC Bin Confidence Intervals For TFC bin results the highest probability of creating a valid confidence interval occurs when all of the statistical checks are passed Not passing several of the checks is an indication that the confidence interval is less likely to be correct A monotonic trend in the mean for the last half of the problem is a strong indicator that the confidence interval is likely to produce incorrect coverage rates The magnitudes of R and the VOV should be less than the recommended values to increase the likelihood of a valid confidence interval Small jumps in the R VOV and or the FOM as a function of N are not threatening to the quality of a result The slope of f x is an especially strong indicator that N has not approached infinity in the sense of the CLT If the slope appears too shallow 3 check the printed plot of f x to see that the estimated Pareto fit is adequate The use of the shifted confidence interval is recommended although it will be a small effect
103. The confidence interval based on the three statistically combined estimator is the recommended result to use for all final confidence interval quotations because all of the available information has been used in the final result This estimator often has a lower estimated standard deviation than any of the three individual estimators and therefore provides the smallest valid confidence interval as well The final estimated keff value estimated standard deviation and the estimated 68 95 and 99 confidence intervals using the correct number of degrees of freedom are presented in the box on the k results summary page of the output If other confidence intervals are wanted they can be formed from the estimated standard deviation of k At least 30 active cycles need to be run for the final k results box to appear Thirty cycles are required so that there are enough degrees of freedom to form confidence intervals using the well known estimated standard deviation multipliers When constructing a confidence interval using any single estimator its standard deviation and a Student s t Table there are J J 1 degrees of freedom For the two and three combined K estimators there are I I 2 and J I 3 degrees of freedom respectively All of the k estimators and combinations by two or three are provided in MCNP so that the user can make an alternate choice of confidence interval if desired Based on statistical st
104. a 1 R bias we pick from the density function C 2nR where C is a normalization constant To pick from p let be a random number on the unit interval Then C ir do 217 1 rcoso y FE ep ode 214 csinq 10 3 05 2 95 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS TALLIES where 2 2 2 2 rex yay a b 2rx C qd p gyn The above expression is valid if a gt b c which is true except for collisions exactly on the ring Solving for tan ian ileum j Letting t tang 2 then x rcoso r 1 D 0 y fixed z rsing 2rt 1 f For ring detectors the 1 2 biasing has been supplemented when it is weak to include a biasing based on angle to select the point on the ring This angle is in the plane of the ring and is relative to the shortest line from the collision point to the detector ring The angle that would most likely be selected would pick the same point on the ring as a straight line through the axis of the problem the collision point and the ring The angle least likely to be picked would choose the point on the opposite side of the ring This approach will thus make scores with smaller attenuations more often This supplemental biasing is achieved by requiring that a lt 3 b in the above equation If the ra
105. a high variance situation see page 2 118 In contrast the track length estimate gets a tally from every particle that enters the cell For this reason MCNP has track length tallies as standard tallies whereas the collision tally is not standard in MCNP except for estimating ke f 2 Nonanalog Monte Carlo Explaining how sampling affects C requires understanding of the nonanalog Monte Carlo model The simplest Monte Carlo model for particle transport problems is the analog model that uses the natural probabilities that various events occur for example collision fission capture etc Particles are followed from event to event by a computer and the next event is always sampled using the random number generator from a number of possible next events according to the 1 8 10 3 05 CHAPTER 1 MCNP OVERVIEW INTRODUCTION TO MCNP FEATURES natural event probabilities This is called the analog Monte Carlo model because it is directly analogous to the naturally occurring transport The analog Monte Carlo model works well when a significant fraction of the particles contribute to the tally estimate and can be compared to detecting a significant fraction of the particles in the physical situation There are many cases for which the fraction of particles detected is very small less than 10 For these problems analog Monte Carlo fails because few if any of the particles tally and the statistical uncertainty in the answer is unacceptable
106. a number of incident energies there is a table of cumulative probabilities typically 20 and the value of the near total elastic fission and radiative capture cross sections and heat deposition numbers corresponding to those probabilities These data supplement the usual continuous data if probability tables are turned off PHYS N card then the usual smooth cross section is used But if the probability tables are turned on default if they exist for the nuclide of a collision and if the energy of the collision is in the unresolved resonance energy range of the probability tables then the cross sections are sampled from the tables The near total is the total of the elastic fission and radiative capture cross sections it is not the total cross section which may include other absorption or inelastic scatter in addition to the near total The radiative capture cross section is not the same as the usual MCNP capture cross section which is more properly called destruction or absorption and includes not only radiative capture but all other reactions not emitting a neutron Sometimes the probability tables are provided as factors multipliers of the average or underlying smooth cross section which adds computational complexity but now includes any structure in the underlying smooth cross section Itis essential to maintain correlations in the random walk when using probability tables to properly model resonance self shielding Suppose we sam
107. a previous MCNP criticality calculation If the SDEF card is used the default WGT value should not be changed Any KSRC points in geometric cells that are void or have zero importance are rejected The remaining KSRC points are duplicated or rejected enough times so the total number of points M in the source spatial distribution is approximately the nominal source size N The energy of each source particle for the first k is selected from a generic Watt thermal fission distribution if it is not available from the SRCTP file 2 Particle Transport for Each k Cycle In each kw cycle M varying with cycle source particles are started isotropically For the first cycle these M points come from one of three user selected source possibilities For subsequent 2 164 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CRITICALITY CALCULATIONS cycles these points are the ones written at collision sites from neutron transport in the previous cycle The total source weight of each cycle is a constant N That is the weight of each source particle is so all normalizations occur as if N rather than M particles started in each cycle Source particles are transported through the geometry by the standard random walk process except that fission is treated as capture either analog or implicit as defined on the PHYS N or CUT N card At each collision point the following four steps are performed for the cycle 1 the three pro
108. absorption estimate differs from the collision estimate in that the collision estimate is based upon the expected value at each collision whereas the absorption estimate is based upon the events actually sampled at a collision Thus all collisions will contribute to the collision estimate of E and D by the probability of fission or capture for 19 in the material Contributions to the absorption estimator will only occur if an actual fission or capture for i event occurs for the sampled nuclide in the case of analog absorption For implicit absorption the contribution to the absorption estimate will only be made for the nuclide sampled The absorption estimate of the prompt removal lifetime for any active cycle is again the average time required for a fission source neutron to be removed from the system by either escape capture n On or fission 10 3 05 2 171 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CRITICALITY CALCULATIONS For implicit absorption A 3 WII T Wer M W where Wi o W W f Sr For analog absorption LAU pU Wer Wet MW where T T and are the times from the birth of the neutron until escape capture 0 fission or collision is the weight lost at each escape W and W are the weights lost to capture n On and fission at each capture n On or fission event with the nuclide sampled for the col
109. ak ak akak ak ak ak akak ak ak ak ak ak ak ak ak ak ak ak 3k 3k ak akk 3k 3k 3K akk 3k 3K 3K 3K gt k 3K gt K mcplib 1982 389 43 0 1 B IV B IV mcplib02 1993 623 82 100 B IV 89 B IV mcplib03 2002 920 82 100 B IV 89 B IV mcplib04 2002 3152 454 100 B VI 8 8 KKK K K KK K Nitrogen K ok mcplib 1982 389 43 0 1 B IV B IV mcplib02 1993 623 82 100 B IV 89 B IV mcplib03 2002 920 82 100 B IV 89 mcplib04 2002 3194 461 100 8 8 Oxygen meplib 1982 389 43 0 1 B IV B IV meplib02 1993 623 82 100 B IV 89 B IV meplib03 2002 920 82 100 B IV 89 B IV meplib04 2002 3272 474 100 B VI 8 8 10 3 05 Fluor CDBD Source Source E amp C n a E amp C n a E amp C BM amp M B VI 8 BM amp M E amp C n a E amp C n a E amp C BM amp M B VL8 BM amp M E amp C n a E amp C n a E amp C BM amp M B VL8 BM amp M E amp C n a E amp C n a E amp C BM amp M B VL8 BM amp M E amp C n a E amp C n a E amp C BM amp M B VL8 BM amp M E amp C n a E amp C n a E amp C BM amp M B VL8 BM amp M E amp C n a E amp C n a E amp C BM amp M B VL8 BM amp M E amp C n a E amp C n a E amp C BM amp M B VL8 BM amp M G 45 APPENDIX G MCNP DATA LIBRARIES PHOTOATOMIC DATA Table G 4 Cont Continuous Energy Photoatomic Data Libraries Maintained by X 5 Library Release Length Emax CS FF Fluor CDBD ZAID Name Date Words GeV Source Source Source Source Z 9 KKK K KKK K Fluorine 9000 01p
110. all nuclides are perturbed generally 1 Finally the expected value of the first order coefficient is m 1 SEIE Bret Ry ty i J k 0 2 Second Order For a second order perturbation the differential operator becomes _ 2 e 1 5 i 2 beB heH h 2 196 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PERTURBATIONS 2 2 2 h 04 O t x Ei eM dels Lin jr Ox Rh Bx 08x 8 5 Whereas t is a linear function of x then 2 O t a Ox h and by taking first and second derivatives of the r terms of q as for the first order perturbation 2 m m 2 2 k 0 k 0 where 20 p xy E _ 2 Op XE 252 28 px E gt o e em xr E beB heH an _ ES 2 x x E The expected value of the second order coefficient is m m 1 U Ri Y Beet Ru p gt itj k 0 k 0 where and are given by one or more terms as described above for track k and R is again the fraction of the perturbation with nuclides participating in the tally 3 Implementation in MCNP The total perturbation printed in the MCNP output file is 10 3 05 2 197 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PERTURBATIONS Ac For each history i and path 2 Ac Agee hy J V 2 di Let th
111. and with those estimates from previous active after the inactive cycles The relative error R of each quantity is estimated in the usual way as 10 3 05 2 175 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CRITICALITY CALCULATIONS 1 XN M 1 where the number of active cycles 1 2 xs and x where x a quantity such as is from cycle m This assumes that the cycle to cycle estimates of each k are uncorrelated This assumption generally is good for but not for the eigenfunction fluxes of optically large systems MCNP also combines the three estimators in all possible ways and determines the covariance and correlations The simple average of two estimators is defined as x 1 2 x x where for example x may be the collision estimator E and x may be the absorption estimator k eff The combined average of two estimators is weighted by the covariances as po pO 0250 a x ii j _ jj ij i ij Cj 2 where the covariance C 5 _ 1 i j 1 i jj 1 j Ci xS __ Note that C x E a for estimator i The correlation between two estimators is a function of their covariances and is given by The correlation will be between unity perfect positive correlation and minus one perfect anti or negative correlation If the correlation is one no new information has been gained by the second estimator I
112. both the detector diagnostic printing and a Russian roulette game played on pseudoparticles in transit to detectors The Russian roulette game is governed by the input parameter k that controls a comparison weight internal to MCNP such that w kifk 0 w Oifk 0 Oifk gt Oand lt 200 we ifk gt 0 and N gt 200 where N number of histories run so far 2 102 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS TALLIES number of pseudoparticles started so far 97 I contribution of the i pseudoparticle to the detector tally When each pseudoparticle is generated W p w and are already known before the expensive tracking process is undertaken to determine 2 If Wp u 2xR lt w the pseudoparticle contribution to the detector o will be less than the comparison weight Playing Russian roulette on all pseudoparticles with lt w avoids the expensive tracking of unimportant pseudoparticles Most are never started Some are started but are rouletted as soon as has increased to the point where Wp 2 nR lt w Rouletting pseudoparticles whose expected detector contribution is small also has the added benefit that those pseudoparticles surviving Russian roulette now have larger weights so the disparity in particle weights reaching the detector is reduced Typically using the DD card will increase the efficiency of detector problems by a factor of ten
113. cells are defined an important concept is that of the sense of all points in a cell with respect to a bounding surface Suppose that s f x y z 0 is the equation of a surface in the problem For any set of points x y z if s the points are on the surface However for points not on the surface if s is negative the points are said to have a negative sense with respect to that surface and conversely a positive sense if 5 15 positive For example a point at x 3 has a positive sense with respect to the plane x 2 0 That is the equation x 3 22 s 1 ispositive for x 3 where D constant Cells are defined on cell cards Each cell is described by a cell number material number and material density followed by a list of operators and signed surfaces that bound the cell If the sense is positive the sign can be omitted The material number and material density can be replaced by a single zero to indicate a void cell The cell number must begin in columns 1 5 The remaining entries follow separated by blanks A more complete description of the cell card format can be found in Volume II Each surface divides all space into two regions one with positive sense with respect to the surface and the other with negative sense The geometry description defines the cell to be the intersection union and or complement of the listed regions The subdivision of the physical space into cells is not necessarily governed only by the differen
114. creation of the empirical f x in MCNP automatically covers nearly all TFC bin tallies that a user might reasonably be expected to make including the effect of large and small tally multipliers A logarithmically spaced grid is used for accumulating the empirical f x because the tail behavior is assumed to be of the form 1 x n gt 3 unless an upper bound for the history scores exists This 2 124 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS ESTIMATION OF THE MONTE CARLO PRECISION grid produces an equal width histogram straight line for f x on a log log plot that decreases n decades in f x per decade increase in x Ten bins per x decade used and cover the unnormalized tally range from 10730 to 1079 The term unnormalized indicates that normalizations that are not performed until the end of the problem such as cell volume or surface area are not included in f x The user can multiply this range at the start of the problem by the 16th entry on the DBCN card when the range is not sufficient Both history score number and history score for the TFC bin are tallied in the x grid With this x grid in place the average empirical f x between x and x is defined to be number of history scores in i score bin N x x where x 1 2589 The quantity 1 2589 is 107 and comes from 10 equally spaced log bins per decade The calculated f x s are available on printed plots or by using the 2
115. data for transport through the resonance region 8 general use the best data available It is understood that the latest evaluations tend to be more complex and therefore require more memory and longer execution times If you are limited by available memory try to use smaller data tables such as thinned or 10 3 05 2 19 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CROSS SECTIONS discrete reaction for the minor isotopes in the calculation Discrete reaction data tables might be used for a parameter study followed by a calculation with the full continuous energy data tables for confirmation In conclusion the additional time necessary to choose appropriate neutron interaction data tables rather than simply to accept the defaults often will be rewarded by increased understanding of your calculation B Photon Interaction Data Photon interaction cross sections are required for all photon problems Photon interactions can now account for both photoatomic and photonuclear events Because these events are different in nature i e elemental versus isotopic the data are stored on separate tables Photoatomic data are stored on ACE tables that use ZAIDs with the form ZZZ000 nnP There are currently four photoatomic interaction data libraries nn equal 01 02 03 and 04 The 01 ACE tables were introduced in 1982 and combine data from several sources The incoherent coherent photoelectric and pair production cross secti
116. density in g cm then DRANGE mp is the length of a substep in cm This quantity can be compared with the smallest dimension of a material region A reasonable rule of thumb is that an electron should make at least ten substeps in any material of importance to the transport problem 2 Condensed Random Walk In the initiation phase of a transport calculation involving electrons all relevant data are either precalculated or read from the electron data file and processed These data include the electron energy grid stopping powers electron ranges energy step ranges substep lengths and probability distributions for angular deflections and the production of secondary particles Although the energy grid and electron steps are selected according to Eqs 2 3 2 4 energy straggling the analog production of bremsstrahlung and the intervention of geometric boundaries and the problem time cutoff will cause the electron s energy to depart from a simple sequence s satisfying Eq 2 4 Therefore the necessary parameters for sampling the random walk will be interpolated from the points on the energy grid At the beginning of each major step the collisional energy loss rate is sampled unless the logic described on page 2 74 is being used In the absence of energy straggling this will be a simple average value based on the nonradiative stopping power described in the next section In general however fluctuations in the energy loss rate will occur The nu
117. dependence 2 142 SPDTL 3 116 Special Treatments 2 106 Special Treatments for Tallies FTn card 3 112 SPH 3 19 3 22 Splitting 2 142 Splitting also see Energy Splitting 3 33 SPn card 3 61 SSR card 3 71 SSW card 3 69 Steradian 3 101 Stochastic Geometry 3 32 Storage Limitations 3 160 Subroutine Usage D 6 Subroutines SOURCE 3 78 SRCDX 3 78 Summary of MCNP Input Cards 3 157 Superimposed Importance Mesh for Mesh Based Weight Window Generator MESH card 3 48 Superimposed Mesh Tally FMESH 3 114 Surface Bins 3 81 Coordinate pairs 3 15 Current F1 Tally 3 80 Flux F2 Tally 3 80 Mnemonics 3 11 3 13 3 23 Normal 3 94 Reflecting 3 11 Source 3 26 3 31 3 50 3 52 3 57 3 69 3 71 White boundaries 2 13 3 11 3 12 Surface Area card 3 25 Surface Cards 3 11 to 3 23 Axisymmetric Surfaces Defined by Points 3 15 General Plane Defined by Three Points 3 17 Surfaces Defined by Equations 3 11 Surfaces Defined by Macrobodies 3 18 Surface Flux F2 2 86 Surface Source Read SSR card 3 71 Index 9 MCNP MANUAL INDEX Surface Source Write SSW card 3 69 Surface Source Write SSW card 3 69 Surface Flagging SFn Card 3 102 Surfaces 2 9 Periodic boundaries 2 13 3 31 SWTM 3 136 S a p scattering 2 28 2 29 T Tally and DXTRAN 3 110 Asterisk 3 80 Bins 3 80 Cell 3 80 Cell flux F4 3 80 Charge deposition F8E Tally 3 80 Comment FCn card 3 91 Detector 2 5 D 6 Detector
118. diagnostics DDn card 3 108 Detector flux F5 2 80 3 80 3 82 Dose 3 99 Fl surface current 3 80 F2 surface flux 3 80 F4 cell flux 3 80 F6 cell avg energy deposition 3 80 F7 cell fission energy deposition 3 80 F8 detector pulse energy distribution 3 80 Fluctuation TFn card 3 107 FMESH 3 114 Fna cards 3 80 FTn special treatments card 3 112 Lattice 3 85 Mesh Tally 2 83 3 114 Multiplier FMn card 3 95 Pulse height 3 85 Radiography 3 82 Repeated Structures 3 85 3 88 Segment FSn card 3 102 Special treatments FTn card 3 112 Specification cards 3 79 to 3 114 Surface current F1 3 80 Surface Flux F2 3 80 Time Tn card 3 92 Types 3 80 Union 3 81 Units 3 80 Index 10 User modification 2 108 Weight 3 80 Tally output format 2 108 TALLYX Subroutine 3 105 3 106 FUn Input card 3 105 TALNP card 3 147 Temperature 3 10 3 121 3 127 TFn card 3 107 Thermal Scattering treatment 2 54 Temperature 3 132 Times THTME card 3 133 Treatment 3 127 Thomson scattering 2 58 Detailed physics treatment 2 61 THTME card 3 133 Time Cutoff 2 69 2 140 3 135 Multiplier TMn card 3 100 Time convolution 2 106 Time Splitting TSPLT card 3 37 Title card 3 2 TMn card 3 100 card 2 30 3 132 Tn card 3 92 Torus 2 9 3 13 3 14 Total Fission TOTNU card 3 122 TOTNU card 2 50 TOTNU Total v card 3 122 Track Length Cell Energy Deposition Tallies 2 87 Track L
119. due to higher modes die off as DR and the source distribution and approach their stationary equilibrium values For typical light water reactor systems the DR is often in the range 0 8 0 99 and 50 100 inactive cycles may be required for errors in the initial guess to die away sufficiently that the source and kep converge For some critical systems e g heavy water reactors fuel storage vaults however the DR may be very close to 1 e g 99 or higher and hundreds or thousands of inactive cycles may be required to attain source convergence It should also be noted that the source distribution and the eigenvalue not converge in the same manner The expression for 0 1 has the additional factor 1 1 on the higher mode error For problems where the DR is very close to 1 the source distribution may take hundreds or thousands of cycles to converge due to errors dying out as DR while kep may converge rapidly since its higher mode error is damped by the additional factor 1 DR which may be very small That is kep will converge more rapidly than the source distribution Thus it is very important to examine the behavior of both k and the source distribution when assessing problem convergence Both and the fission source distribution must converge before starting active cycles for tallies It is up to the user to specify the number of inactive cycles to run in order to attain convergence Most users will
120. for a well converged problem The last half of the problem is determined from the TFC The more information available about the last half of the problem the better the N dependent checks will be Therefore a problem that has run 40 000 histories will have 20 TFC N entries which is more N entries than a 50 000 history problem with 13 entries It is possible that a problem that passes all tests at 40 000 may not pass all the tests at 40 001 As is always the case the user is responsible for deciding when a confidence interval is valid These statistical diagnostics are designed to aid in making this decision J A Statistically Pathological Output Example A statistically pathological test problem is discussed in this section The problem calculates the surface neutron leakage flux above 12 MeV from an isotropic 14 MeV neutron point source of unit strength at the center of a 30 cm thick concrete shell with an outer radius of 390 cm Point and ring detectors were deliberately used to estimate the surface neutron leakage flux with highly inefficient long tailed f x s The input is shown on page 5 49 The variance reduction methods used were implicit capture with weight cutoff low score point detector Russian roulette and a 0 5 mean free path 4 cm neighborhood around the detectors to produce large but finite higher moments Other tallies or variance reduction methods could be used to make this calculation much more efficient but that is not t
121. for the data set x h Ky h e beB heH where K h is some constant B represents a set of macroscopic cross sections and H represents set of energies or an energy interval For a track based response estimator cz where 1 is the response estimator is the probability of path segment j path segment j is comprised of segment 1 plus the current track This gives 44 4 Ch RE gt ur beB heH or 1 Un Ynt gt j where a i v With some manipulations presented in Refs 163 and 164 the path segment estimator can be converted to a particle history estimator of the form YX beB heH h EN Pars gt i where 15 the probability of the i history and 15 the n order coefficient estimator for history i given by uM 10 3 05 2 193 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PERTURBATIONS Note that this sum involves only those path segments j in particle history i The Monte Carlo expected value of becomes u EE Vni 1 py for a sample of N particle histories The probability of path segment j is the product of the track probabilities m dj 0 where r is probability of track k and segment j contains 1 tracks If the k track starts with a neutron undergoing reaction type at energy E and is scattered from angle 0 to angle 0 and E continues for a length and collides the
122. from the XSDIR will be used If a particular evaluation set 15 desired the PLIB option on the Mn card may be used to select all photoatomic tables from a given library It is recommended in all cases that the photoatomic tables for any given problem all be from the same library these data sets are created in masse and thus are self consistent across a library The most complicated case for material definition is the selection of tables for coupled neutron photon problems where photonuclear events are not ignored In such a case the composition must be chosen based on the availability of most appropriate isotopic neutron and photonuclear tables as needed for the specific problem at hand The MPNn card may be used to accommodate mismatches in the availability of specific isotopes see page 3 120 As always a fully specified ZAID e g 13027 24u will ensure that a specific table is selected The PNLIB option on the material card may be used to select all photonuclear tables from a specific evaluation set nn Otherwise the isotope ZZZAAA will select the first match in the XSDIR file Note that if no photonuclear table is available for the isotope ZZZAAA the problem will report the error and will not run See the discussion in the description of the MPNn card for more information on page 3 120 2 22 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CROSS SECTIONS C Electron Interaction Data Electron interaction data tables are
123. i emitted by a multiplying sample can be expressed as a function of the factorial moments for spontaneous and induced fission Therefore for many applications it is not necessary to know the details of the neutron multiplicity distribution but it is more important to know the corresponding first three factorial moments A reevaluation of the existing spontaneous fission and neutron induced fission data has been performed where the widths of Gaussians are adjusted to fit the measured second and third factorial moments This reevaluation was done by minimizing the chi squared 3 vP x c E pee eos 2 4 i 2 L 1 4 These results are summarized in Table 2 1 Despite the change in emphasis from the detailed shape to the moments of the distributions the inferred widths are little changed from those obtained by others However by minimizing the chi squared in Eq 2 4 the inferred widths are guaranteed to be in reasonable agreement with the measured second and third factorial moments The widths obtained using Eq 2 4 give Gaussian distributions that reproduce the experimental second and third factorial moments to better than 0 6 The adjustment parameter b ensures that the first moment is accurately reproduced If the chi squared in Eq 2 3 is used then the second and third factorial moments can differ from the experimental values by as much as 10 Table 2 1 Recommended Gaussian Widths from E
124. if Otherwise E E Lik and m j if If 3 lt H Bici isis then 5 Eiti jtk and 1 if J i 1 Otherwise and if b i 1 A random number on the unit interval is used to sample a secondary energy bin from the cumulative density function Cr mk 54 Opa k l For histogram interpolation the sampled energy is 10 3 05 2 49 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS S4 _ E mkt For linear linear interpolation sampled energy is 2 Pim k 1 Pi m k Pi net 2 E F E S Sac m k Prax Lm k 1 Lm k roll Eb mkt Pim k 1 Pi m k Et m ke E1 m kl The final outgoing energy uses scaled interpolation Let E r E qu Eig and Ex E k r E Erp Eg E K 1 e Emission from Fission For any fission reaction a number of neutrons is emitted according to the value of v E Depending on the type of problem fixed source or KCODE and on user input TOTNU card MCNP may use either prompt v Ein or total v E For either case the average number of neutrons per fission v E n may be a tabulated function of energy or a polynomial function of energy Then E E out If the fifth entry on the PHYS N card is zero default then n is sampled between 7 the largest integer less than v and Z 1 by 1 1 if amp lt
125. in establishing more reliable confidence intervals The VOV is the estimated relative variance of the estimated R The VOV involves the estimated third and fourth moments of the empirical history score PDF f x and is much more sensitive to large history score fluctuations than is R The magnitude and NPS behavior of the VOV are indicators of tally fluctuation chart TFC bin convergence Early work was done by Estes and Cashwell and Pederson later reinvestigated this statistic to determine its usefulness The VOV is a quantity that is analogous to the square of the R of the mean except it is for R instead of the mean The estimated relative VOV of the mean is defined as VOV S S S 2 120 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS ESTIMATION OF THE MONTE CARLO PRECISION P PME NE t where S is the estimated variance of x S 5 is the estimated variance in 5 The VOV is a measure of the relative statistical uncertainty in the estimated R and is important because S must be a good approximation of o to use the Central Limit Theorem to form confidence intervals The VOV for a tally bin is 2 VOV X x X X x X 1 N 2 26 This is the fourth central moment minus the second central moment squared normed by the product of N and the second central moment squared When Eq 2 23 is expanded in terms of sums of powers of x it becomes 42x Ex N 62x Ex N 3 Xx
126. includes the atomic weight ratio of the target nucleus the Q values of each reaction and nubar v data the average number of neutrons per fission for fissionable isotopes In many cases both prompt and total are given Prompt is the default for all but KCODE criticality problems and total is the default for KCODE criticality problems The TOTNU input card can be used to change the default Approximations must be made when processing an evaluated data set into ACE format As mentioned above cross sections are reproduced to within a certain tolerance generally less than 1 Until recently evaluated angular distributions for non isotropic secondary particles could only be approximated on ACE tables by 32 equally probable cosine bins This approximation is extremely fast to use but may not adequately represent a distribution originally given as a 20th order Legendre polynomial Starting with MCNP version 4C tabular angular distributions may be used to represent the scattering angle with a tolerance generally between 0 1 to 1 or better On the whole the approximations within more recent ACE tables are small and MCNP interaction data tables for neutron and photonuclear collisions are extremely faithful representations of the original evaluated data Discrete reaction tables are identical to continuous energy tables except that in the discrete reaction tables all cross sections have been averaged into 262 groups The averaging is don
127. increasing the FOM is equivalent to increasing t S decreasing S with variance reduction techniques often decreases It is usually worthwhile to optimize the tally efficiency by intelligently running various variance reduction methods and using the largest FOM consistent with good phase space sampling good sampling can often be inferred by examining the cell particle activity in Print Table 126 MCNP prints both the empirical f x and signal to noise ratio for the tally fluctuation chart bin of each tally in Print Table 161 In summary the FOM has three uses One important use is as a tally reliability indicator If the FOM is not approximately a constant except for statistical fluctuations early in the problem the confidence intervals may not overlap the expected score value E x the expected fraction of the time see page 2 109 A second use for the FOM is to optimize the efficiency of the Monte Carlo calculation by making several short test runs with different variance reduction parameters and then selecting the problem with the largest FOM Remember that the statistical behavior of FOM that is R for a small number of histories may cloud the selection of techniques competing at the same level of efficiency A third use for the FOM is to estimate the computer time required to reach a desired value of R by using T lI R FOM F Separation of Relative Error into Two Components Three factors that affect the efficiency of a Monte C
128. is based on the selection of random numbers analogous to throwing dice in a gambling casino hence the name Monte Carlo In particle transport the Monte Carlo technique is pre eminently realistic a numerical experiment It consists of actually following each of many particles from a source throughout its life to its death in some terminal category absorption escape etc Probability distributions are randomly sampled using transport data to determine the outcome at each step of its life Event Log Neutron scatter photon production 2 Fission photon production Incident 3 Neutron capture Neutron 4 Neutron leakage 5 Photon scatter SS 6 Photon leakage EY 7 Photon capture Void Fissionable Material Figure 1 1 Figure 1 1 represents the random history of a neutron incident on a slab of material that can undergo fission Numbers between 0 and 1 are selected randomly to determine what if any and where interaction takes place based on the rules physics and probabilities transport data governing the processes and materials involved In this particular example a neutron collision occurs at event 1 The neutron is scattered in the direction shown which is selected randomly from the physical scattering distribution A photon is also produced and is temporarily stored or banked for later analysis At event 2 fission occurs resulting in the termination of the incoming neutron and the birth of two outgoin
129. is omitted if the neutron energy is greater than 500 K7 A At that energy the adjustment of the elastic cross section would be less than 0 1 b Sampling the Velocity of the Target Nucleus The second aspect of the free gas thermal treatment takes into account the velocity of the target nucleus when the kinematics of a collision are being calculated The target velocity is sampled and subtracted from the velocity of the neutron to get the relative velocity The collision is sampled in the target at rest frame and the outgoing velocities are transformed to the laboratory frame by adding the target velocity There are different schools of thought as to whether the relative energy between the neutron and target E or the laboratory frame incident neutron energy target at rest should be used for all the kinematics of the collision E is used in MCNP to obtain the distance to collision select the collision nuclide determine energy cutoffs generate photons generate fission sites for the next generation of a KCODE criticality problem for S a scattering and for capture is used for everything else in the collision process namely elastic and inelastic scattering including fission and n xn reactions It is shown in Eqn 2 1 that is based upon v that is based upon the elastic scattering cross section and therefore is truly valid only for elastic scatter However the only significant thermal reactions for stable isot
130. k KK K Protactinium EEEE E E E K oe oe K K k K K k K K K kK k k Kk k KK KKK KK K K 231 91231 60 229 0500 endf60 0 1977 293 6 19835 2610 91231 61c 229 0500 endf6dn 0 1977 293 6 24733 2610 91231 65 229 0500 endf66e 0 1977 3000 1 31463 2422 91231 66 229 0500 endf66c 0 1977 293 6 45111 4128 233 91233 42c 231 0383 endl92 LLNL 1992 300 0 27720 1982 91233 50d 231 0380 dre5 B V 0 1974 293 6 3700 263 91233 50c 231 0380 endfSu B V 0 1974 293 6 19519 2915 91233 51d 231 0380 drmccs B V 0 1974 293 6 3700 263 91233 51 231 0380 rmccs B V 0 1974 293 6 5641 637 91233 65c 231 0380 endf66e 0 1974 3000 1 34848 3993 91233 66 231 0380 endf66c B VLO 1974 293 6 50577 6240 G 32 10 3 05 150 0 20 0 150 0 150 0 20 0 150 0 150 0 20 0 150 0 150 0 30 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 30 0 30 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 30 0 20 0 20 0 20 0 20 0 30 0 20 0 20 0 20 0 20 0 20 0 20 0 yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes no no yes yes no yes yes yes yes yes yes yes yes yes no no no no yes no no no no no no 0 CP DN UR no no no no no no no no no no no no no no no no no tot tot both both both both both both both both both both both both both both both both both tot tot tot
131. later in time For example if a detector responds primarily to late time particles then it may be useful to split the particles as time increases Russian roulette In some cases there may be too many late time particles for optimal calculational efficiency and the late time particles can be rouletted 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VARIANCE REDUCTION 5 Weight Cutoff In weight cutoff Russian roulette is played if a particle s weight drops below a user specified weight cutoff The particle is either killed or its weight is increased to a user specified level The weight cutoff was originally envisioned for use with geometry splitting Russian roulette and implicit capture see page 2 150 Because of this intent 1 weight cutoffs in cell depend not only on WC and WC2 on the CUT card but also on the cell importances 2 Implicit capture is always turned on except in detailed photon physics whenever a nonzero is specified Referring to item 1 above the weight cutoff is applied when the particle s weight falls below WC2 where R is the ratio of the source cell importance IMP card to cell 5 importance With probability W WCI the particle survives with new weight otherwise the particle is killed When WC and WC2 on the CUT card are negative the weight cutoff is scaled to the minimum source weight of a particle so that source particles are not immediate
132. lends itself to uncomplicated biasing schemes It is obviously not microscopically correct It is not possible to perform microscopically correct sampling given the current set of data tables Because of the low probability of a photon undergoing a photonuclear interaction the use of biased photonuclear collisions may be necessary However caution should be exercised when using this option as it can lead to large variations in particle weights It is important to check the summary tables to determine if appropriate weight cutoff or weight windows have been set That is check to see if weight cutoffs or weight windows are causing more particle creation and destruction than expected It is almost always necessary to adjust the default neutron weight cutoff when using only weight cutoffs with photonuclear biasing as it will roulette a large fraction of the attempts to create secondary photoneutrons More information about the photonuclear physics included in MCNP be found in White 70 E Electron Interactions The transport of electrons and other charged particles is fundamentally different from that of neutrons and photons The interaction of neutral particles is characterized by relatively infrequent isolated collisions with simple free flight between collisions By contrast the transport of electrons is dominated by the long range Coulomb force resulting in large numbers of small interactions As an example a neutron in aluminum sl
133. major version of the library is indicated by a Roman numeral e g ENDF B V or ENDF B VI Changes in the major version are generally tied to changes in the standard cross sections Many cross section measurements are made relative to the standard cross sections e g elastic scattering off hydrogen or the U235 n f cross section When one of the standard cross sections is changed the evaluated data that were based on that standard must be updated Within a major release revisions are generally indicated as ENDF B VI 2 or ENDF B VI 6 where the 2 and 6 indicate release 2 and release 6 respectively A release indicates that some evaluations have been revised added or deleted Users should note that neither a major release nor an interim release guarantee that a particular evaluation has been updated In fact only a few evaluations change in each release and 2 16 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CROSS SECTIONS often the change is limited to a certain energy region This numbering scheme simply indicates that something within the data library has changed It is up to the user to read the accompanying documentation to determine exactly what if anything changed Each ACE table provided with the MCNP package is listed in Appendix where its lineage e g ENDF B V 0 or ENDF B VI 2 is given The ENDF B evaluations are available through the National Nuclear Data Center at Brookhaven National Laboratory http
134. model neutron photon interactions The code has been known as MCNP ever since Though at first MCNP stood for Monte Carlo Neutron Photon now it stands for Monte Carlo N Particle Other major advances in the 70s included the present generalized tally structure automatic calculation of volumes and a Monte Carlo eigenvalue algorithm to determine k for nuclear criticality KCODE In 1983 MCNP3 was released entirely rewritten in ANSI standard Fortran 77 MCNP3 was the first MCNP version internationally distributed through the Radiation Shielding and Information Center at Oak Ridge Tennessee Other 1980s versions of MCNP were MCNP3A 1986 and MCNP3B 1988 that included tally plotting graphics MCPLOT the present generalized source surface sources repeated structures lattice geometries and multigroup adjoint transport MCNPA was released in 1990 and was the first UNIX version of the code It accommodated N particle transport and multitasking on parallel computer architectures MCNP4 added electron transport patterned after the Integrated TIGER Series ITS electron physics the pulse height tally F8 a thick target bremsstrahlung approximation for photon transport enabled detectors and DXTRAN with the S a B thermal treatment provided greater random number control and allowed plotting of tally results while the code was running MCNPAA released in 1993 featured enhanced statistical analysis distributed processor multitasking for r
135. multiplication is the product of the fraction of the weight scattering into the cone E Q2 dQ and the weight correction for sampling P Q instead of 0 Thus the weight correction on scattering is P Q Par O If u is the cosine of the angle between the scattering direction and the particle s incoming direction then P Q P u 27 because the scattering is symmetric in the azimuthal angle If is the cosine of the angle with respect to the cone axis see Figure 2 25 and if the azimuthal angle about the cone axis is uniformly sampled then P 2 n Y 2n Thus EE weight multiplier for DXTRAN particle arb This result can be obtained more directly but the other derivation does not explain why is not sampled Because P n is arbitrary MCNP can choose a scheme that samples n from a two step density that favors particles within the larger interval In fact the inner DXTRAN sphere has to do only with this arbitrary density and is not essential to the DXTRAN concept The DXTRAN particles are always created on the outside DXTRAN sphere with the inner DXTRAN sphere defining only the boundary between the two steps in the density function After cos has been chosen the azimuthal angle is sampled uniformly on 0 27 this completes the scattering Recall however that the DXTRAN particle arrives at the DXTRAN sphere without collision Thus the DXTRAN particle also has its weight m
136. no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no G 25 APPENDIX G MCNP DATA LIBRARIES NEUTRON CROSS SECTION LIBRARIES Table G 2 Cont Continuous Energy and Discrete Neutron Data Libraries Maintained by X 5 Library Eval Temp Length Emax ZAID AWR Name Source Date K words NE MeV GPD 0 CP DN UR Ba 138 56138 50c 136 7150 rmccs B V 0 1978 293 6 6018 292 20 0 yes no no no no 56138 50d 136 7150 drmccs 0 1978 293 6 6320 263 20 0 yes no no no no 56138 60c 136 7150 endf60 0 1978 293 6 7347 267 20 0 yes no no no 56138 66c 136 7150 endf66b 3 1994 293 6 79268 8920 20 0 yes no no no no 7 59 Praseodymium k kakkaa kkk pr 4 59141 50c 139 6970 kidman B V 0 1980 293 6 15620 1354 20 0 no no no no no Nd 143 60143 50c 141 6820 kidman B V 0 1980 293 6 17216 1701 20 0 no no no no no Nd 145 60145 50c 143 6680 kidman B V 0 1980 293 6 38473 3985 20 0 no no no no no Nd 147 60147 50c 145 6540 kidman B V 0 1979 293 6 1816 251 20 0 no no no no no Nd 148 60148 50c
137. no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no 0 CP DN UR yes yes no no no no no yes yes yes yes yes yes yes yes no no no no no yes yes yes yes yes yes yes yes no no no no no yes yes yes yes yes yes no no no no no yes yes no no no no no yes yes APPENDIX G MCNP DATA LIBRARIES NEUTRON CROSS SECTION LIBRARIES Table G 2 Cont Continuous Energy and Discrete Neutron Data Libraries Maintained by X 5 Library Eval Temp Length Emax ZAID AWR Name Source Date K words NE MeV GPD 7 77 Indium o ao rnat 77000 55 190 5630 misc5xs 7 LANL T 1986 300 0 43071 3704 20 0 no r 9 77191 49c 189 3200 uresa B VI A 1995 300 0 83955 8976 20 0 yes 77191 65c 189 3200 endf66e 1995 3000 1 64690 6116 200 yes 77191 66c 189 3200 endf66c B VL4 X 1995 293 6 90082 9290 20 0 yes 193 77193 49 191 3050 uresa B VI A 1995 300 0 82966 8943 20 0 yes 77193 65c 191 3050 endf66e B VL4 X 1995 3000 1 69056 6751 20 0 yes 77193 66c 191 3050 endf66c 1995 293 6 88688 9205 20 0 yes Pt nat 78000 35c 193 4141 rmccsa LLNL 1985 0 0 15371 1497 20 0 yes 78000 35d 193 4141 drmccs LLNL lt 1985 0 0 6933 263 20 0 yes 78000 40c 193 4141 endl92 LLNL lt 1992 300 0 43559 5400 30 0 yes 78000 42c 193 4141 endl92 LLNL X lt 19
138. nuclei in a homogeneous system results in Doppler broadening of resonances and an increase in resonance absorption Furthermore a constant cross section at zero K goes to 1 v behavior as the temperature increases You should not only use the best evaluations but also use evaluations that are at temperatures approximating the temperatures in your application The total length of a particular cross section file in words It is understood that the actual storage requirement in an MCNP problem will often be less because certain data that are not needed for a problem may be expunged The number of energy points NE on the grid used for the neutron cross section for that data file In general a finer energy grid or greater 10 3 05 max GPD DN UR APPENDIX G MCNP DATA LIBRARIES NEUTRON CROSS SECTION LIBRARIES number of points indicates a more accurate representation of the cross sections particularly through the resonance region The maximum incident neutron energy for that data file For all incident neutron energies greater than MCNP assumes the last cross section value given yes means that photon production data are included means that such data are not included for fissionable material indicates the type of fission nu data available indicates that only prompt nu data are given tot indicates that only total nu data are given both indicates that pro
139. obtain event logs for those particles causing the estimate to be erratic The event logs should be studied to learn what is special about these particles When the special nature of these particles is understood the user can adjust the variance reduction techniques to sample these particles more often Thus their weight will be smaller and they will not be as likely to cause erratic estimates Under absolutely no circumstances should these particles be discarded or ignored The fact that these particles contribute very heavily to the tally indicates that they are important to the calculation and the user should try to sample more of them 6 Biasing Against Random Walks of Presumed Low Importance It was mentioned earlier that one should be cautious and conservative when applying variance reduction techniques Many more people get into trouble by overbiasing than by underbiasing Note that preferentially sampling some random walks means that some walks will be sampled for a given computer time less frequently than they would have been in an analog calculation Sometimes these random walks are so heavily biased against that very few or even none are ever sampled in an actual calculation because not enough particles are run Suppose that on average for every million histories only one track enters cell 23 Further suppose that a typical run is 100 000 histories On any given run it is unlikely that a track enters cell 23 Now suppose that track
140. on many platforms MCNP takes advantage of parallel computer architectures using three parallel models MCNP supports threading using the OpenMP model Distributed processing is supported through the use of both the Message Passing Interface MPI model and the Parallel Virtual Machine PVM software from Oak Ridge MCNP also combines threading with both MPI and PVM A History The Monte Carlo method is generally attributed to scientists working the development of nuclear weapons in Los Alamos during the 1940s However its roots go back much farther Perhaps the earliest documented use of random sampling to solve a mathematical problem was that of Compte de Buffon in 1772 A century later people performed experiments in which they threw a needle in a haphazard manner onto a board ruled with parallel straight lines and inferred the value of from observations of the number of intersections between needle and lines Laplace suggested in 1786 that could be evaluated by random sampling Lord Kelvin appears to have used random sampling to aid in evaluating some time integrals of the kinetic energy that appear in the kinetic theory of gasses and acknowledged his secretary for performing calculations for more than 5000 collisions 10 3 05 2 1 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS INTRODUCTION According to Emilio Segr Enrico Fermi s student and collaborator Fermi invented a form of the Monte Carlo method when he
141. or laboratory system as specified by the ENDF 6 scattering law from which they are derived Angular distributions are given on a reaction dependent grid of incident energies 10 3 05 2 17 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CROSS SECTIONS The sampled angle of scattering uniquely determines the secondary energy for elastic scattering and discrete level inelastic scattering For other inelastic reactions energy distributions of the scattered particles are provided in each table As with angular distributions the energy distributions are given on a reaction dependent grid of incident energies The energy and angle of particles scattered by inelastic collisions is sampled in a stochastic manner such that the overall emission distribution and energy are preserved for many collisions but not necessarily for any single collision When neutron evaluations contain data about secondary photon production that information appears in the MCNP neutron interaction tables Many processed data sets contain photon production cross sections photon angular distributions and photon energy distributions for each neutron reaction that produces secondary photons However the user should be aware that not all evaluations include this information and the information is sometimes approximate e g individual gamma lines may be lumped into average photon emission bins Other miscellaneous information on the neutron and photonuclear interaction tables
142. required both for problems in which electrons are actually transported and for photon problems in which the thick target bremsstrahlung model is used Electron data tables are identified by ZAIDs of the form ZZZ000 nnE and are selected by default when the problem mode requires them There are two electron interaction data libraries el ZAID endings of 01e and el03 ZAID endings of 03e The electron libraries contain data on an element by element basis for atomic numbers from Z equal 1 to 94 The library data contain energies for tabulation radiative stopping power parameters bremsstrahlung production cross sections bremsstrahlung energy distributions K edge energies Auger electron production energies parameters for the evaluation of the Goudsmit Saunderson theory for angular deflections based on the Riley cross section calculation and Mott correction factors to the Rutherford cross sections also used in the Goudsmit Saunderson theory The el03 library also includes the atomic data of Carlson used in the density effect calculation Internal to the code at run time data are calculated for electron stopping powers and ranges K x ray production probabilities knock on probabilities bremsstrahlung angular distributions and the Landau Blunck Leisegang theory of energy loss fluctuations The el03 library is derived from the ITS3 0 code system Discussions of the theoretical basis for these data and references to the relevant literature are pres
143. sampling is biased to be uniform in the pinhole area Ap that is Ap To account for this biased sampling the weight W of the sample must be multiplied by Thus unbiased estimate of the sampled weight going through dA at the pinhole is Wp 23 Ww or N 0 E W dA 5 fon dA Now that an unbiased estimate of the weight through dA is obtained an unbiased estimate of the weight arriving on the image plane can also be obtained If is the optical path along from the sampled pinhole point to the image plane then the weight Q arriving at the pixel in the image plane is Woixei 9 W Q e Apo Q u e MQ The surface flux at the image plane is estimated by the divided by u note that the pinhole plane and image plane are parallel divided by pixel area Therefore the surface flux pixe at the intersected pixel is 9 A pixel 2 0 Thus the flux at the pixel is just the e attenuated flux at the pinhole scaled by the ratio of pixe pixei 9 is scored If a perfect pinhole with no pinhole area is used then Ap is defined to be unity A p where the weight W passes through to the the pixel where the flux 4 General Considerations of Point Detector Estimators a Pseudoparticles and detector reliability Point and ring detectors are Monte Carlo methods wherein t
144. satisfactory accuracy since the Goudsmit Saunderson theory is valid for arbitrary angular deflections However the representation of the electron s trajectory as the result of many small steps will be more accurate if the angular deflections are also required to be small Therefore the ETRAN codes and MCNP further break the electron steps into smaller substeps major step of path length s is divided into m substeps each of path length s m Angular deflections and the production of secondary particles are sampled at the level of these substeps The integer depends 2 68 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS only on material average atomic number Z Appropriate values for m have been determined empirically and range from m 2 for Z lt 6 to m 15 for Z gt 91 In some circumstances it may be desirable to increase the value of m for a given material In particular a very small material region may not accommodate enough substeps for an accurate simulation of the electron s trajectory In such cases the user can increase the value of m with the ESTEP option on the material card The user can gain some insight into the selection of m by consulting Print Table 85 in the MCNP output Among other information this table presents a quantity called DRANGE as a function of energy DRANGE is the size of an energy step in g cm Therefore DRANGE m is the size of a substep in the same units and if p is the material
145. section for a GDR reaction becomes negligible A more complete description of this process can be found in the text by Bohr and Mottelson The quasi deuteron QD absorption mechanism can be conceptualized as the electromagnetic wave interacting with the dipole moment of a correlated neutron proton pair In this case the neutron proton pair can be thought of as a QD having a dipole moment with which the photon can interact This mechanism is not as intense as the GDR but it provides a significant background cross section for all incident photon energies above the relevant particle separation threshold The seminal work describing this process was published Levinger 9 9 Recent efforts to model this process include the work of Chadwick et 1 5 Once the photon has been absorbed by the nucleus one or more secondary particle emissions occur For the energy range in question that is below 150 MeV these reactions may produce a combination of gamma rays neutrons protons deuterons tritons helium 3 particles alphas and fission fragments The threshold for the production of a given secondary particle is governed by the separation energy of that particle typically a few MeV to as much as a few 10s of MeV Most of the these particles are emitted via pre equilibrium and equilibrium mechanisms though it is possible but rare to have a direct emission Pre equilibrium emission can be conceptualized as a particle within the nucleus that r
146. sections 1 eV Inelastic cross sections are never broadened by NJOY a Adjusting the Elastic Cross Section The first aspect of the free gas thermal treatment is to adjust the zero temperature elastic cross section by raising it by the factor 1 0 5 2 exp a a n where a JAE KT atomic weight neutron energy and temperature For speed F is approximated by F 1 0 5 a when a gt 2 and by linear interpolation in a table of 51 values of aF when a 2 Both approximations have relative errors less than 0 0001 The total cross section also is increased by the amount of the increase in the elastic cross section The adjustment to the elastic and total cross sections is done partly in the setup of a problem and partly during the actual transport calculation No adjustment is made if the elastic cross section in the data library was already processed to the temperature that is needed in the problem If all of the cells that contain a particular nuclide have the same temperature which is constant in time that is different from the temperature of the library the elastic and total cross sections for that nuclide are adjusted to that temperature during the setup so that the transport will run a little faster Otherwise these cross sections are reduced if necessary to zero temperature during the setup and the thermal adjustment is made when the cross sections are used For speed the thermal adjustment
147. sections not requested on an FM card FM numbers should be used when available rather than MT numbers If an MT number is requested the equivalent FM number will be displayed on the legend of cross section plots 10 3 05 G 1 APPENDIX G MCNP DATA LIBRARIES ENDF B REACTION TYPES Neutron Continuous energy and Discrete Reactions MT 1 2 16 17 18 19 20 21 22 28 32 33 38 51 52 90 91 101 102 103 104 105 106 107 1 3 Microscopic Cross Section Description Total see Note 1 Elastic see Note 1 n 2n n 3n Total fission n fx if and only if MT 18 is used to specify fission in the original evaluation Total fission cross section equal to MT 18 if MT 18 exists otherwise equal to the sum of MTs 19 20 21 and 38 n f n n f n 2nf n n a n n p n n d n n t n 3nf n n to 1 excited state n n to 2 excited state n n to 40 excited state to continuum Absorption sum of MT 102 117 neutron disappearance does not include fission n y n p n d n t n He n a In addition the following special reactions are available for many nuclides 202 203 204 205 206 207 301 5 n 8 total photon production total proton production see Note 2 total deuterium production see Note 2 total tritium production see Note 2 total He production see Note 2 total alpha production see Note 2 average heatin
148. show unphysical artifacts in the ITS algorithm as well as in the MCNP logic 10 3 05 2 75 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS The nearest group boundary treatment is selected by setting the 18th entry of the DBCN card to For example the card DBCN 177 1 selects this straggling logic without affecting any of the other DBCN options c New Energy and Step Specific Method It is easy to express what we would like to see in the straggling logic For an electron with energy E about to traverse a step of length s we would like to sample the straggling from the operator L E s without regard to the prearranged energy boundaries In the MCNP5 RSICC release 1 40 we have now brought this situation about A new Fortran 90 module has been installed to deal with straggling data Those parameters that are separate from the individual straggling events are still precomputed but each electron transport step can now sample its energy loss separately from adjacent steps and specifically for its current energy and planned step length Using this approach we largely eliminate the linear interpolations and energy misalignments of the earlier algorithms and obviate the need for a choice of energy group At the time of the 5 1 40 release the new straggling logic is included in the code but is still being tested Preliminary results indicate that a more accurate and stable estimate of the straggling is obtained
149. the largest history scores decrease faster than 1 x The 201 largest history scores for each TFC bin are continuously updated and saved during the calculation A generalized Pareto function Pareto f x a 1 79 1 is used to fit the largest x s This function fits a number of extreme value distributions including 1 exponential 0 and constant 1 The large history score tail fitting technique uses the robust simplex algorithm which finds the values of a and k that best fit the largest history scores by maximum likelihood estimation The number of history score tail points used for the Pareto fit is a maximum of 201 points because this provides about 10 precision in the slope estimator at n 3 The precision increases for smaller values of n and vice versa The number of points actually used in the fit is the lesser of 5 of the nonzero history scores or 201 The minimum number of points used for a Pareto fit is 25 with at least two different values which requires 500 nonzero history scores with the 5 criterion If less than 500 history scores are made in the TFC bin no Pareto fit is made From the Pareto fit the slope of f jq g 1s defined to be SLOPE 1 k 1 2 126 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS ESTIMATION OF THE MONTE CARLO PRECISION A SLOPE value of zero is defined to indicate that not enough f x tail information exists for a SLOPE estimate
150. the VOV as a function of N for the TFC bin is printed in the OUTP file Because the VOV involves third and fourth moments the VOV is a much more sensitive indicator to large 10 3 05 2 121 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS ESTIMATION OF THE MONTE CARLO PRECISION history scores than the R which is based on first and second moments The desired VOV behavior is to decrease inversely with N This criterion is deemed to be a necessary but not sufficient condition for a statistically well behaved tally result A tally with a VOV that matches this criteria is NOT guaranteed to produce a high quality confidence interval because undersampling of high scores will also underestimate the higher score moments To calculate the VOV of every tally bin put a nonzero 15th entry on the DBCN card This option creates two additional history score moment tables each of length MXF in the TAL array to sum x and x see Figure 2 18 This option is not the default because the amount of tally storage will increase by 2 5 which could be prohibitive for a problem with many tally bins The magnitude of the VOV in each tally bin is reported in the Status of Statistical Checks table History dependent checks of the VOV of all tally bins can be done by printing the tallies to the output file at some frequency using the PRDMP card Empirical History Score Probability Density Function f x l Introduction This section discusses another statisti
151. the projected energy loss for the substep is based on the nonradiative stopping power The reason for this difference is that the sampling of bremsstrahlung photons is treated as an essentially analog process When a bremsstrahlung photon is generated during a substep the photon energy is subtracted from the projected electron energy at the end of the substep Thus the radiative energy loss is explicitly taken into account in contrast to the collisional nonradiative energy loss which is treated probabilistically and is not correlated with the energetics of the substep Two biasing techniques are available to modify the sampling of bremsstrahlung photons for subsequent transport However these biasing methods do not alter the linkage between the analog bremsstrahlung energy and the energetics of the substep MCNP uses identical physics for the transport of electrons and positrons but distinguishes between them for tallying purposes and for terminal processing Electron and positron tracks are subject to the usual collection of terminal conditions including escape entering a region of zero importance loss to time cutoff loss to a variety of variance reduction processes and loss to energy cutoff The case of energy cutoff requires special processing for positrons which will annihilate at rest to produce two photons each with energy m 0 511008 MeV 3 Stopping Power a Collisional Stopping Power Berger gives the restricted electro
152. the standard tallies have been implemented in the mesh tallies For example no tally fluctuation statistics are given for mesh tallies the only error information provided is the relative error for each mesh cell Features that can be used with the mesh tallies are multiplying the result by the particle energy FMESH format dose functions and tally multipliers Time binning is not a feature of the mesh tallies The definitions of the current and flux in the sections that follow come from nuclear reactor theory 1 but are related to similar quantities in radiative transfer theory The MCNP angular 10 3 05 2 83 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS TALLIES flux multiplied by the particle energy is the same as the intensity in radiative transfer theory The MCNP total flux at energy E multiplied by the particle energy equals the integrated energy density times the speed of light in radiative transfer theory The MCNP current multiplied by the particle energy is analogous to the radiative flux crossing an area in radiative transfer theory The MCNP particle fluence multiplied by the particle energy is the same as the fluence in radiative transfer theory Nuclear reactor theory has given the terms flux and current quite different meanings than they have in other branches of physics terminology from other fields should not be confused with that used in this manual Rigorous mathematical derivations of the basic tallies a
153. to raise the energy cutoff The much improved scoring efficiency will result in a much larger FOM for the high energy tally bins To further illustrate the components of the relative error consider the five examples of selected discrete probability density functions shown in Figure 2 19 Cases I and II have no dispersion in the nonzero scores cases III and IV have 10046 scoring efficiency and case V contains both 10 3 05 2 119 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS ESTIMATION OF THE MONTE CARLO PRECISION elements contributing to R The most efficient problem is case III Note that the scoring inefficiency contributes 7590 to in case V the second worst case of the five FIVE CASES WITH A MEAN OF 0 5 0 5 0 1 0 5 R Reff 1 sqart R 0 1 int 0 0 75 0 1 4 2 3 3 4 0 5 d 95 R Reff 0 58 sqrt N n Rint 70 0 2 3 1 E x 1 2x1 3 1 2x2 3 0 5 R R 4 0 33 sqrt 0 0 5 x 1 2 1 4 1 2 3 4 0 5 pcd 0 5 0 1 4 3 41 1 3 0 1 3 1 3 1 2 1 3 1 0 5 V f R 0 82 sqrt 0 0 5 1 Rant 0 41 sqrt N 25 H Raff 0 71 sqrt N 75 Figure 2 19 G Variance of the Variance Previous sections have discussed the relative error R and figure of merit FOM as measures of the quality of the mean A quantity called the relative variance of the variance VOV is another useful tool that can assist the user
154. to the variation in the number of contributing tracks rather than the variation in track score Thus far two things remain unspecified about the weight window the constant of inverse proportionality and the width of the window It has been observed empirically that an upper weight bound five times the lower weight bound works well but the results are reasonably insensitive to this choice anyway The constant of inverse proportionality is chosen so that the lower weight bound in some reference cell is chosen appropriately In most instances the constant should be chosen so that the source particles start within the window 1 Weight Window Compared to Geometry Splitting Although both techniques use splitting and Russian roulette there are some important differences a weight window is space energy dependent or space time dependent Geometry splitting is only space dependent b The weight window discriminates on particle weight before deciding appropriate action Geometry splitting is done regardless of particle weight c The weight window works with absolute weight bounds Geometry splitting is done on the ratio of the importance across a surface d The weight window can be applied at surfaces collision sites or both Geometry splitting is applied only at surfaces 10 3 05 2 145 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VARIANCE REDUCTION 2 146 e The weight window can control weight fluctuations introduce
155. treatment based on the free gas approximation to account for the thermal motion It also has an explicit 5 8 capability that takes into account the effects of chemical binding and crystal structure for incident neutron energies below about 4 eV but is available for only a limited number of substances and temperatures The S a capability is described later on page 2 54 The free gas thermal treatment in MCNP assumes that the medium is a free gas and also that in the range of atomic weight and neutron energy where thermal effects are significant the elastic scattering cross section at zero temperature is nearly independent of the energy of the neutron and that the reaction cross sections are nearly independent of temperature These assumptions allow MCNP to have a thermal treatment of neutron collisions that runs almost as fast as a completely nonthermal treatment and that is adequate for most practical problems With the above assumptions the free gas thermal treatment consists of adjusting the elastic cross section and taking into account the velocity of the target nucleus when the kinematics of a collision are being calculated The MCNP free gas thermal treatment effectively applies to elastic scattering only 2 28 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS Cross section libraries processed by NJOY already include Doppler broadening of elastic capture fission and other low threshold absorption cross
156. up Vo W are rotated to new outgoing target at rest system cosines v w through a polar angle whose cosine is and through an azimuthal angle sampled uniformly For random numbers and amp on the interval 1 1 with rejection criterion E 1 rotation scheme is Ref 2 page 54 Marone cU AT Hiab S uw 7 529 hie ws 50 nom 11 619 w uus 2 5 2 1 1 blab C o 1 55 If 1 w 0 then I UoHlab t N1 bawo ot m v W WoHjap amp 52 N l TC B 52 22901 02 If the scattering distribution is isotropic in the target at rest system it is possible to use an even simpler formulation that takes advantage of the exiting direction cosines u v w being independent of the incident direction cosines u V W In this case sr caet DEC 2 2750 7 516 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS where amp and amp are rejected if E 25 gt 1 b Energy from Elastic Scattering Once the particle direction is sampled from the appropriate angular distribution tables then the exiting energy Epu is dictated by two body kinematics our E out 1 5 Ei o 14 aa 4 where incident neutron energy Uom center of mass cosine of the angle between incident and exiting particle direction
157. user interested in particle production from light isotopes should check for the existence of pseudolevels and thus possible deviations from the above standard reaction list Two electron transport libraries el and 103 are maintained The electron transport algorithms and data in MCNP where adapted from the ITS code The el library was developed and released in 1990 in conjunction with the addition of electron transport into MCNPA the electron transport algorithms and data correspond roughly to that found in ITS version 1 The el03 library was developed and released in 2000 in conjunction with upgrades to the electron physics package these upgrades correspond roughly to that of ITS version 3 The MT numbers for use in plotting the cross section values for these tables should be taken from the Print Table 85 column headings and are not from ENDF 10 3 05 APPENDIX G MCNP DATA LIBRARIES S o B DATA FOR USE WITH THE MTn CARD S o B DATA FOR USE WITH THE MTn CARD Table 1 lists all the S a B data libraries that are maintained The number s in parentheses following the description in words Beryllium Metal 4009 specify the nuclides for which the S a data are valid For example lwtr 01t provides scattering data only for 190 would still be represented by the default free gas treatment The entries in each of the columns of Table G 1 are described as follows ZAID Source Library Date Processed Temperature
158. well behaved in the sense of the CLT to form the most valid confidence intervals Monotonically decreasing in checks 3 and 5 allows for some increases in both and the VOV Such increases in adjacent TFC entries are acceptable and usually do not by themselves cause poor confidence intervals A TFC bin R that does not pass check 3 by definition in MCNP does not pass check 4 Similarly a TFC bin VOV that does not pass check 6 by definition does not pass check 7 A table is printed after each tally for the TFC bin result that summarizes the results and the pass or no pass status of the checks Both asymmetric and symmetric confidence intervals are printed for the one two and three o levels when all of the statistical checks are passed These intervals can be expected to be correct with improved probability over historical rules of thumb This is NOT A GUARANTEE however there is always a possibility that some as yet unsampled portion of the problem would change the confidence interval if more histories were calculated A WARNING is printed if one or more of these ten statistical checks is not passed and one page of printed plot information about f x is produced for the user to examine An additional information only check is made on the largest five f x score grid bins to determine if there are bins that have no samples or if there is a spike in an f x that does not appear to have an upper limit The result of the check is included in the
159. when the source or tally region is large and the detector region is small MCNP can be run in multigroup adjoint mode There is no continuous energy adjoint capability As alluded to above the smaller the tally region the harder it becomes to get good tally estimates An efficient tally will average over as large a region of phase space as practical In this connection 10 3 05 2 111 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS ESTIMATION OF THE MONTE CARLO PRECISION tally dimensionality is extremely important A one dimensional tally is typically 10 to 100 times easier to estimate than a two dimensional tally which is 10 to 100 times easier than a three dimensional tally This fact is illustrated in Figure 2 22 later in this section Variance reduction techniques can be used to improve the precision of a given tally by increasing the nonzero tallying efficiency and by decreasing the spread of the nonzero history scores These two components are depicted in a hypothetical f x shown in Figure 2 17 See page 2 122 for Zeros FREQUENCY OF SAMPLING 0 E Xx TALLY HISTORY Figure 2 17 more discussion about the empirical f x for each tally fluctuation chart bin A calculation will be more precise when the history scoring efficiency is high and the variance of the nonzero scores is low The user should strive for these conditions in difficult Monte Carlo calculations Examples of these two components of precision are given on page
160. where N is greater than about 200 neutrons per cycle and as long as too many active cycles are not used It has been shown that this bias is less probably much less than one half of one standard deviation for 400 active cycles when the ratio of the true keg standard deviation to keg is 0 0025 at the problem end In MCNP the definition of kp is 10 3 05 2 167 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CRITICALITY CALCULATIONS _ fission neutrons in generation i 1 ko Un fission neutrons in generation 1 Pal V EF V eJdVdidEdO p o o baVdraEdO V O E O V O E O where the phase space variables are t E and Q for time energy direction and implicitly r for position with incremental volume dV around r The denominator is the loss rate which is the sum of leakage capture n On fission and multiplicity n xn terms By particle balance the loss rate is also the source rate which is unity in a criticality calculation If the number of fission neutrons produced in one generation is equal to the number in the previous generation then the system is critical If it is greater the system is supercritical If it is less then the system is subcritical The multiplicity term is sf f f f o 2 e f f ff m s PAV dtdE dQ Se f on s PdVdtdEdO The above defin
161. x at the largest history scores The most important use for the empirical f x is to help determine if N has approached infinity in the sense of the CLT so that valid confidence intervals can be formed It is assumed that the underlying f x satisfies the CLT requirements therefore so should the empirical f x Unless there is a largest possible history score the empirical f x must eventually decrease more steeply than E m D x for the second moment f x to exist It is postulated that if such decreasing 90 behavior in the empirical f x with no upper bound has not been observed then N is not large enough to satisfy the CLT because f x has not been completely sampled Therefore a larger is required before a confidence interval can be formed It is important to note that this convergence criterion is NOT affected by any correlations that may exist between the estimated mean and the estimated R In principle this lack of correlation should make the f x diagnostic robust in assessing complete sampling Both the analytic and empirical history score distributions suggest that large score fill in and one or more extrapolation schemes for the high score tail of the f x could provide an estimate of scores not yet sampled to help assess the impact of the unsampled tail on the mean The magnitude of the unsampled tail will surely affect the quality of the tally confidence interval 6 Creation of f x for TFC Bins The
162. yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no yes no yes yes yes yes yes no yes yes yes yes yes no yes yes yes yes yes no yes yes yes yes no no no no no no yes yes yes yes no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no ZAID 54 26054 24c 26054 60c 26054 61c 26054 62c 26054 64c 26054 66c 56 26056 24 26056 60 26056 61c 26056 62c 26056 64c 26056 66c 57 26057 24 26057 60 26057 61c 26057 62c 26057 64c 26057 66c 58 26058 60 26058 61c 26058 62c 26058 64c 26058 66c Z 227 Co 59 27059 42 27059 504 27059 50 27059 51d 27059 51 27059 60 27059 66 7 28 Nickel kkk AWR 53 4760 53 4760 53 4
163. 0 1997 1997 1997 1989 2000 2000 1997 1997 1997 1989 2000 2000 1997 1997 1997 1989 2000 2000 1997 1997 1992 1977 1977 1977 1977 1988 2000 2000 1988 1988 1989 1992 1978 1978 1986 1986 300 0 293 6 293 6 293 6 293 6 77 0 293 6 77 0 293 6 293 6 293 6 77 0 293 6 77 0 293 6 293 6 293 6 77 0 293 6 77 0 293 6 293 6 293 6 77 0 293 6 77 0 293 6 300 0 293 6 293 6 293 6 293 6 293 6 77 0 293 6 77 0 293 6 12573 30714 134454 391112 119178 405367 390799 403120 388600 346350 117680 344811 342461 344376 342098 286602 114982 292322 287642 289469 284837 259040 98510 262192 260423 259591 257750 10262 9681 105093 9681 25727 184269 279378 272554 270711 263887 300 0 149855 300 0 38653 293 6 115447 293 6 33896 293 6 72632 293 6 178392 10 3 05 377 263 11050 28453 11918 29959 28138 29954 28139 21232 10679 21143 20849 21132 20847 13873 10073 14242 13657 14231 13652 13750 9699 13814 13593 13819 13589 460 263 12525 263 1578 8207 11967 11114 11967 11114 15598 3385 10957 263 263 6899 30 0 20 0 20 0 150 0 20 0 150 0 150 0 150 0 150 0 150 0 20 0 150 0 150 0 150 0 150 0 150 0 20 0 150 0 150 0 150 0 150 0 150 0 20 0 150 0 150 0 150 0 150 0 30 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 100 0 30 0 20 0 20 0 20 0 20 0 yes yes yes
164. 0 1 293 6 3000 1 293 6 300 0 293 6 293 6 293 6 293 6 293 6 77 0 293 6 300 0 293 6 77 0 3000 1 293 6 300 0 293 6 293 6 293 6 300 0 293 6 293 6 293 6 293 6 293 6 77 0 293 6 3000 1 77 0 3000 1 293 6 SRA RS ACR SCS ACR Hafnijum 108989 4751 52231 84369 35072 39545 55807 66727 115867 219075 58452 67580 79130 106850 112444 145939 Tantalum 47852 16361 60740 21527 16361 91374 158545 140345 20850 12085 29837 25028 28577 194513 50639 34272 246875 150072 94367 17729 122290 26387 113177 269718 0 258342 0 232047 0 257611 219900 246251 E max NE MeV GPD 14113 263 8270 13634 3834 4473 6869 8429 15278 30022 7291 8595 10151 14111 15082 19867 4927 263 6341 753 263 10352 17152 14877 2463 1698 3020 2333 2840 21386 1816 263 16896 16495 11128 263 13865 263 12283 18237 16815 13528 18238 13524 16818 30 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 30 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 100 0 20 0 20 0 150 0 20 0 20 0 20 0 20 0 20 0 20 0 150 0 150 0 150 0 150 0 150 0 150 0 yes no no no no no no no no no no no no no no no yes yes yes yes yes yes yes yes no no no no no yes yes yes yes
165. 0 1972 880 8 38017 1402 20 0 yes no no 8016 60c 15 8532 endf60 B VLO 1990 293 6 58253 1609 20 0 yes no no 8016 62c 15 8575 actia 8 2000 293 6 407432 2759 150 0 yes no yes 8016 66c 15 8532 endf66a 6 1996 293 6 164461 1935 150 0 yes no yes 8017 60c 16 8531 endf60 B VLO 1978 293 6 4200 335 20 0 no no no 8017 66c 16 8531 endf66a 0 1978 293 6 8097 612 20 0 no no no 9019 42c 18 8352 492 LLNL 1992 300 0 37814 1118 30 0 yes no no 9019 50c 18 8350 endf5p 0 1976 293 6 44130 1560 20 0 yes no no 9019 50d 18 8350 dre5 B V 0 1976 293 6 23156 263 200 yes no no 9019 51d 18 8350 drmccs B V 0 1976 293 6 23156 263 200 yes no no 9019 51c 18 8350 rmccs B V 0 1976 293 6 41442 1541 20 0 yes no no 9019 60c 18 8350 endf60 B VLO 1990 300 0 93826 1433 20 0 yes no no 9019 62c 18 8350 actia 8 2000 293 6 127005 1888 20 0 9019 66 18 8350 endf66a 0 1990 293 6 122324 1870 20 0 yes no yes 20 10020 42c 19 8207 endl92 LLNL 1992 300 0 14286 1011 30 0 yes no no Na 23 11023 42c 22 7923 endl92 LLNL 1992 300 0 19309 1163 30 0 yes no no 11023 50c 22 7920 endf5p 0 1977 293 6 52252 2703 20 0 yes no no 11023 50d 227920 dre5 0 1977 293 6 41665 263 20 0 yes no no 11023 51d 22 7920 drmccs B V 0 1977 293 6 41665 263 20 0 yes no no 11023 51 22 7920 rmccs B V 0 1977 293 6 48863 2228 200 yes no no 11023 60c 22 7920 endf60 B VI 1 1977 293 6 50294 2543 20 0 yes no no 11023 62c 22 7920 acti
166. 0 2 Questionable 0 10 Generally reliable except for point detector 0 05 Generally reliable for point detector 5 X and represents the estimated statistical relative error at the 16 level These interpretations of R assume that all portions of the problem phase space have been well sampled by the Monte Carlo process Please use statistical checks for detailed information Point detector tallies generally require a smaller value of R for valid confidence interval statements because some contributions such as those near the detector point are usually extremely important and may be difficult to sample well Experience has shown that for R less than 0 05 point detector results are generally reliable For an of 0 10 point detector tallies may only be known within a factor of a few and sometimes not that well see the pathological example on page 2 131 MCNP calculates the relative error for each tally bin in the problem using Eq 2 19b Each x is defined as the total contribution from the i starting particle and all resulting progeny This definition is important in many variance reduction methods multiplying physical processes such as fission or xn neutron reactions that create additional neutrons and coupled neutron photon electron problems The i source particle and its offspring may thus contribute many times to a tally and all of these contributions are correlated because they are from the same source particle
167. 0 3900 180 3900 180 3900 180 3900 Library Name endl92 newxsd newxs endf60 endf66e endf66b endf66e endf66b endf66e endf66b endf66e endf66b endf66e endf66b endf66e endf66b 192 dre5 5 rmccs drmccs endf60 endf66d endf66b uresa endf60 endf66d endf66e endf66b 100xs 3 rmccs drmccs lal50n uresa 16 endf5p dre5 rmccsa drmccs endf60 actib actia actib endf66d endf66e endf66b Source LLNL B V 0 B V 0 0 2 2 2 2 2 2 2 B VI2 2 B VI2 2 2 LLNL B V 0 0 B V 0 0 B VLO B VLO 0 0 0 0 B VLO 0 LANL T X B V 2 B V 2 6 0 B V 0 B V 0 B V 2 B V 2 0 B VL8 B VL8 B VL8 6 6 6 APPENDIX MCNP DATA LIBRARIES NEUTRON CROSS SECTION LIBRARIES Table G 2 Cont Continuous Energy and Discrete Neutron Data Libraries Maintained by X 5 Eval Date 1992 1976 1976 1976 1992 1992 1992 1992 1991 1991 199 1991 1992 1992 1991 1991 1992 1972 1972 1972 1972 1972 1972 1972 1971 1971 1971 1971 1971 1989 1982 1982 1996 1980 1973 1973 1980 1980 1980 2000 2000 2000 1996 1996 1996 10 3 05 Temp Length words CK 300 0 293 6 293 6 293 6 3000 1 293 6 3000 1 293 6 3000 1 293 6 3000 1 293 6 300
168. 0 B IV 89 B IV E amp C BM amp M 39000 04p mcplib04 2002 7583 1007 100 8 B VL8 B VI8 BM amp M Z 40 Zirconium eese epe 2 oe he k he oe k akk kk k ak akak k 40000 01p moplib 1982 461 51 0 1 B IV B IV E amp C n a 40000 02p mcplib02 1993 695 90 100 89 B IV E amp C n a 40000 03p mcplib03 2002 2081 90 100 B IV 89 B IV E amp C BM amp M 40000 04p meplib04 2002 7703 1027 100 B VL8 B VL8 B VI8 BM amp M 10 3 05 G 49 APPENDIX G MCNP DATA LIBRARIES PHOTOATOMIC DATA Table G 4 Cont Continuous Energy Photoatomic Data Libraries Maintained by X 5 Library Release Length Emax CS FF Fluor CDBD ZAID Name Date Words GeV Source Source Source Source Z 41 Niobium 25 kk k 41000 01 moplib 1982 461 51 0 1 B IV B IV E amp C n a 41000 02p moplib02 1993 695 90 100 89 B IV E amp C n a 41000 03p mcplib03 2002 2081 90 100 B IV 89 B IV E amp C BM amp M 41000 04p meplib04 2002 7667 1021 100 B VL8 B VL8 B VI8 BM amp M Z 42 Molybdenum KEK K K K K K K K K 2K KK K K K K K K K K 42000 01p mcplib 1982 461 51 0 1 B IV B IV E amp C n a 42000 02p meplib02 1993 695 90 100 89 B IV E amp C n a 42000 03p mcplib03 2002 2180 90 100 B IV 89 B IV E amp C BM amp M 42000 04p meplib04 2002 7592 992 100 B VL8 8 B VI8 BM amp M Z 43 Technetium
169. 0 drmccs B V 0 1978 293 6 4358 263 36078 66c 77 2510 endf66a 0 1978 293 6 27045 2221 36080 504 79 2298 drmccs B V 0 1978 293 6 4276 263 36080 50c 79 2298 rmccsa B V 0 1978 293 6 10165 1108 36080 66c 79 2298 endf66a 0 1978 293 6 26039 2361 36082 504 81 2098 drmccs B V 0 1978 293 6 4266 263 36082 50c 81 2098 rmccsa B V 0 1978 293 6 7220 586 36082 59c 81 2098 misc5xs 7 8 LANL T 1982 293 6 7010 499 36082 66c 81 2098 endf66a 0 1978 293 6 19674 1296 36083 50c 82 2018 rmccsa 0 1978 293 6 8078 811 36083 50d 82 2018 drmccs B V 0 1978 293 6 4359 263 36083 59c 82 2018 misc5xs 7 8 LANL T 1982 293 6 8069 704 36083 66c 82 2018 endf66a 0 1978 293 6 21271 1760 36084 50 83 1906 rmccsa B V 0 1978 293 6 9364 944 36084 50d 83 1906 drmccs B V 0 1978 293 6 4463 263 36084 59c 83 1906 misc5xs 7 8 LANL T 1982 293 6 10370 954 36084 66c 83 1906 endf66a 0 1978 293 6 24427 2098 36086 50 85 1726 rmccsa B V 0 1975 293 6 10416 741 36086 50d 85 1726 drmccs B V 0 1975 293 6 4301 263 36086 59c 85 1726 misc5xs 7 8 LANL T 1982 293 6 8740 551 36086 66c 85 1726 endf66a 0 1978 293 6 22203 1425 37085 55 84 1824 misc5xs 7 9 LANL T 1982 293 6 27304 4507 37085 66c 84 1824 endf66a 0 1979 293 6 179843 15316 37087 55c 86 1626 misc5xs 7 9 LANL T 1982 293 6 8409 1373 37087 66c 86 1624 endf66b 0 1979 293 6 42718 3637 39088 42 87 1543 endl92 LLNL lt 1992 300 0 11682 181 39089 35c 88 1421 misc5xs 7 LLNL lt 1985 0
170. 000 1 293 6 293 6 293 6 293 6 293 6 3000 1 293 6 6926 6654 37421 147572 68057 10013 35199 86575 96099 98867 155078 81509 5655 49313 53516 89485 129446 11244 55231 36372 72971 86490 93021 135491 72804 37008 5458 54676 80218 4532 27638 7878 6833 26251 5899 32590 32760 263235 341562 5930 49572 59814 67662 218806 286357 Emax NE MeV GPD 364 20 0 yes 263 20 0 yes 4498 30 0 yes 10471 200 yes 5465 20 0 yes 263 20 0 yes 263 20 0 yes 4749 20 0 yes 7394 20 0 yes 5220 20 0 yes 10841 20 0 yes 6540 20 0 no 263 20 0 no 4553 20 0 no 3563 20 0 no 6833 20 0 no 8784 20 0 yes 263 200 yes 4636 20 0 yes 263 20 0 yes 4174 20 0 yes 6198 200 yes 4791 20 0 yes 9038 20 0 yes 6627 20 0 no 4030 20 0 no 263 20 0 no 4078 20 0 no 6916 20 0 no 273 20 0 no 2440 20 0 no 454 20 0 yes 263 20 0 yes 3285 200 no 263 200 no 3285 20 0 yes 4391 20 0 no 20777 200 no 29480 200 no 263 200 no 7167 20 0 no 7167 20 0 yes 10189 20 0 no 21530 20 0 no 31180 20 0 no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no
171. 02 2933 100 100 B IV 89 B IV E amp C 77000 04 mcplib04 2002 9665 1222 100 B VL8 8 8 Z 78 eek Platinum 78000 01p meplib 1982 521 61 0 1 B IV B IV E amp C 78000 02 meplib02 1993 755 100 100 B IV 89 E amp C 78000 03 mcplib03 2002 2933 100 100 B IV 89 B IV E amp C 78000 04 mcplib04 2002 9377 1174 100 B VL8 8 8 79000 01 mcplib 1982 521 61 0 1 B IV B IV E amp C 79000 02 meplib02 1993 755 100 100 B IV 89 E amp C 79000 03 mcplib03 2002 2933 100 100 B IV 89 B IV E amp C 79000 04 meplib04 2002 9881 1258 100 B VL8 8 8 Z 80 eee Mercury 80000 01p mcplib 1982 521 61 0 1 B IV B IV E amp C 80000 02p mcplib02 1993 755 100 100 B IV 89 E amp C 80000 03p meplib03 2002 2933 100 100 B IV 89 B IV E amp C 80000 04p mcplib04 2002 9281 1158 100 B VL8 8 8 G 354 10 3 05 CDBD Source n a n a BM amp M BM amp M n a n a BM amp M BM amp M n a n a BM amp M BM amp M n a n a BM amp M BM amp M n a n a BM amp M BM amp M n a n a BM amp M BM amp M n a n a BM amp M BM amp M n a n a BM amp M BM amp M APPENDIX G MCNP DATA LIBRARIES PHOTOATOMIC DATA Table G 4 Cont Continuous Energy Photoatomic Data Libraries Maintained by X 5 Library Release Length Emax CS FF Fluor CDBD ZAID Name Date Words NE GeV Source Source Source Source 7 81
172. 06 116 4906 116 4906 116 4906 Sn nat 50000 40c 50000 42c G 24 117 6704 117 6704 Library Name endl92 rmccsa drmccs endf60 endf66b endl92 dre5 endfSu rmccs drmccs endf66e endf66b endf66e endf66b endf66e endf66b endf66b endf66e endf66b endf66b endf66e endf66b endf66e endf66b endl92 endf60 endf66b Fission Products 2222222822624 9824 55 21 21 8 2 2 2 ok endl92fp 12 endl92fp 12 rmccs drmccs 192 192 Source LLNL B V 0 B V 0 0 0 LLNL B V 0 B V 0 B V 0 B V 0 4 4 4 4 B VL4 X B VL4 X 4 4 4 4 4 4 LLNL 0 0 LLNL LLNL LLNL LLNL LLNL LLNL X Table G 2 Cont Eval Date 1992 1978 1978 1983 1983 1992 1974 1974 1974 1974 1996 1996 1996 1996 1996 1996 1995 1996 1996 1995 1996 1996 1996 1996 1992 1990 1990 1992 1992 1985 1985 1992 1992 Temp CK 300 0 293 6 293 6 293 6 293 6 300 0 293 6 293 6 293 6 293 6 3000 1 293 6 3000 1 293 6 3000 1 293 6 293 6 3000 1 293 6 293 6 3000 1 293 6 3000 1 293 6 300 0 293 6 293 6 300 0 300 0 yes yes Length words 33603 14585 3823 76181 121474 211537 3026 19714 6734 3026 121059 151365 112404 141658 105350
173. 0y 22 99410 LLNL ACTL 1983 333 12024 26y 23 98500 532dos ENDF B V 1979 165 12024 30y 23 98500 Illdos LLNL ACTL 1983 309 12025 30y 24 98580 LLNL ACTL 1983 309 12026 30y 25 98260 LLNL ACTL 1983 321 12027 30y 26 98430 Illdos LLNL ACTL 1983 309 Z 13 K K K K Aluminum 13026 30 25 98690 LLNL ACTL 1983 447 13027 24 26 75000 531405 ENDF B V 1973 1165 13027 26y 26 75000 532dos ENDF B V 1973 1753 13027 30y 26 98150 LLNL ACTL 1983 49 Z 14 FK K K K K K K K K K KK K K K K K K Silicon 14027 30 26 98670 LLNL ACTL 1983 401 14028 30y 27 977690 LLNL ACTL 1983 3T 14029 30y 28 97650 Illdos LLNL ACTL 1983 389 14030 30y 29 97380 Illdos LLNL ACTL 1983 395 14031 30y 30 97540 Illdos LLNL ACTL 1983 337 10 3 05 APPENDIX G MCNP DATA LIBRARIES DOSIMETRY DATA ZAID Z 15 Phosphorus K K K K K K K K K K K K K K K KK K K K K K K K K K K K K 15031 26y 15031 30y 16 9000 Sulfur 16031 30 16032 24 16032 26 16032 30y 16033 30y 16034 30y 16035 30y 16036 30y 16037 30y 7 17 Chlorine 78 2 kk petet kk k ak ak kk k k k k 17034 30y 17035 30y 17036 30y 17037 30y 7038 30y Z2 1 8 oo Argon KKK K K K K K K K K K K K K K K K K K KK K K K KK K K K K K K K K K K KK K 18036 30y 18037 30y 18038 30y 18039 30y 18040 26y 18040 30y 18041 30y 18042 30y 18043 30y 7 19
174. 1 B V 1975 293 6 5529 704 54135 53c 133 7480 endfSmt 1 B V 1975 587 2 5541 706 54135 54c 133 7480 endfSmt 1 B V 1975 880 8 5577 712 Xe 136 54136 66c 134 7400 endf66b 0 1978 293 6 10700 764 75 133 55133 50c 131 7640 kidman 0 1978 293 6 26713 4142 55133 55c 131 7640 misc5xs 7 9 LANL T 1982 293 6 67893 11025 55133 60c 131 7640 endf60 0 1978 293 6 54723 8788 55133 66c 131 7640 endf66b 0 1978 293 6 141927 19648 75 134 55134 60c 132 7570 endf60 0 1988 293 6 10227 1602 Cs 135 55135 50 133 7470 B V 0 1974 293 6 1903 199 55135 60c 133 7470 endf60 0 1974 293 6 3120 388 05 136 55136 60 134 7400 endf60 0 1974 293 6 10574 1748 75 127 55137 60c 135 7310 endf60 0 1974 293 6 2925 369 10 3 05 30 0 30 0 20 0 30 0 30 0 20 0 20 0 30 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 30 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 NE MeV GPD yes yes no yes yes no no yes no no no no no no no no yes no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no yes no no no no no
175. 1 144201 16318 200 no both no yes yes 92234 66c 232 0300 endf66c B VLO 1978 293 6 196273 22827 200 no both no yes yes 92234 68c 232 0304 t16 2003 LANL T16 2003 3000 0 286070 16719 30 0 yes both no yes yes 92234 69c 232 0304 t16 2003 LANL T16 2003 293 6 344651 23228 300 yes both no yes yes 92235 11 233 0250 endf62mt 2 1993 77 0 696398 78912 20 0 yes both no no 92235 12c 233 0250 endf62mt 2 1993 4000 411854 43344 20 0 yes both no no 92235 13c 233 0250 endf62mt 2 1993 500 0 379726 39328 20 0 yes both no 92235 14c 233 0250 endf62mt 2 1993 600 0 353678 36072 20 0 yes both no 92235 15c 233 0250 endf62mt 2 1993 800 0 316622 31440 20 0 yes both no 92235 16c 233 0250 endf62mt 2 1993 900 0 300278 29397 20 0 yes both no no 92235 l7c 233 0250 endf62mt 2 1993 1200 0 269062 25495 20 0 yes both no 92235 42c 233 0248 92 LLNL 1992 300 0 72790 5734 30 0 yes both no no no 92235 49c 233 0250 uresa 4 1996 300 0 647347 72649 20 0 yes both no yes 92235 50c 233 0250 rmccs B V 0 1977 293 6 60489 5725 20 0 yes both no no no 92235 50d 233 0250 drmccs B V 0 1977 293 6 11788 263 20 0 yes both no no 92235 52c 233 0250 endf5mt 1 B V 0 1977 587 2 65286 6320 20 0 yes both no no no 92235 53c 233 0250 endf5mt 1 B V 0 1977 587 2 36120 2685 20 0 yes both no no no 92235 54c 233 0250 endf5mt 1 B V 0 1977 880 8 36008 2671 20 0 yes both no no no 92235 60c 233 0250 endf
176. 13 MS January 1980 B Spain Analytical Conics Pergamon 1957 J S Hendricks Effects of Changing the Random Number Stride in Monte Carlo Calculations Nucl Sci Eng 109 1 pp 86 91 September 1991 J E Olhoeft The Doppler Effect for a Non Uniform Temperature Distribution in Reactor Fuel Elements WCAP 2048 Westinghouse Electric Corporation Atomic Power Division Pittsburgh 1962 Takahashi Monte Carlo Method for Geometrical Perturbation and its Application to the Pulsed Fast Reactor Nucl Sci Eng 41 p 259 1970 M C Hall Monte Carlo Perturbation Theory in Neutron Transport Calculations Ph D Thesis University of London 1980 M C Hall Cross Section Adjustment with Monte Carlo Sensitivities Application to the Winfrith Iron Benchmark Nucl Sci Eng 81 p 423 1982 Rief Generalized Monte Carlo Perturbation Algorithms for Correlated Sampling and a Second Order Taylor Series Approach Ann Nucl Energy 11 p 455 1984 G McKinney A Monte Carlo MCNP Sensitivity Code Development and Application M S Thesis University of Washington 1984 W McKinney Theory Related to the Differential Operator Perturbation Technique Los Alamos National Laboratory Memo X 6 GWM 94 124 1994 Hess L L Carter J S Hendricks W McKinney Verification of the MCNP Perturbation Correction Feature for Cross Section Dependent Tallies Los Alamos Nat
177. 15 if cell 1 is inside the solid black line and cell 2 is the entire region outside the solid line then the MCNP cell cards in two dimensions are assuming both cells are voids 101 2 03 4 5 2 0 5 1 2 3 4 Cell 1 is defined as the region above surface 1 intersected with the region to the left of surface 2 intersected with the union of regions below surfaces 3 and 4 and finally intersected with the region 1 16 10 3 05 CHAPTER 1 MCNP OVERVIEW MCNP GEOMETRY to the right of surface 5 Cell 2 contains four concave corners all except between surfaces 3 and 4 and its specification is just the converse or complement of cell 1 Cell 2 is the space defined by the region to the left of surface 5 plus the region below 1 plus the region to the right of 2 plus the space defined by the intersections of the regions above surfaces 3 and 4 A simple consistency check can be noted with the two cell cards above All intersections for cell 1 become unions for cell 2 and vice versa The senses are also reversed Note that in this example all corners less than 180 degrees in a cell are handled by intersections and all corners greater than 180 degrees are handled by unions To illustrate some of the concepts about parentheses assume an intersection is thought of mathematically as multiplication and a union is thought of mathematically as addition Parentheses are removed first with multiplication being performed before addition The cell cards for
178. 15 MeV and trace their cross section data back to the Storm and Israel 1970 data compilation which is available from RSICC as data package DLC 15 The form factor data for the excluded elements is of forgotten origin The fluorescence data were produced by Everett and Cashwell from the Storm and Israel 1970 data supplemented as necessary MCPLIB does not contain momentum profile CDBD data MCPLIBO2 was officially released in 199328 and was created as an extension to MCPLIB The form factor and fluorescence data on MCPLIB and MCPLIBO2 are identical The cross section data below 10 MeV are also identical From the maximum energy on the original MCPLIB table up to 100 GeV the cross section data are derived from EPDL89 Between 10 MeV and the highest energy of the MCPLIB data the data are smoothly transitioned MCPLIBO2 does not contain momentum profile CDBD data MCPLIBOS3 was officially released in 200239 as another extension of MCPLIB MCPLIBO2 data set The cross section form factor and fluorescence data on MCPLIBO2 and MCPLIBO3 are identical The only change is the addition of the momentum profile CDBD data derived from the work of Biggs Mendelsohn and Mann MCPLIB04 was officially released in 2002 The cross section form factor and fluorescence data are all derived from the ENDF B VI 8 data library that are derived from EPDL97 Cross section data are given for incident photon energies from 1 keV to 100 GeV Fluoresce
179. 150 0 150 0 20 0 150 0 150 0 150 0 150 0 150 0 20 0 150 0 150 0 150 0 150 0 20 0 20 0 20 0 20 0 20 0 30 0 20 0 20 0 20 0 20 0 20 0 20 0 30 0 20 0 20 0 150 0 30 0 20 0 150 0 150 0 150 0 150 0 150 0 20 0 150 0 150 0 150 0 150 0 yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no yes no yes yes yes yes yes no yes yes yes yes yes no yes yes yes yes no yes yes yes yes no no no no no no no no no no yes no no yes yes yes yes yes no yes yes yes yes no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no APPENDIX G MCNP DATA LIBRARIES NEUTRON CROSS SECTION LIBRARIES Table G 2 Cont Continuous Energy and Discrete Neutron
180. 1978 1978 1978 1978 1988 1988 1996 1996 1996 1996 1978 1978 1992 1978 1978 1978 1978 1978 1978 1978 1978 1992 1978 1978 1978 1992 1978 1978 1978 1978 1978 1978 1978 1978 1992 1979 1979 1979 1979 1992 1976 1976 10 3 05 Temp CK 300 0 293 6 293 6 293 6 293 6 3000 1 293 6 300 0 293 6 293 6 293 6 293 6 293 6 293 6 3000 1 293 6 3000 0 293 6 293 6 293 6 300 0 293 6 293 6 293 6 293 6 293 6 293 6 3000 1 293 6 300 0 293 6 3000 1 293 6 300 0 300 0 293 6 293 6 293 6 293 6 293 6 3000 1 293 6 300 0 293 6 293 6 3000 1 293 6 300 0 293 6 293 6 Length words 21828 8593 9048 9048 8502 27193 27625 52074 92015 11742 11742 13684 104257 109155 160276 308812 160276 308812 3132 9515 37766 30897 8903 8903 9767 34374 39269 54517 62059 21543 18860 29796 32793 46590 97975 9509 45991 9509 10847 73001 91371 116265 25678 29535 34433 44920 52336 24550 37948 56186 NE MeV GPD 1368 323 263 263 317 945 933 4867 11921 263 263 757 11984 11984 10268 26772 10268 26772 278 598 3141 3113 263 263 472 3544 3544 4410 5248 1099 1445 1965 2298 4198 11389 263 4919 263 566 8294 8861 11627 1564 2636 2636 3214 4038 1376 3311 4704 20 0 20 0 20 0 20 0 20 0 20 0 20 0 30 0 20 0 20 0 20 0 20 0 20 0 20 0 30 0 30 0 30 0
181. 1982 417 45 0 1 22000 02p meplib02 1993 651 84 100 22000 03p meplib03 2002 1344 84 100 22000 04p mcplib04 2002 5742 817 100 Z 23 Vanadium 23000 01 moeplib 1982 417 45 0 1 23000 02p moeplib02 1993 651 84 100 23000 03p meplib03 2002 1344 84 100 23000 04p meplib04 2002 5814 829 100 Z 24 Chromium 24000 01p mcplib 1982 417 45 0 1 24000 02p meplib02 1993 651 84 100 24000 03p meplib03 2002 1344 84 100 24000 04p mcplib04 2002 5682 807 100 10 3 05 CDBD Source n a n a BM amp M BM amp M n a n a BM amp M BM amp M n a n a BM amp M BM amp M n a n a BM amp M BM amp M n a n a BM amp M BM amp M n a n a BM amp M BM amp M n a n a BM amp M BM amp M n a n a BM amp M BM amp M G 47 APPENDIX G MCNP DATA LIBRARIES PHOTOATOMIC DATA Table G 4 Cont Continuous Energy Photoatomic Data Libraries Maintained by X 5 Library Release Length Emax CS FF Fluor ZAID Name Date Words NE GeV Source Source Source Z 25 Manganese 25000 01p meplib 1982 417 45 0 1 B IV B IV E amp C 25000 02p meplib02 1993 651 84 100 B IV 89 E amp C 25000 03p meplib03 2002 1344 84 100 B IV 89 B IV E amp C 25000 04p mcplib04 2002 5598 793 100 B VL8 8 8 7 26 KKK KK KKK Iron 26000 01p mcplib 1982 417 45 0 1 B IV B IV E amp C 26000 02p mcplib02 1993 651 84 100 B IV 89 E amp C 26000 03p mepl
182. 2 Bins 3 80 Cutoffs 3 135 Distribution sampling 2 36 From elastic scattering 2 30 Multiplier 2 45 Multiplier EMn Card 3 100 Physics Cutoff PHYS card 3 127 to 3 132 Roulette 2 142 3 35 Spectra Evaporation 3 64 Gaussian fusion 3 64 Maxwell fission 3 64 Muir velocity Gaussian fusion 3 64 Watt fission 3 64 Splitting 2 142 3 35 Tally 3 92 Tally F6 tally 3 80 Entropy 2 179 3 77 Errors Geometry 3 8 Input 3 7 ESPLT card 3 35 Evaporation energy spectrum 3 64 Event log 3 8 3 143 Printing 3 142 Examples Macrobody surfaces 3 18 Surfaces by points 3 16 Exponential transform 3 10 3 40 EXT card 3 40 10 3 05 MCNP MANUAL INDEX Free Gas F F1 surface current Tally 3 80 F2 surface flux Tally 3 80 F4 cell flux Tally 3 80 F4 F7 Tally Equivalence 2 89 F5 detector flux tally 3 80 F6 Neutrons 2 88 F6 Photons 2 88 F6 cell energy tally 3 80 F7 Neutrons 2 89 F7 cell fission energy Tally 3 80 F8 detector pulse energy Tally 3 80 Facets 3 21 Fatal error message 3 7 FATAL option 3 7 FCL card 3 42 FCn card 3 91 Figure of Merit 2 116 3 35 3 108 3 140 File Creation FILES Card 3 144 FILES file creation card 3 144 FILL card 3 29 Fission 3 122 Neutron Multiplicity 2 50 Spectra 3 64 Turnoff NONU card 3 122 Flagging 2 105 Cell 3 101 Surface 3 102 Floating Point Array RDUM card 3 139 Fluorescence 2 57 2 62 Flux at a Detector 2 91 Flux Image Radi
183. 2 rmccs drmccs endf60 actia endf66a 6 LLNL 0 B V 0 LANL T B VL8 6 1997 lt 1992 1973 1973 1992 2000 1997 10 3 05 293 6 300 0 293 6 293 6 293 6 293 6 293 6 144740 20528 45457 26793 60397 145340 144740 NE MeV GPD 127 316 619 329 263 276 514 538 175 263 514 700 673 1035 244 263 487 263 860 263 1762 2969 3442 1267 263 875 978 1267 919 191 263 875 429 1824 770 1196 263 1379 1824 1824 30 0 100 0 100 0 20 0 20 0 20 0 20 0 20 0 30 0 20 0 20 0 20 0 20 0 20 0 30 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 150 0 20 0 20 0 32 0 150 0 100 0 30 0 20 0 20 0 30 0 150 0 30 0 20 0 20 0 20 0 150 0 150 0 yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes no no yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no yes no no no yes yes no no no no no no no no no no no no no no yes yes no no no yes no no no no no yes no no no no yes yes no no no no no no no no no no no no no no no no no no no no no no no no no no no no n
184. 2 118 More histories can be run to improve precision see subsection C below Because the precision is proportional to 1 N running more particles is often costly in computer time and therefore is viewed as the method of last resort for difficult problems C The Central Limit Theorem and Monte Carlo Confidence Intervals To define confidence intervals for the precision of a Monte Carlo result the Central Limit Theorem of probability theory is used stating that og lim Pri E x x lt E x BH ade No JN a 1 T Tal where a and p can be any arbitrary values and Pr Z means the probability of Z In terms of the estimated standard deviation of this may be rewritten in the following approximation for large N ES 2 2027 This crucial theorem states that for large values of N that is as N tends to infinity and identically distributed independent random variables x with finite means and variances the distribution of the X s approaches a normal distribution Therefore for any distribution of tallies an example is 2 112 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS ESTIMATION OF THE MONTE CARLO PRECISION shown in Figure 2 17 the distribution of resulting x s will be approximately normally distributed as shown in Figure 2 16 with a mean of E x If S is approximately equal to o which is valid for a statistically signific
185. 2 3890 14150 6 1998 293 6 329768 23123 150 0 yes 29063 60c 62 3890 endf60 B VI2 1989 293 6 119097 11309 20 0 yes 29063 61c 62 3890 actib B VL8 2000 77 0 348384 24556 150 0 yes 29063 62c 62 3890 actia B VL8 2000 293 6 335072 22892 150 0 yes 29063 64c 62 3890 endf66d B VL6 1997 77 0 339601 24549 150 0 yes 29063 66c 62 3890 endf66a 6 1997 2936 326281 22884 150 0 65 29065 24c 64 3700 lal50n 6 1998 293 6 285628 17640 150 0 yes 29065 60c 64 3700 endf60 B VI2 1989 293 6 118385 11801 20 0 yes 29065 61c 64 3700 actib 8 2000 77 0 304772 18575 150 0 29065 62 64 3700 actia B VI 8 2000 293 6 296916 17593 150 0 yes 29065 64c 64 3700 endf66d B VL6 1997 770 291518 18562 150 0 yes 29065 66c 64 3700 endf66a 6 1997 2936 283630 17576 150 0 Zn nat 30000 40c 64 8183 endl92 LLNL lt 1992 300 0 271897 33027 30 0 yes 30000 42c 64 8183 endl92 LLNL X lt 1992 300 0 271897 33027 30 0 yes QGa nat 31000 42c 69 1211 endl92 LLNL lt 1992 300 0 6311 219 30 0 yes 31000 50c 69 1211 rmccs B V 0 1980 293 6 7928 511 20 0 yes 31000 50d 69 1211 drmccs B V 0 1980 293 6 6211 263 20 0 yes 31000 60c 69 1211 endf60 0 1980 293 6 9228 566 20 0 yes 31000 66c 69 1211 endf66a 0 1980 293 6 14640 1130 20 0 yes Z E 33 Arsenic oe ete As 74 33074 42c 73 2889 endl92 LLNL lt 1992 300 0 55752 6851 30 0 yes G 20 10 3 05 no no no no no no no no no no
186. 2 Potassium k 2 k k kkk k 19038 30y 19039 30y 19040 30y 19041 26y 19041 30y 19042 30y 19043 30y 19044 30y 19045 30y 19046 30y Dosimetry Data Libraries for MCNP Tallies AWR 30 70800 30 97380 30 97960 31 69740 31 69700 31 97210 32 97150 33 96790 34 96900 35 96710 36 97110 33 97380 34 96890 35 96830 36 96590 37 96800 35 96750 36 96680 37 962770 38 96430 39 61910 39 96240 40 96450 41 96300 42 96570 37 96910 38 96370 39 96400 40 60990 40 96180 41 96240 42 96070 43 96160 44 96070 45 96200 Table 6 Cont Library 532dos 531405 53240 Idos 53240 Idos 532405 10 3 05 Source ENDF B V LLNL ACTL LLNL ACTL ENDF B V ENDF B V LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL ENDF B V LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL ENDF B V LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL Date 1977 lt 1983 lt 1983 1979 1977 lt 1983 lt 1983 lt 1983 lt 1983 lt 1983
187. 20 0 yes yes yes no no no no yes yes yes yes yes no no no no no no yes no no no no no no no no no yes yes yes yes yes yes yes yes yes yes yes both both both tot tot both both both both both both both tot tot tot both both tot tot both both tot tot tot tot both both both both both both both both both both both both both both both no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no yes yes yes no no no no no no no no no no no no no no no yes yes yes no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no yes no no no no no no yes yes no no no no no no no no yes no no G 35 APPENDIX G MCNP DATA LIBRARIES NEUTRON CROSS SECTION LIBRARIES ZAID 94239 554 94239 55 94239 60 94239 61 94239 64 94239 65 94239 66 94239 67 94239 68 94239 69 Pu 240 94240 42c 94240 49c 94240 50d 94240 50c 94240 60c 94240 61c 94240 65c 94240 66c 241 94241 42c 94241 49c 94241 50c 94241 50d 94241 51c 94241 51d 94241 60c 94241 61c 94241 65c 94241 66c Pu 242 94242 42c 94242 49c 94242 50c 94242 50d 94242 51c 94242 51d
188. 24 Useof COPLO bd ba i camisa Ras 27 Normalization of Energy Dependent Tally Plots 27 REFERENCES T 41 APPENDIXI PTRAC TABLES 1 APPENDIX J MESH BASED WWINP WWOUT AND WWONE FILE FORMAT scsisnssossssisescescossessncscscenseossvestasasnesesasensevacsscnsetessiassinnsiwostovavaes 1 APPENDIX XSDIR DATA DIRECTORY FILE 204 0 04 0 201 4 4400 01 00 1 10 3 05 TOC 5 Table of Contents Volume III Developer s Guide APPENDIX C INSTALLING AND RUNNING MCNP ON VARIOUS SYSTEMS 1 A NEW BUILD SYSTEM FOR MCNP FORTRAN 90 ON UNIX 1 NEW UNIX BUILD SYSTEM DESCRIPTION 2 THE UIC INSTALL UTILITY ab aaa 4 UNIX CONFIGURATION WITH INSTALL UTILITY 22224 5 UNIX CONFIGURATION WITHOUT INSTALL UTILITY 9 UNIX MODES OF OPERATION 12 Source Directory 12 Sou rce config Directory M 12 SOUFGE SrC Bo EMI Mu E M MM EM eu T 15 Sourc dataste Directory assensu 15 SOUrcedobcomim sre M RM UM EEE 16 Testimg Re gres
189. 3 263 263 8083 9131 14449 13086 9757 14446 9751 13078 10180 9794 6173 263 263 7835 7368 10902 10107 8443 10906 8440 10109 10848 10485 263 6866 263 8342 7193 11635 10833 9128 11635 9127 10829 1488 2214 1168 263 16719 24470 55623 1296 1821 959 263 15624 24518 49888 150 0 20 0 20 0 20 0 20 0 20 0 20 0 150 0 150 0 150 0 150 0 150 0 150 0 150 0 20 0 20 0 20 0 20 0 20 0 20 0 150 0 150 0 150 0 150 0 150 0 150 0 150 0 20 0 20 0 20 0 20 0 20 0 20 0 150 0 150 0 150 0 150 0 150 0 150 0 20 0 30 0 20 0 20 0 20 0 20 0 20 0 20 0 30 0 20 0 20 0 20 0 20 0 20 0 yes no yes yes yes yes yes yes yes yes yes yes yes yes no yes yes yes yes yes yes yes yes yes yes yes yes no yes yes yes yes yes yes yes yes yes yes yes yes yes no no no no no yes yes no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no yes no no no no no no yes yes yes yes yes yes yes no no no no no no yes yes yes yes yes yes yes no no no no no no yes yes yes yes yes yes no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no
190. 3 1 MGOPT card 3 125 Mm card also see Material Card 3 118 MODE card 3 24 Monte Carlo Method History 2 1 MPLOT card 3 147 MPN Card 3 120 10 3 05 MCNP MANUAL INDEX Particle card 3 134 Muir velocity Gaussian fusion energy spectrum 3 64 Multigroup Adjoint Transport Option Card 3 125 Multigroup Tables 2 24 Multipliers and modification 2 105 Multiply xM 3 4 N Neutron Absorption 2 34 2 171 Capture 2 28 2 34 Cross sections 3 118 Cutoffs 3 135 Dosimetry cross sections 2 23 Interaction data 2 16 Interactions 2 27 Spectra F 20 Thermal S a f tables 2 24 Neutron Emission Delayed 2 52 Prompt 2 52 nI also see Interpolate 3 4 nJ also see Jump 3 5 Normal surface 3 94 NOTRN card 3 137 NPS card 3 137 nR repeat 3 4 Nuclide identifier 3 118 O Output Print Tables PRINT Card 3 145 3 147 P Pair Production Detailed physics treatment 2 63 Simple physics treatment 2 58 Parentheses 3 9 3 81 3 95 Particle Designators 3 7 Index 7 MCNP MANUAL INDEX Particle Track Output History flow 2 5 D 7 Tracks 2 27 Weight 2 25 Particle Track Output PTRAC card 3 148 to 3 152 Periodic boundaries 2 7 2 13 3 31 Limitations 2 14 Perturbation PERTn Card 3 152 to 3 156 Photoelectric Effect Detailed physics treatment 2 62 Simple physics treatment 2 58 Photon Cross sections F 38 Cutoffs 3 136 Generation optional 2 31 Interaction Data 2 20 Interaction Tre
191. 3 2002 3335 101 100 S amp I 89 Unknown E amp C BM amp M 89000 04 meplib04 2002 10133 1234 100 B VL8 B VL8 B VI8 BM amp M Z 90 rere Thorium Yee xe pe 2 ee espe ese oe k kk kk ak ak akk k ak 90000 01p mcplib 1982 533 63 0 1 B IV B IV E amp C n a 90000 02p 502 1993 767 102 100 B IV 89 B IV E amp C n a 90000 03p mcplib03 2002 3341 102 100 B IV 89 B IV E amp C BM amp M 90000 04p mcplib04 2002 10565 1306 100 B VL8 B VL8 B VI8 BM amp M Z 91 RRR Protactinium 7 8 7 gt k k k kkk k k k kk k k k k kk k k 91000 01 mcplib 1982 479 54 0 015 S amp I Unknown E amp C n a 91000 02p mcplib02 1993 761 101 100 S amp I 89 Unknown E amp C n a 91000 03p 03 2002 3434 101 100 564 89 Unknown E amp C BM amp M 91000 04p mcplib04 2002 10670 1307 100 B VL8 8 8 BM amp M Z 92 Dranium EP kk k kkk 2 92000 01p meplib 1982 533 63 0 1 B IV B IV E amp C n a 92000 02p meplib02 1993 767 102 100 B IV 89 B IV E amp C n a 92000 03p mcplib03 2002 3440 102 100 B IV 89 B IV E amp C BM amp M 92000 04p mcplib04 2002 10808 1330 100 B VL8 B VL8 B VI8 BM amp M 7 93 mhi Neptunium 93000 01p mcplib 1982 479 54 0 015 S amp I Unknown E amp C n a 93000 02p meplib02 1993 761 101 100 S amp I 89 Unknown E amp C n a 93000 03p mcplib03 2002 3434 101 100 S amp I 89 Unknown E amp C BM amp M 93000 04p mcplib04 2002 11120 1382 100
192. 3 42c 231 0377 endl92 LLNL 1992 300 0 29521 2163 30 0 yes both no no no 92233 49c 231 0430 uresa B VLO 1978 300 0 47100 4601 20 0 yes both no no yes 92233 50d 231 0430 drmcecs 0 1978 293 6 4172 263 20 0 no both no no no 92233 50c 231 0430 rmccs B V 0 1978 293 6 18815 2293 20 0 both no no 92233 60c 231 0430 endf60 15 0 1978 293 6 32226 3223 20 0 yes both no no no 92233 61c 231 0430 B VLO 1978 293 6 37218 3223 20 0 yes both no yes 92233 65c 231 0430 endf66e B VLO 1978 3000 1 49260 3354 20 0 yes both no yes yes 92233 66c 231 0430 endf66c B VLO 1978 293 6 62463 4821 20 0 yes both no yes yes 92233 68c 231 0377 t16 2003 LANL T16 2003 3000 0 323539 11206 30 0 yes both no yes yes 92233 69c 231 0377 t16 2003 LANL T16 2003 293 6 441295 24290 30 0 yes both yes yes 92234 42c 232 0304 endl92 LLNL 1992 300 0 13677 149 30 0 yes both no no no 92234 49c 232 0300 uresa 0 1978 300 0 161296 22539 20 0 both no no yes 92234 50c 232 0300 endf5p B V 0 1978 293 6 89433 12430 20 0 no tot no no 92234 50d 232 0300 dre5 0 1978 293 6 4833 263 20 0 tot no no no 92234 51d 232 0300 drmccs B V 0 1978 293 6 4833 263 20 0 no tot no no no 92234 51c 232 0300 rmccs B V 0 1978 293 6 6426 672 200 no tot no no 92234 60c 232 0300 endf60 0 1978 293 6 77059 10660 17 5 no both no no no 92234 61c 232 0300 0 1978 293 6 82047 10660 175 no both no yes no 92234 65c 232 0300 endf66e B VLO 1978 3000
193. 30 0 20 0 20 0 30 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 30 0 20 0 20 0 20 0 30 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 30 0 20 0 20 0 20 0 20 0 30 0 20 0 20 0 yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes no no yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes both tot tot tot tot both both both tot tot tot tot both both both both both both tot tot both tot tot tot tot both both both both both tot tot tot both pr tot tot tot tot tot tot tot both both both both both both tot tot no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no yes yes no no no no no no yes yes yes yes yes no no no no no no no no yes yes yes no no no no no no no no no no no no no no no yes yes yes no no no no no no no no yes yes no no no no no no no yes yes yes yes no no no no no no no no no yes yes no no yes yes no yes no no no no no yes yes no no no yes yes no no no G 37 APPENDIX G MCNP DATA LIBRARIES NEUTRON CROSS
194. 3484 357 100 0 yes 1001 62c 0 9992 actia B VL8 1998 293 6 10128 688 150 0 yes 1001 66c 0 9992 endf66a 6 1998 293 6 10128 688 150 0 yes 1002 24c 1 9968 la150n 6 1997 293 6 10270 538 150 0 yes 1002 50c 1 9968 endf5p 0 1967 293 6 3987 214 20 0 1002 504 1 9968 dre5 0 1967 293 6 4686 263 20 0 yes 1002 55c 1 9968 rmccs LANL T 1982 293 6 5981 285 200 yes 1002 55d 1 9968 drmccs LANL T 1982 293 6 5343 263 20 0 yes 1002 60c 1 9968 endf60 B VLO 1967 2 293 6 2704 178 200 yes 1002 66c 1 9968 endf66a 6 1997 293 6 10270 538 150 0 yes 3 1003 42 2 9901 endl92 LLNL lt 1992 300 0 2308 52 30 0 1003 50 2 9901 rmccs 0 1965 293 6 2428 184 20 0 1003 504 2 9901 drmccs 0 1965 293 6 2807 263 20 0 no 1003 60c 2 9901 endf60 B VLO 1965 293 6 3338 180 200 no 1003 66c 2 9901 endf66a B VLO 1965 293 6 5782 389 20 0 1003 69 2 9896 16 2003 LANL T16 2001 293 6 11206 468 200 7 2 Helijum He 3 2003 42c 2 9901 endl92 LLNL 1992 300 0 1477 151 30 0 yes 2003 50d 2 9901 drmccs B V 0 1971 293 6 2612 263 20 0 no 2003 50c 2 9901 rmccs 0 1971 293 6 2320 229 20 0 2003 60 2 9890 endf60 1990 293 6 2834 342 20 0 2003 66 2 9890 endf66a 1990 293 6 9679 668 20 0 4 2004 42 3 9682 endl92 LLNL 1992 300 0 1332 49 30 0 no 2004 50c 4 0015 rmccs B V 0 1973 2
195. 4241 30 707682 31 788823 35 148180 39 604489 38 762423 39 733857 47 455774 50 503856 51 549253 54 466099 55 366466 58 426930 58 182641 62 999157 69 124270 74 211979 83 080137 90 439594 92 108263 95 106691 102 021490 105 513949 106 941685 111 442363 117 667336 130 165202 136 146809 150 657141 155 900158 Length 583 583 583 583 583 583 583 583 583 583 557 583 583 583 583 583 583 583 583 583 583 583 557 583 583 583 583 583 557 583 583 557 557 583 557 557 G 41 APPENDIX G MCNP DATA LIBRARIES MULTIGROUP DATA ZAID 67165 55m 73181 50m 74000 55m 74182 55m 74183 55m 74184 55m 74186 55m 75185 50m 75187 50m 78000 35m 79197 56m 82000 50m 83209 50m 90232 50m 91233 50m 92233 50m 92234 50m 92235 50m 92236 50m 92237 50m 92238 50m 92239 35m 93237 55m 94238 50m 94239 55m 94240 50m 94241 50m 94242 50m 95241 50m 95242 50m 95243 50m 96242 50m 96244 50m Notes G 42 1 neutron transport data for ZAIDs 6012 50m and 6000 50m are the same Neutron AWR 163 512997 179 394458 182 270446 180 386082 181 379499 182 371615 184 357838 183 365036 185 350629 193 415026 195 274027 205 437162 207 186158 230 045857 231 039442 231 038833 232 031554 233 025921 234 018959 235 013509 236 006966 236 997601 235 012957 236 005745 236 999740 237 992791 238 987218 239 980508 238 987196 239 98 1303 240 974535 239 980599 241 967311
196. 459 20 0 16000 62c 31 7888 actia B VL8 2000 293 6 160505 10272 20 0 16000 64c 317882 endf66d B VLO 1979 77 0 162138 10460 20 0 16000 66c 31 7882 endf66a 0 1979 293 6 159894 10273 20 0 16032 42c 31 6974 endl92 LLNL 1992 300 0 6623 307 30 0 16032 50c 31 6970 endf5u B V 0 1977 293 6 6789 363 20 0 16032 50d 31 6970 dre5 B V 0 1977 293 6 6302 263 20 0 16032 51 31 6970 rmccs B V 0 1977 293 6 6780 362 20 0 16032 514 31 6970 drmccs B V 0 1977 293 6 6302 263 200 16032 60c 31 6970 endf60 B VLO 1977 293 6 7025 377 200 16032 61c 31 6970 actib B VL8 2000 77 0 14930 885 20 0 16032 62c 31 6970 actia B VL8 2000 293 6 16050 993 200 16032 64c 31 6970 endf66d 0 1977 77 0 12714 885 20 0 16032 66c 31 6970 endf66a B VLO 1977 293 6 13834 993 20 0 7 17 Chlorine Cl nat 17000 42c 35 1484 endl92 LLNL 1992 300 0 12012 807 30 0 17000 50d 35 1480 dre5 0 1967 293 6 18209 263 20 0 17000 50 35 1480 endf5p B V 0 1967 293 6 23313 1499 20 0 17000 51 35 1480 rmccs B V 0 1967 293 6 21084 1375 20 0 17000 51d 35 1480 drmccs B V 0 1967 293 6 18209 263 20 0 17000 60c 35 1480 endf60 B VLO 1967 293 6 24090 1816 200 17000 64c 35 1480 endf66d 0 1967 77 0 44517 2799 20 0 17000 66 35 1480 endf66a 0 1967 293 6 45407 2888 200 17035 61c 34 6684 actib B VL8 2000 77 0 316441 7217 20 0 17035 62c 34 6684 actia B VL8 2000 293 6 311841 6987 200 17037 61c 36
197. 47675 42396 300 yes both no yes yes 92238 69c 236 0058 t16 2003 LANL T16 2003 293 6 874492 78709 30 0 yes both no yes yes 92239 35d 237 0007 drmccs LLNL lt 1985 yes 9286 263 20 0 yes pr no no no 92239 35c 237 0007 rmccsa LLNL 1985 yes 9809 394 20 0 yes pr no no no 92239 42c 237 0007 endl92 LLNL 1992 300 0 14336 205 30 0 yes both no no 92239 68c 237 0007 t16 2003 LANL T16 2000 3000 0 111013 6340 30 0 yes both no yes yes 92239 69c 237 0007 t16 2003 LANL T16 2000 293 6 125557 7956 30 0 yes both no yes yes 92240 42 237 9944 end192 LLNL lt 1992 300 0 14000 128 30 0 yes both no no no 92240 68c 237 9944 t16 2003 LANL T16 2003 3000 0 243398 11524 30 0 yes both no yes yes 92240 69c 237 9944 t16 2003 LANL T16 2003 293 6 276968 15254 30 0 yes both no yes yes 92241 68c 238 9890 t16 2003 LANL T16 2000 3000 0 117572 6309 30 0 yes both no yes yes 92241 69c 238 9890 t16 2003 LANL T16 2000 293 6 132260 7941 30 0 yes both no yes yes G 34 10 3 05 ZAID 7 93 Neptunium a 235 93235 42c Np 236 93236 42c Np 237 93237 42 93237 50 93237 50 93237 55d 93237 55c 93237 60c 93237 61c 93237 66c 93237 69 Np 238 93238 42 Np 239 93239 60 93239 66 7 94 Plutonjium aa Pu 236 94236 60c 94236 66c Pu 237 94237 42c 94237 60c 94237 66c Pu 238 94238 42c 94238 49c 94238 50d 94238 50c 94238 51c 94238 51d 94238 60c
198. 49 5170 49 5170 49 5170 49 5170 49 5170 51 4940 51 4940 51 4940 51 4940 51 4940 51 4940 52 4860 52 4860 52 4860 52 4860 52 4860 52 4860 53 4760 53 4760 53 4760 53 4760 53 4760 53 4760 Mn 55 25055 42c 54 4661 25055 50d 54 4661 25055 50c 54 4661 25055 51d 54 4661 25055 51 54 4661 25055 60 54 4661 25055 61 54 4661 25055 62 54 4661 25055 64 54 4661 25055 66 54 4661 7 26 nop Fe nat 26000 21c 26000 42c 26000 50c 26000 50d 26000 55d 26000 55c 55 3650 55 3672 55 3650 55 3650 55 3650 55 3650 endl92 drmccs rmccs lal50n endf60 actib actia endf66d endf66a lal50n endf60 actib actia endf66d endf66a lal50n endf60 actib actia endf66d endf66a 1 150 endf60 actib actia endf66d endf66a endl92 dre5 endfSu drmccs rmccs endf60 actib actia endf66d endf66a 100xs 3 192 endf5p dre5 drmccs rmccs LLNL B V 0 B V 0 6 B VI 1 B VL8 B VL8 6 6 6 B VI 1 B VL8 B VL8 6 6 6 B VI 1 8 B VL8 6 6 6 B VI 1 B VL8 B VL8 6 6 LLNL B V 0 0 B V 0 B V 0 B VLO B VL8 B VL8 5 5 LLNL 0 0 LANL T LANL T 1992 1977 1977 1997 1989 2000 200
199. 5 The result is clearly improving but does not meet the acceptable criteria for convergence This tally did not pass 3 out 10 statistical checks 2 132 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS ESTIMATION OF THE MONTE CARLO PRECISION E 44 44 M 5 54 ean 5 gt 44 4 T T T 5 o 5000 10000 15000 20006 o 2 4 5 NPS NPS 2 g g zo 5 5 d o 5000 10000 15000 20000 20 1 2 4 5 E6 NPS NPS 8 So 5 o 5000 10000 15000 20000 9 1 2 4 5 E6 NPS NPS 54 4 wu w i Slope amp 9 a a 2 5 5 amp g gt gt m 5 244 3 z 5000 10000 15000 20000 2 22 1 2 4 5 E6 NPS igure NPS When you compare the empirical point detector f x s for 14 000 and 200 million histories you see that the 14 000 history f x clearly has unsampled regions in the tail indicating incomplete f x sampling For the point detector seven decades of x have been sampled by 200 million histories 10 3 05 2 133 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VARIANCE REDUCTION compared to only three decades for 14 000 histories The largest x s occur from the extremely difficult to sample histories that have multiple small energy loss collisions close to t
200. 6 6 10 3 05 APPENDIX H FISSION SPECTRA CONSTANTS AND FLUX TO DOSE FACTORS REFERENCES Table H 2 Photon Flux to Dose Rate Conversion Factors ANSI ANS 6 1 1 1977 ICRP 21 Energy E DF E Energy E DF E MeV rem hr p cm s MeV rem hr p em2 s 6 75 7 11E 06 7 5 7 66 06 9 0 8 77 06 11 0 1 03 05 13 0 1 18 05 15 0 1 33 05 IIl REFERENCES 1 ANS 6 1 1 Working Group M E Battat Chairman American National Standard Neutron and Gamma Ray Flux to Dose Rate Factors ANSI ANS 6 1 1 1977 3666 American Nuclear Society LaGrange Park Illinois 1977 2 NCRP Scientific Committee 4 on Heavy Particles Rossi chairman Protection Against Neutron Radiation NCRP 38 National Council on Radiation Protection and Measurements January 1971 3 Committee 3 Task Group P Grande and M C O Riordan chairmen Data for Protection Against Ionizing Radiation from External Sources Supplement to ICRP Publication 15 ICRP 21 International Commission on Radiological Protection Pergamon Press April 1971 4 ASTM Committee E 10 on Nuclear Technology and Applications Characterizing Neutron Energy Fluence Spectra in Terms of an Equivalent Monoenergetic Neutron Fluence for Radiation Hardness Testing of Electronics American Society for Testing and Materials Standard E722 80 Annual Book of ASTM Standards 1980 10 3 05 H 7 H 8 10 3 05 Absorption MCNP MANUAL INDEX A Absorption
201. 6 61c 234 0180 0 1989 293 6 87807 10454 20 0 both no yes no 92236 65c 234 0180 endf66e B VLO 1989 3000 1 153474 15331 20 0 no both no yes yes 92236 66c 234 0180 endf66c 0 1989 293 6 199786 21120 200 no both no yes yes 92236 68c 234 0178 t16 2003 LANL T16 2003 3000 0 276138 15549 30 0 yes both no yes yes 92236 69c 234 0178 t16 2003 LANL T16 2003 293 6 328212 21335 30 0 yes both no yes yes 92237 42c 235 0123 endl92 LLNL 1992 300 0 13465 210 30 0 yes both no no no 92237 50c 235 0120 endf5p B V 0 1976 293 6 32445 3293 200 yes tot no no 92237 50d 235 0120 dre5 0 1976 293 6 8851 263 20 0 yes tot no no 92237 51 235 0120 rmccs B V 0 1976 293 6 10317 527 200 yes tot no no no 92237 51d 235 0120 drmccs B V 0 1976 293 6 8851 263 20 0 yes tot no no no 92237 65 235 0120 endf66e B VI2 1976 3000 1 72824 6381 20 0 yes both no yes yes 92237 66c 235 0120 endf66c B VI2 1976 293 6 87188 7977 200 yes both no yes yes 92237 68c 235 0124 t16 2003 LANL T16 2000 3000 0 120768 6401 300 yes both no yes yes 92237 69 235 0124 t16 2003 LANL T16 2000 293 6 135303 8016 30 0 yes both no yes yes 92238 11c 236 0060 endf62mt 2 1993 77 0 621385 74481 20 0 yes both no no 92238 12c 236 0060 endf62mt 2 1993 400 0 456593 53882 20 0 yes both 92238 13c 236 0060 endf62mt 2 1993 500 0 433681 51018 20 0 yes both 92238 14c 236 0060 endf62mt 2 1993 600 0 414185 48581 20 0 yes both no no
202. 60 2 1993 293 6 289975 2810 20 0 yes both no no 92235 61c 233 0250 endf6dn B VI2 1993 293 6 294963 28110 20 0 yes both no yes no 92235 64c 233 0250 endf66d 5 1997 77 0 1115810 111154 200 yes both no yes yes 92235 65c 233 0250 endf66e 5 1997 3000 1 332639 24135 20 0 yes both no yes yes 92235 66c 233 0250 endf66c 5 1997 293 6 1722105 67409 200 yes both no yes yes 92235 67c 233 0250 t16 2003 LANL T16 2003 770 1119233 111037 200 yes both no yes yes 92235 68c 233 0250 t16 2003 LANL T16 2003 3000 0 337079 24131 20 0 yes both no yes yes 92235 69c 233 0250 t16 2003 LANL T16 2003 293 6 726320 67380 200 yes both no yes yes 10 3 05 G 33 APPENDIX G MCNP DATA LIBRARIES NEUTRON CROSS SECTION LIBRARIES Table G 2 Cont Continuous Energy and Discrete Neutron Data Libraries Maintained by X 5 Library Eval Temp Length _ ZAID AWR Name Source Date words NE MeV GPD 0 CP DN UR 92236 42c 234 0178 end192 LLNL lt 1992 300 0 14595 311 30 0 yes both no no no 92236 49c 234 0180 uresa 0 1989 300 0 159074 20865 20 0 both no no yes 92236 50c 234 0180 endf5p B V 0 1978 293 6 138715 19473 200 no tot no no no 92236 50d 234 0180 dre5 0 1978 293 6 4838 263 20 0 tot no no no 92236 51c 234 0180 rmccs B V 0 1978 293 6 7302 800 20 0 no tot no no 92236 51d 234 0180 drmccs B V 0 1978 293 6 4838 263 20 0 no tot no no 92236 60c 234 0180 endf60 0 1989 293 6 82819 10454 20 0 no both no no no 9223
203. 63t endf6 3 sab2002 hortho 64t endf6 3 sab2002 hortho 65t 3 sab2002 hortho 66t 3 sab2002 Date of Processing 09 08 86 09 08 86 09 08 86 09 08 86 09 08 86 09 08 86 09 14 99 09 14 99 09 14 99 09 14 99 09 14 99 09 14 99 10 22 85 10 22 85 10 22 85 10 22 85 10 22 85 09 14 99 09 14 99 09 14 99 09 14 99 09 14 99 09 14 99 03 03 89 01 21 03 06 14 00 06 14 00 06 14 00 06 14 00 06 14 00 06 14 00 10 3 05 APPENDIX G MCNP DATA LIBRARIES S o B DATA FOR USE WITH THE MTn CARD Table G 1 Cont Thermal S o p Cross Section Libraries Temp CK 300 600 800 1200 1600 2000 294 400 600 800 1000 1200 300 400 600 800 1200 294 400 600 800 1000 1200 Num of Num of Elastic Angles Energies Data coh coh coh coh coh coh coh coh coh coh coh coh inco inco inco inco inco inco inco inco inco inco inco none none none none none none none none APPENDIX G MCNP DATA LIBRARIES 5 DATA FOR USE WITH THE MTn CARD Table G 1 Cont Thermal S o p Cross Section Libraries Library ZAID Source Name Para Hydrogen 1001 hpara 01t lanl89 therxs hpara 60t endf6 3 sab2002 hpara 6lt endf6 3 sab2002 hpara 62t endf6 3 sab2002 hpara 63t endf6 3 sab2002 hpara 64t endf6 3 sab2002 hpara 65t endf6 3 sab2002 hpara 66t endf6 3 sab2002 Deuterium in Heavy Water 1002 hwtr 01t endf5 tmccs hwtr 02t endf5 tmcces hwtr 03t en
204. 6483 actib B VL8 2000 77 0 137963 3495 20 0 17037 62c 36 6483 actia B VL8 2000 293 6 137404 3425 20 0 7 18 Argon debeleleleleleletootoloteleleloletoletolotloteleteloleloletolotoloteloteloleleletelelolot Ar nat 18000 35c 39 6048 rmccsa LLNL 1985 0 0 5585 259 20 0 18000 35d 39 6048 drmccs LLNL lt 1985 0 0 14703 263 20 0 18000 42c 39 6048 endl92 LLNL 1992 300 0 5580 152 30 0 18000 59c 39 6048 misc5xs 7 8 LANL T 1982 293 6 3473 252 20 0 G 16 10 3 05 yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no yes no no no no no no yes no no no no no no no no no no no no no no no no no no no no no no no yes yes yes yes no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no U CP DN UR no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no APPENDIX G MCNP DATA LIBRARIES NEUTRON CROSS SECTION LIBRARIES Table G 2 Cont Continuous
205. 7 28 20 30 31 32 33 34 35 36 2 202 J A Halblieb and T A Mehlhorn ITS The Integrated TIGER Series of Coupled Electron Photon Monte Carlo Transport Codes Sandia National Laboratory Report SAND 84 0573 1984 American National Standard for Programming Language Fortran Extended American National Standards Institute ANSI X3 198 1992 New York NY September 1992 E D Cashwell and C J Everett Intersection of a Ray with a Surface of Third of Fourth Degree Los Alamos Scientific Laboratory Report LA 4299 December 1969 Kinsey Data Formats and Procedures for the Evaluated Nuclear Data File ENDF Brookhaven National Laboratory Report BNL NCS 50496 ENDF 102 2nd Edition ENDF B V October 1979 J Howerton D E Cullen R C Haight M MacGregor 5 T Perkins and E F Plechaty The LLL Evaluated Nuclear Data Library ENDL Evaluation Techniques Reaction Index and Descriptions of Individual Reactions Lawrence Livermore Scientific Laboratory Report UCRL 50400 Vol 15 Part A September 1975 E D Arthur and P Young Evaluated Neutron Induced Cross Sections for Fe to 40 MeV Los Alamos National Laboratory report LA 8626 MS ENDF 304 December 1980 D Foster Jr and E D Arthur Average Neutronic Properties of Prompt Fission Products Los Alamos National Laboratory report LA 9168 MS February 1982 E D Arthur
206. 7 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS GEOMETRY A Complement Operator The complement operator provides no new capability over the intersection and union operators It is just a shorthand cell specifying method that implicitly uses the intersection and union operators The complement operator is the symbol The complement operator can be thought of as standing for not in There are two basic uses of the operator means that the description of the current cell is the complement of the description of cell n means complement the portion of the cell description in the parentheses usually just a list of surfaces describing another cell In the first of the two above forms MCNP performs five operations 1 the symbol is removed 2 parentheses are placed around 3 any intersections in n become unions 4 any unions in n are replaced by back to back parentheses which is an intersection and 5 the senses of the surfaces defining n are reversed A simple example is a cube We define a two cell geometry with six surfaces where cell 1 is the cube and cell 2 is the outside world 1 0 12 34 56 2 0 1 2 3 24 5 6 Note that cell 2 is everything in the universe that is not in cell 1 or 2 081 The form n is not allowed it is functionally available as the equivalent of n CAUTION Using the complement operator can destroy some of the necessary conditions for some cell volume and surface ar
207. 7 R can be written for large N as 5 1 2 d 1 2 R zu cT ES 1 2 22b N x N 2 2 15 Several important observations about the relative error can be made from Eq 2 19b First if all the x s are nonzero and equal R is zero Thus low variance solutions should strive to reduce the spread in the x s If the x s are all zero R is defined to be zero If only one nonzero score is made approaches unity as becomes large Therefore for x s of the same sign S can never be greater than x because never exceeds unity For positive and negative can exceed unity The range of R values for x s of the same sign is therefore between zero and unity 10 3 05 2 113 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS ESTIMATION OF THE MONTE CARLO PRECISION To determine what values of R lead to results that can be stated with confidence using Eqs 2 6 consider Eq 2 19b fora difficult problem in which nonzero scores occur very infrequently In this case N 2 1 N 2 2 1 2 23a For clarity assume that there are n out of N n N nonzero scores that are identical and equal to x With these two assumptions R for difficult problems becomes 241 2 ne 2 23b This result is expected because the limiting form of a binomial distribution with infrequent nonzero scores and large N is the Poisson distribution which is the form in Eq 2 20b used in detector co
208. 70740 5105 82208 66c 206 1900 endf66c B VL6 X 1996 293 6 344865 6634 209 83209 24c 207 1850 lal50n LANL 1999 293 6 249386 11047 83209 42c 207 1851 endl92 LLNL 1992 300 0 20921 1200 83209 50c 207 1850 5 B V 0 1980 293 6 14939 1300 83209 50d 207 1850 dre5 B V 0 1980 293 6 7516 263 83209 51d 207 1850 drmccs B V 0 1980 293 6 7516 263 83209 51 207 1850 rmccs B V 0 1980 293 6 13721 1186 83209 60c 207 1850 endf60 B VLO 1989 293 6 100138 8427 83209 66c 207 1850 endf66c B VI 3 1989 293 6 161302 10906 7 90 Thorium 8 a Ea Ea aE of o AC CR AOAC kokk 230 90230 60c 228 0600 endf60 0 1977 293 6 35155 5533 90230 66c 228 0600 endf66c 0 1977 293 6 64761 8428 Th 23 90231 42c 229 0516 endl92 LLNL 1992 300 0 15712 187 232 90232 42c 230 0447 endl92 LLNL 1992 300 0 109829 13719 90232 48c 230 0400 uresa 16 B VLO 1977 300 0 305942 41414 90232 50d 230 0400 dre5 B V 0 1977 293 6 11937 263 90232 50c 230 0400 endfSu B V 0 1977 293 6 152782 17901 90232 51d 230 0400 drmccs B V 0 1977 293 6 11937 263 90232 51c 230 0400 rmccs B V 0 1977 293 6 17925 1062 90232 60c 230 0400 endf60 0 1977 293 6 127606 16381 90232 61c 230 0400 endf6dn 0 1977 293 6 132594 16381 90232 65 230 0400 endf66e 0 1977 3000 1 238295 25915 90232 66c 230 0400 endf66c B VLO 1977 2936 362871 41487 Th 233 90233 42c 231 0396 endl92 LLNL 1992 300 0 16015 206 Z 91 k KK
209. 76 65c 71176 66c G 28 167 4830 173 4380 173 4380 174 4300 174 4300 Library Name endf5u dre5 misc5xs 7 14 endf60 endf66e endf66b endfSu dre5 misc5xs 7 14 endf60 endf66b dre5 endfSu misc5xs 7 14 endf60 endf66e endf66b dre5 endfSu misc5xs 7 14 endf60 endf66b dre5 endfSu misc5xs 7 14 endf60 endf66b rmccsa drmccs endl92 newxs newxsd endf60 endf66b misc5xs 7 endf66e endf66b endf66e endf66b Source B V 0 B V 0 B V 0 T 0 B VLO 0 B V 0 B V 0 B V 0 T 0 0 0 B V 0 B V 0 T 0 B VLO 0 0 0 B V 0 T 0 0 B V 0 B V 0 B V 0 T 0 0 LLNL LLNL LLNL LANL T LANL T B VLO 5 LANL T 0 B VLO B VLO B VLO Table G 2 Cont Eval Date 1977 1977 1986 1977 1977 1977 1977 1977 1986 1977 1977 1977 1977 1986 1977 1977 1977 1977 1977 1986 1977 1977 1977 1977 1986 1977 1977 1985 1985 1992 1986 1986 1988 1988 1986 1967 1967 1967 1967 Temp Length words 293 6 44965 293 6 6528 293 6 54346 293 6 61398 3000 1 62954 293 6 106795 293 6 37371 293 6 6175 293 6 44391 293 6 42885 293 6 79827 293 6 6346 293 6 38975 293 6 47271 293 6 56957 3000 1 71857 293 6 99199 293 6 5811 293 6 95876 293 6 113916 293 6 59210 2903 6 152895 293 6 5030 293 6 53988 293 6 65261 293 6
210. 760 53 4760 53 4760 53 4760 55 4540 55 4540 55 4540 55 4540 55 4540 55 4540 56 4460 56 4460 56 4460 56 4460 56 4460 56 4460 57 4360 57 4360 57 4360 57 4360 57 4360 58 4269 58 4269 58 4269 58 4269 58 4269 58 4269 58 4269 Ni nat 28000 42c 28000 50c 28000 50d Ni 58 28058 24c 28058 42c 28058 60c 28058 61c 28058 62c 28058 64c 28058 66c Ni 60 28060 24c 28060 60c 28060 61c 28060 62c 28060 64c 28060 66c 58 1957 58 1826 58 1826 57 4380 57 4376 57 4380 57 4380 57 4380 57 4380 57 4380 59 4160 59 4160 59 4160 59 4160 59 4160 59 4160 Library Name lal50n endf60 actib actia endf66d endf66a lal50n endf60 actib actia endf66d endf66a 1 150 endf60 actib actia endf66d endf66a endf60 actib actia endf66d endf66a endl92 dre5 endfSu drmccs rmccs endf60 endf66a endl92 rmccs drmccs lal50n endl92 endf60 actib actia endf66d endf66a lal50n endf60 actib actia endf66d endf66a Source 6 B VI 1 8 B VL8 6 6 6 B VI 1 B VL8 B VL8 6 6 6 B VI 1 B VL8 B VL8 6 6 B VI 1 B VL8 B VL8 5 5 LLNL 0 0 B V 0 B V 0 B VI2 B VI2 LLNL B V 0 B V 0 6 LLNL B VI 1 8 B VL8 6 6 6 B VI 1 B VL8 B VL8 6 6 APPENDIX MCNP DATA LIBRARIES NEUTRON
211. 8 05 7 4 5 0E 01 9 26E 05 11 0 7 14 05 11 0 1 0 1 32E 04 11 0 1 18 04 10 6 2 0 1 43 04 9 3 2 5 1 25 04 9 0 5 0 1 56 04 8 0 1 47 04 7 8 7 0 1 47 04 7 0 10 0 1 47 04 6 5 1 47 04 6 8 14 0 2 08 04 7 5 20 0 2 27 04 8 0 1 54 04 6 0 Extracted from American National Standard ANSI ANS 6 1 1 1977 with permission of the publisher the American Nuclear Society 10 3 05 H 5 APPENDIX H FISSION SPECTRA CONSTANTS AND FLUX TO DOSE FACTORS FLUX TO DOSE CONVERSION FACTORS Table H 2 Photon Flux to Dose Rate Conversion Factors ANSI ANS 6 1 1 1977 ICRP 21 Energy E DF E Energy E DF E MeV rem hry p cm s MeV rem hr p cm s 0 01 3 96E 06 0 01 2 78E 06 0 03 5 82E 07 0 015 1 11E 06 0 05 2 90E 07 0 02 5 88E 07 0 07 2 58E 07 0 03 2 56E 07 0 1 2 83E 07 0 04 1 56E 07 0 15 3 79 07 0 05 1 20 07 0 2 5 01 07 0 06 1 11 07 0 25 6 31 07 0 08 1 20 07 0 3 7 59 07 0 1 1 47E 07 0 35 8 78E 07 0 15 2 38E 07 0 4 9 85E 07 0 2 3 45E 07 0 45 1 08E 06 0 3 5 56E 07 0 5 1 17E 06 0 4 7 69 07 0 55 1 27 06 0 5 9 09 07 0 6 1 36 06 0 6 1 14 06 0 65 1 44 06 0 8 1 47 06 0 7 1 52 06 1 1 79 06 0 8 1 68 06 1 5 2 44 06 1 0 1 98 06 2 3 03E 06 1 4 2 51E 06 3 4 00E 06 1 8 2 99E 06 4 4 76 06 2 2 3 42E 06 5 5 56E 06 2 6 3 82E 06 6 6 25E 06 2 8 4 01E 06 8 7 69 06 3 25 4 41E 06 10 9 09E 06 3 75 4 83E 06 4 25 5 23E 06 4 75 5 60 06 5 0 5 80E 06 5 25 6 01E 06 5 75 6 37E 06 6 25 6 74 0
212. 856 293 6 23654 3000 1 51446 293 6 61726 300 0 32579 293 6 42084 293 6 9971 293 6 12374 293 6 997 300 0 168924 300 0 173822 3000 1 162566 2936 267137 3000 0 163034 293 6 267605 10 3 05 E max NE MeV GPD 263 10318 26847 26847 83969 29320 63868 83969 29320 63868 16626 41596 263 6549 15676 15676 29451 41912 203 17753 3744 263 623 263 8112 8112 9145 18196 4287 14922 7636 263 728 263 7896 7896 11409 15167 745 4452 6413 9436 3695 6450 7931 2011 4420 263 713 263 13556 13556 8011 19630 8020 19639 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 30 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 30 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 30 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 30 0 20 0 20 0 20 0 20 0 20 0 20 0 30 0 20 0 20 0 20 0 20 0 30 0 30 0 30 0 30 0 30 0 30 0 yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes no no no yes yes yes yes yes yes yes yes yes yes yes CP DN UR both no no both no both no no both no yes both no yes both no yes both no yes both no yes both no yes both no yes both no both no both no both no both no both no yes both no yes both no yes both no
213. 8855 2 113 376 02 8 where is the fine structure constant is the rest mass of the electron and v c MCNP now follows the recommendation of Seltzer and the implementation in the Integrated TIGER Series by using the slightly modified form 1 y 2 3 2 t zz n 3 40 885p where 1 is the electron energy in units of electron rest mass The multiplicative factor in the final term is an empirical correction which improves the agreement at low energies between the factored cross section and the more accurate partial wave cross sections of Riley 7 Bremsstrahlung When using data from the el library for the sampling of bremsstrahlung photons MCNP relies primarily on the Bethe Heitler Born approximation results that have been used until rather recently in ETRAN A comprehensive review of bremsstrahlung formulas and approximations relevant to the present level of the theory in MCNP can be found in the paper of Koch and Motz Particular prescriptions appropriate to Monte Carlo calculations have been developed by Berger and Seltzer For the ETRAN based codes this body of data has been converted to tables including bremsstrahlung production probabilities photon energy distributions and photon angular distributions For data tables on the e103 library the production cross section for bremsstrahlung photons and energy spectra are from the evaluation by Seltzer and Berger 86 87 We sum
214. 9 3 124 3 132 3 143 Default Values INP File 3 7 Index 4 Electron Transport 2 67 Defaults Card 3 157 Delayed Neutron Data G 11 Density Atomic 3 9 Dependent source distribution card 3 65 Detailed physics 2 3 2 7 2 57 3 129 D 8 Treatment 2 59 Detectors Diagnostics card 3 108 Point 3 82 Reflecting white periodic surfaces 2 101 Ring 3 82 S o p thermal treatment 2 104 Tallies 2 5 D 6 F5 tallies 2 80 3 82 Dimension Declarators 3 30 Direct vs total contribution 2 104 Direction Biasing 2 153 Discrete Reaction Cross Section Card 3 121 Discrete Reaction data 2 16 Doppler Broadening Neutron 2 29 Photon 2 61 Dose Energy Card 3 99 Dose Function Card 3 99 DRXS Card 3 121 DSn Card 3 65 Dump cycle 3 139 DXC Card 3 51 DXTRAN 2 12 2 156 to 2 163 Contribution Card DXC 3 51 Sphere 2 6 D 7 D 8 Warnings 3 74 DXT card 3 110 E Elastic Inelastic Scattering 2 35 Elastic cross section adjusting 2 29 Energy from elastic scattering 2 39 Electron Cutoffs 3 136 Interaction data 2 23 Electron Transport 2 67 Angular Deflections 2 76 Bremsstrahlung 2 77 Condensed Random Walk 2 69 Energy Straggling 2 72 10 3 05 Electrons from photons 2 57 Knock On Electrons 2 79 Multigroup 2 79 Steps 2 68 Stopping Power 2 70 Electrons from photons 2 57 Elements 3 118 ELPT Card 3 136 EMAX 3 130 EMn Card 3 100 En card 3 92 Emission Laws 2 41 Energy Biasing 3 5
215. 92 300 0 43559 5400 30 0 yes Au 197 79197 50d 195 2740 dre5 B V 0 1977 293 6 4882 263 20 0 no 79197 50c 195 2740 endf5p B V 0 1977 293 6 139425 22632 20 0 no 79197 55c 195 2740 rmccsa LANL T 1983 4 203 6 134325 17909 20 0 yes 79197 55d 195 2740 drmccs LANL T 1983 4 293 6 7883 263 20 0 yes 79197 56d 195 2740 newxsd LANL T 1984 293 6 38801 263 20 0 yes 79197 56c 195 2740 newxs LANL T 1984 203 6 122482 11823 30 0 yes 79197 60c 195 2740 endf60 1984 293 6 161039 17724 30 0 yes 79197 66c 195 2740 endf66c 1984 293 6 377905 39417 30 0 yes Z 280 Mercury spese sk sje sje ke te ke ole sb zl sk sk oe oe ke obe ole ob obe ok ok oj oe oe de ode obe obe ok 2 ok ok ok obe ke aK ok ok ok ok ok ok ok Hg nat 80000 40c 198 8668 endl92 LLNL lt 1992 300 0 29731 2507 30 0 yes 80000 42c 198 8668 endl92 LLNL X lt 1992 300 0 29731 2507 30 0 yes 80196 24c 194 2820 lal50n LANL 1998 293 6 153206 1690 150 0 yes 80198 24c 196 2660 lal50n LANL 1998 293 6 172481 3205 150 0 yes 80199 24c 197 2590 lal50n LANL 1998 203 6 173336 4126 150 0 yes Hg 200 80200 24c 198 2500 lal50n LANL 1998 293 6 192339 2560 150 0 yes 80201 24c 199 2440 lal50n LANL 1998 293 6 166179 3492 150 0 yes Hg 202 80202 24c 200 2360 lal50n LANL 1998 203 6 154736 1887 150 0 yes Hg 204 80204 24c 202 2210 lal50n LANL 1998 203 6 140754 832 150 0 yes Pb nat 82000 42c 205 4200 endl92 LLNL lt 1992 300 0 270244 18969 30 0 yes 82000 50d 205 4300 drmccs B
216. 93 6 3061 345 20 0 no 2004 50d 4 0015 drmccs B V 0 1973 293 6 2651 263 20 0 no 2004 60c 4 0015 endf60 0 1973 293 6 2971 327 20 0 2004 62 3 9682 B VI 8 1973 293 6 5524 588 20 0 no 2004 66c 3 9682 endf66a B VI 0 X 1973 293 6 5524 588 20 0 no 3006 42c 5 9635 endl92 LLNL 1992 300 0 7805 294 30 0 yes 3006 50c 5 9634 rmccs B V 0 1977 293 6 9932 373 20 0 yes 3006 50d 5 9634 drmccs B V 0 1977 293 6 8716 263 200 yes 3006 60c 5 9634 endf60 1989 293 6 12385 498 200 yes 3006 66c 5 9634 endf66a 1989 293 6 28012 870 20 0 yes 3007 42c 6 9557 endl92 LLNL lt 1992 300 0 5834 141 30 0 yes 3007 50d 6 9557 dre5 B V 0 1972 293 6 4935 263 20 0 yes 3007 50c 6 9557 endf5p 0 1972 293 6 4864 343 20 0 3007 55 6 9557 rmccs B V 2 1979 293 6 13171 328 200 yes 3007 55d 6 9557 drmccs B V 2 1979 293 6 12647 263 20 0 yes 3007 60c 6 9557 endf60 B VLO 1988 293 6 14567 387 200 yes 3007 66c 6 9557 endf66a B VLO 1988 293 6 19559 677 20 0 yes G 12 10 3 05 no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no yes no no no no no yes yes yes no no no no no yes no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no
217. 96243 65c 240 9730 96243 66c 240 9730 Cm 244 96244 42c 241 9661 96244 49c 241 9660 96244 50d 241 9660 96244 50c 241 9660 96244 51d 241 9660 96244 51c 241 9660 96244 60c 241 9660 96244 65c 241 9660 96244 66c 241 9660 Cm 245 96245 42c 242 9602 96245 60c 242 9600 96245 61c 242 9600 96245 65c 242 9600 96245 66c 242 9600 Cm 246 96246 42c 243 9534 96246 60c 243 9530 96246 66c 243 9530 Library Name Source endl92 LLNL endf5u B V 0 dre5 B V 0 drmccs B V 0 rmccs B V 0 endf66e endf66c endl92 LLNL endfSu B V 0 dre5 B V 0 drmccs B V 0 rmccs B V 0 endf60 0 endf6dn 0 endf66e B VI 5 endf66c B VL5 t16 2003 ENDF B VL5 t16 2003 ENDF B VL5 Curium endf60 0 endf66c 0 endl92 LLNL endfSu B V 0 dre5 B V 0 drmccs B V 0 rmccs 0 endf60 0 endf6dn 0 endf66e 0 endf66c 0 endl92 LLNL endf60 B VLO endf66e B VLO endf66c 0 endl92 LLNL uresa 0 dre5 B V 0 endfSu B V 0 drmccs 0 rmccs B V 0 endf60 0 endf66e 0 endf66c 0 endl92 LLNL endf60 2 endf6dn B VI 2 endf66e B VI 2 endf66c 2 endl92 LLNL endf60 B VI 2 endf66c B VI 2 APPENDIX G MCNP DATA LIBRARIES NEUTRON CROSS SECTION LIBRARIES Table G 2 Cont Continuous Energy and Discrete Neutron Data Libraries Maintained by X 5 Eval Date 1992 1978 1978 1978 1978 1978 1978 1992
218. 99 65c 98 1500 endf66e 0 1978 3000 1 67583 8545 20 0 no no no no yes 43099 66c 98 1500 endf66b B VLO 1978 293 6 90039 11753 20 0 no no no no yes 22 10 3 05 APPENDIX G MCNP DATA LIBRARIES NEUTRON CROSS SECTION LIBRARIES Table G 2 Cont Continuous Energy and Discrete Neutron Data Libraries Maintained by X 5 Library Eval Temp Length Emax ZAID AWR Name Source Date K words NE MeV GPD 7 44 RS RIOR Ruthenium kkk kk Ru 101 44101 50c 100 0390 kidman B V 0 1980 293 6 5299 543 20 0 no Ru 103 44103 50c 102 0220 kidman B V 0 1974 293 6 3052 235 20 0 no 7 45 Rhodium OH I HO 45103 50d 102 0210 0 1978 293 6 4663 263 20 0 45103 50 102 0210 0 1978 293 6 18870 2608 20 0 45103 65 102 0210 endf66e 0 1978 3000 1 83883 10715 20 0 45103 66c 102 0210 endf66b 0 1978 2936 116685 15401 20 0 Rh 105 45105 50c 104 0050 kidman B V 0 1974 293 6 1591 213 20 0 no 72 45 Average fission product from Uranium 235 U 235 fp 45117 90d 115 5446 LANL T 1982 293 6 9507 263 20 0 yes 45117 90c 115 5446 rmccs LANL T 1982 293 6 10314 399 20 0 yes 7 46 Reese Palladium oook Pd 102 46102 66c 101 0302 endf66b 5 1996 2936 148683 659 30 0 Pd 104 46104 66c 103 0114 endf66b B VI 5 1996 293 6 155873 1197 30 0 yes
219. ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL 1978 1983 1983 1983 1983 1983 1983 1983 1983 Z 93 Neptunium FKK K K K K K K K K K K K K 93237 30y 237 04800 LLNL ACTL 1983 Z 2094 FRR Hi ae ae oie oe ae he ie hee ie ey CO PUL he he k k k k k akk 94237 30y 94238 30y 94239 30y 94240 30y 94241 30y 94242 30y 94243 30y G 72 237 04800 238 05000 239 05200 240 05400 241 05700 242 05900 243 06200 Idos 10 3 05 LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL 1983 1983 1983 1983 1983 1983 1983 Length 409 551 421 421 441 209 599 347 561 37 2861 361 629 ZAID 7 295 Americium k k k k kk oe he kk k k k 95241 30y 95242 30y 95243 30y Z 96 FOK K K K K K K K K K KK K K K K K Curium 96242 30 96243 30 96244 30y 96245 30y 96246 30y 96247 30y 96248 30y Z 209 Berkelim 87 7 2 k 2 k k k kkk 97249 30y 7 298 Californium 98249 30 98250 30 98251 30 98252 30 AWR 241 05700 242 06000 243 06100 242 05900 243 06100 244 06300 245 06500 246 06700 247 07000 248 07200 249 07500 249 07500 250 07600 251 08000 252 08200
220. ANL T16 LANL T16 LANL T16 LLNL B VI2 0 0 2 2 B VI2 B VI2 LLNL B VI3 0 0 B V 0 0 B VI 1 B VI 1 3 LLNL B VLO 0 0 B V 0 0 0 0 0 0 LLNL 2 B VI2 B VI2 0 B VLO B VLO LLNL 0 0 B V 0 B V 0 LANL T LANL T B VL3 X B VL3 X LANL T16 LANL T16 Table G 2 Cont Continuous Energy and Discrete Neutron Data Libraries Maintained by X 5 Eval Date 1983 1983 1993 1993 1997 1997 1997 2003 2003 2003 lt 1992 1986 1977 1977 1986 1986 1986 1986 lt 1992 1994 1977 1977 1977 1977 1988 1988 1994 1994 lt 1992 1978 1978 1978 1978 1978 1978 1978 1978 1978 lt 1992 1976 1976 1976 1978 1978 1978 lt 1992 1978 1978 1978 1978 1994 1994 1994 1994 2003 2003 Temp Length K words 293 6 20727 293 6 102099 203 6 283354 293 6 288252 77 0 866231 3000 1 374390 293 6 685322 77 0 887458 3000 0 395617 293 6 706549 300 0 198041 300 0 341542 293 6 9569 293 6 58917 2936 133071 2936 137969 3000 1 283740 2936 395889 300 0 14108 300 0 155886 293 6 38601 293 6 11575 293 6 13403 293 6 11575 293 6 76453 293 6 81351 3000 1 104019 203 6 185478 300 0 48688 300 0 130202 293 6 71429 293 6 12463 293 6 15702 293 6 12463 293 6 73725 293 6 78623 3000 1 123314 203 6 157136 300 0 20253 293 6 45142 3000 1 70649 293 6 97
221. Although the analog Monte Carlo model is the simplest conceptual probability model there are other probability models for particle transport that estimate the same average value as the analog Monte Carlo model while often making the variance uncertainty of the estimate much smaller than the variance for the analog estimate This means that problems that would be impossible to solve in days of computer time with analog methods can be solved in minutes of computer time with nonanalog methods A nonanalog Monte Carlo model attempts to follow interesting particles more often than uninteresting ones An interesting particle is one that contributes a large amount to the quantity or quantities that needs to be estimated There are many nonanalog techniques and all are meant to increase the odds that a particle scores contributes To ensure that the average score is the same in the nonanalog model as in the analog model the score is modified to remove the effect of biasing changing the natural odds Thus if a particle is artificially made q times as likely to execute a given random walk then the particle s score is weighted by multiplied by 1 4 The average score is thus preserved because the average score is the sum over all random walks of the probability of a random walk multiplied by the score resulting from that random walk A nonanalog Monte Carlo technique will have the same expected tallies as an analog technique if the expe
222. B VL8 B VL8 B VI8 BM amp M Z 94 Plutonium kk ek kk ok ok ok ok ok 2s 2 2 fs 94000 01p meplib 1982 533 63 0 1 B IV B IV E amp C n a 94000 02p meplib02 1993 767 102 100 B IV 89 B IV E amp C n a 94000 03p mcplib03 2002 3341 102 100 B IV 89 B IV E amp C BM amp M 94000 04p mcplib04 2002 10451 1287 100 B VL8 8 8 BM amp M Z 95 Americium BEA kk kkk k kkk k kk kk k k k 95000 04p mcplib04 2002 10640 1302 100 8 B VL8 B VI8 amp Z 96 Curium 8 EP i k kkk kkk kkk kkk kkk kk k k k k kk k k k k kk k 96000 04p mcplib04 2002 10421 1249 100 B VL8 B VI8 8 BM amp M 7 97 Berkeljum ak k k akak kak k k ak k kak k k ak kk k k k k 97000 04p mcplib04 2002 10478 1275 100 B VL8 B VI 8 8 BM amp M Z 98 Californium 98000 04p mcplib04 2002 10634 1301 100 B VL8 B VL8 B VI8 BM amp M G 56 10 3 05 APPENDIX G MCNP DATA LIBRARIES PHOTOATOMIC DATA Table G 4 Cont Continuous Energy Photoatomic Data Libraries Maintained by X 5 Library Release Length Emax CS FF Fluor CDBD ZAID Name Date Words GeV Source Source Source Source Z 99 Einsteinium 99000 04p mcplib04 2002 11126 1383 100 B VL8 B VL8 B VI8 BM amp M Z 100 Fermium
223. BM amp M Z 56 Barium 56000 01p mcplib 1982 497 57 0 1 B IV B IV E amp C n a 56000 02p mcplib02 1993 731 96 100 B IV 89 B IV E amp C n a 56000 03p mcplib03 2002 2513 96 100 B IV 89 B IV E amp C BM amp M 56000 04p mcplib04 2002 8465 1088 100 B VL8 8 8 10 3 05 APPENDIX G MCNP DATA LIBRARIES PHOTOATOMIC DATA Table G 4 Cont Continuous Energy Photoatomic Data Libraries Maintained by X 5 Library Release Length Emax CS FF Fluor CDBD ZAID Name Date Words GeV Source Source Source Source Z 57 Lanthanum 57000 01p mcplib 1982 497 57 0 1 B IV B IV E amp C n a 57000 02p meplib02 1993 731 96 100 B IV 89 E amp C n a 57000 03p mcplib03 2002 2612 96 100 B IV 89 B IV E amp C BM amp M 57000 04p mcplib04 2002 8744 1118 100 B VL8 8 B VI8 BM amp M Z 58 KKK KK KKK Cerium 58000 01p mcplib 1982 497 57 0 1 B IV B IV E amp C n a 58000 02p meplib02 1993 731 96 100 B IV 89 E amp C n a 58000 03p mcplib03 2002 2711 96 100 B IV 89 B IV E amp C BM amp M 58000 04p mcplib04 2002 9173 1173 100 B VL8 B VI8 B VI8 BM amp M Z 59 Praseodymium 59000 01p mcplib 1982 497 57 0 1 B IV B IV E amp C n a 59000 02p mcplib02 1993 731 96 100 B IV 89 E amp C n a 59000 03p mcplib03 2002 2612 96 100 B IV 89 B IV E amp C BM amp M 59000 04p mcplib04 2002 8750 1119 100 B VL8
224. CROSS SECTION LIBRARIES Table G 2 Cont Continuous Energy and Discrete Neutron Data Libraries Maintained by X 5 Eval Temp Date K 1996 293 6 1989 293 6 2000 77 0 2000 293 6 1996 77 0 1996 293 6 1996 293 6 1989 293 6 2000 77 0 2000 293 6 1996 77 0 1996 293 6 1996 293 6 1989 293 6 2000 77 0 2000 293 6 1996 77 0 1996 293 6 1989 293 6 2000 77 0 2000 293 6 1989 77 0 1989 293 6 lt 1992 300 0 1977 293 6 1977 293 6 1977 293 6 1977 293 6 1992 293 6 1992 293 6 lt 1992 300 0 1977 293 6 1977 293 6 1997 293 6 lt 1992 300 0 1989 293 6 2000 77 0 2000 293 6 1997 77 0 1997 293 6 1997 293 6 1991 293 6 2000 77 0 2000 293 6 1997 77 0 1997 293 6 10 3 05 Length words 311741 121631 318575 311639 317271 310335 461888 174517 475976 466257 468162 458443 315349 133995 319262 318268 316191 315197 93450 169389 165829 165636 162076 119231 11769 117075 11769 28355 186618 266952 44833 139913 21998 613673 38930 172069 630981 617974 623330 610483 408148 110885 424742 407398 420274 403014 E max NE MeV GPD 19323 10701 20129 19262 20129 19262 25792 11618 26821 25606 26821 25606 14285 7606 14390 14266 14390 14266 6788 11556 11111 11556 11111 13098 263 14502 263 1928 11838 19759 3116 8927 263 39258 4914 16445 40646 39020 40632 39026 21448 10055 22574 21131 22569 21133 150 0 20 0 150 0 150 0 150 0
225. Carlo Transport Codes Version 3 0 IEEE Transactions on Nuclear Science Volume 39 pp 1025 1030 1992 J Adams Electron Upgrade for MCNP4B Los Alamos National Laboratory internal memorandum X 5 RN U 00 14 May 25 2000 available URL http www xdiv lanl gov PROJECTS DATA nuclear pdf X 5 RN 00 14 pdf J U Koppel and D H Houston Reference Manual for ENDF Thermal Neutron Scattering Data General Atomics report GA 8774 also revised and reissued as ENDF 269 by the National Nuclear Data Center at the Brookhaven National Laboratory July 1978 Robert E MacFarlane Cold Moderator Scattering Kernals Advanced Neutron Sources 1988 Proceedings of the 10th Meeting of the International Collaboration on Advanced Neutron Sources ICANS X held at Los Alamos 3 7 October 1986 Institute of Physics Conferences Series Number 97 p 157 Institute of Physics Bristol and New York 1988 E MacFarlane Cold Moderator Scattering Kernals International Workshop on Cold Neutron Sources March 5 8 1990 Los Alamos New Mexico Los Alamos National Laboratory report LA 12146 C August 1991 E MacFarlane New Thermal Neutron Scattering Files for ENDF B VI Release 2 Los Alamos National Laboratory report LA 12639 MS also released as ENDF 356 by the National Nuclear Data Center at the Brookhaven National Laboratory August 1994 R C Little Summary Documentation for the 100XS Neutron Cross Section Libra
226. DIX G MCNP DATA LIBRARIES MULTIGROUP DATA MGXSNP A Coupled Neutron Photon Multigroup Data Library Neutron AWR 13 882849 14 871314 15 857588 18 835289 22 792388 24 096375 26 749887 27 844378 30 707833 31 697571 35 148355 39 605021 38 762616 39 734053 47 455981 50 504104 51 549511 54 466367 55 366734 58 427218 58 182926 62 999465 69 124611 74 278340 71 251400 79 230241 81 210203 82 202262 83 191072 85 173016 90 440039 92 108717 95 107162 102 021993 115 544386 117 525231 106 941883 105 987245 107 969736 111 442911 115 995479 228 025301 228 025301 130 171713 136 721230 150 654333 149 623005 151 608005 155 898915 Length 3501 2743 3346 3261 2982 3802 3853 3266 2123 2185 2737 2022 2833 3450 3015 2775 3924 2890 4304 2889 3373 2803 2084 2022 2108 2257 2312 2141 2460 2413 2466 2746 1991 2147 2709 2629 2693 2107 1924 1841 1929 1382 1413 1929 2115 1933 2976 2691 1929 10 3 05 ZAID 7000 01g 8000 01g 9000 01g 11000 01g 12000 01g 13000 01g 14000 01g 15000 01g 16000 01g 17000 01g 18000 01g 19000 01g 20000 01g 22000 01g 23000 01g 24000 01g 25000 01g 26000 01g 27000 01g 28000 01g 29000 01g 31000 01g 33000 01g 36000 01g 40000 01g 41000 01g 42000 01g 45000 01g 46000 01g 47000 01g 48000 01g 50000 01g 54000 01g 56000 01g 63000 01g 64000 01g Photon AWR 13 886438 15 861942 18 835197 22 792215 24 096261 26 749756 27 84
227. E gt 2 ioo where x is a positive real number specifying the line of integration For purposes of sampling is negligible for lt 4 so that this range is ignored B rsch Supan originally tabulated in the range 4 lt lt 100 and derived for the range gt 100 the asymptotic form W tT in terms of the auxiliary variable w where wnwey 3 Recent extensions of B rsch Supan s tabulation have provided a representation of the function in the range 4 lt 100 in the form of five thousand equally probable bins in In MCNP the boundaries of these bins are saved in the array eqlm mlam where mlam 5001 Sampling from this tabular distribution accounts for approximately 98 96 of the cumulative probability for For the remaining large A tail of the distribution MCNP uses the approximate form A w which is easier to sample than w 2 1 but is still quite accurate for gt 100 Blunck and Leisegang have extended Landau s result to include the second moment of the expansion of the cross section Their result can be expressed as a convolution of Landau s distribution with a Gaussian distribution pre F s A fis cA ay E p 26 Blunck and Westphal provided a simple form for the variance of the Gaussian obw 10eV wk 10 3 05 2 73 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS Subsequently C
228. ER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CRITICALITY CALCULATIONS In a fixed source MCNP problem the net multiplication M is defined to be unity plus the gain in neutrons from fission plus the gain G from nonfission multiplicative reactions Using neutron weight balance creation equals loss M 1 G G WoW 2 30 where W is the weight of neutrons escaped per source neutron and W is the weight of neutrons captured per source neutron In a criticality calculation fission is treated as an absorptive process the corresponding relationship for the net multiplication is then M 1 G 231 where the superscript o designates results from the criticality calculation and Wr is the weight of neutrons causing fission per source neutron Because k is the number of fission neutrons produced in a generation per source neutron we can also write k W 2 32 where v is the average number of neutrons emitted per fission for the entire problem Making same assumptions as above for the fixed source used in the standard MCNP calculation and using equations 2 26 2 27 and 2 28 we obtain 25122 eff eff or by using 2 28 and 2 29 1 Tx k eff Dien the nonfission multiplicative reactions 1 This implies that kp can be approximated by eff from an appropriate Fixed Source calculation x ERE 2 33 koe ef
229. GA Hills 0 or 1 s t FA B t t Thus finding the equation of a curve to be plotted is a matter of finding the QM matrix given the PL matrix and the coefficients of the surface Any surface in MCNP except for tori can be readily written as Ax By Cc Dxy Eyz Gxt Hy Jz K 0 or in matrix form as G 2 H 2 1 2 G 2 2 F 2 H 2D 2 B E 2 JZ2 F72 E 2 1 x y z HO nm or 1 x y z AM NS x The transpose of the transformation between 5 and x y z is x y z 1 s PL where PL is the transpose of the PL matrix Substitution in the surface equation gives 1 1 s t PL AM PL 0 t Therefore QM AM PL A convenient set of parametric equations for conics is straight lines C t parabola s Cap t ellipse s C C sinp C cosp 10 3 05 2 189 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PLOTTER t C4 Cssinp Cgcosp hyperbola s C sinh p cosh p t C sinh Cg cosh The type of a conic is determined by examination of the conic invariants gt which are simple functions of the elements of QM Some of the surfaces produce two curves such as the two branches of a hyperbola or two straight lines A separate set of parametric coefficients C4 through is needed for each curve in such cases The parametric coefficients are found by transformi
230. I 8 B IV B IV B IV B VI 8 B IV B IV 89 B IV 89 B VI 8 B IV B IV B IV B VI 8 Fluor Source E amp C E amp C E amp C B VI 8 E amp C E amp C E amp C B VI 8 E amp C E amp C E amp C B VI 8 E amp C E amp C E amp C B VI 8 E amp C E amp C E amp C B VI 8 E amp C E amp C E amp C B VI 8 E amp C E amp C E amp C B VI 8 E amp C E amp C E amp C B VI 8 Library Release Length Emax ZAID Name Date Words NE GeV Z 17 Chlorine 17000 01p meplib 1982 409 45 0 1 17000 02p mcplib02 1993 643 84 100 17000 03p mcplib03 2002 1138 84 100 17000 04p mcplib04 2002 4738 684 100 Z 18 Argon 18000 01p 1982 409 45 0 1 18000 02p meplib02 1993 643 84 100 18000 03p mcplib03 2002 1138 84 100 18000 04p mcplib04 2002 4696 677 100 7 19 Potassium 19000 01 meplib 1982 409 45 0 1 19000 02p mcplib02 1993 643 84 100 19000 03p mcplib03 2002 1237 84 100 19000 04p mcplib04 2002 5047 719 100 Z 20 Calcium 20000 01 1982 417 45 0 1 20000 02p meplib02 1993 651 84 100 20000 03p meplib03 2002 1245 84 100 20000 04p meplib04 2002 5013 712 100 Z 21 Scandium 21000 01p 1982 417 45 0 1 21000 02p meplib02 1993 651 84 100 21000 03p meplib03 2002 1344 84 100 21000 04p mcplib04 2002 5532 782 100 Z 22 Titanium 22000 01 meplib
231. IX G MCNP DATA LIBRARIES DOSIMETRY DATA Table 6 Cont Dosimetry Data Libraries for MCNP Tallies ZAID AWR Library Source Date Length 60 Neodymium 60142 30 141 90800 LLNL ACTL 1983 207 60148 30y 147 91700 LLNL ACTL 1983 255 60150 30y 149 92100 LLNL ACTL 1983 259 Z 62 FOK K K K K K K K K K K K K K Samarium K K K K K K K K K K KK K K K KK K 62144 30y 143 91200 LLNL ACTL 1983 189 62148 30y 147 91500 LLNL ACTL 1983 245 62152 30y 151 92000 LLNL ACTL 1983 237 62154 30y 153 92200 LLNL ACTL 1983 247 Z 63 Europium 63151 30 150 92000 LLNL ACTL 1983 731 63153 30y 152 92100 LLNL ACTL 1983 565 Z 64 Gadolinium 64150 30 149 91900 LLNL ACTL 1983 237 64151 30y 150 92000 LLNL ACTL 1983 241 Z 66 se K K tee Dysprosium KEK K K K K K K K K K KK K K K K K K K K K K K KK K K K K K K K K 66164 26y 162 52000 532dos ENDF B V 1967 581 Z 67 Holmium 67163 30 162 92900 LLNL ACTL 1983 533 67164 30y 163 93000 LLNL ACTL 1983 327 67164 31y 163 93000 LLNL ACTL 1983 327 67165 30y 164 93000 LLNL ACTL 1983 589 67166 30y 165 93200 LLNL ACTL 1983 333 67166 31y 165 93200 LLNL ACTL 1983 333 Z 69 FKK K K K K K K K K KK se K K tee Thulium KKK K K K K K K K K K K K K K K K K K K K K K KK K K K K K
232. J E Morel Coupled Electron Photon Transport Calculations Using the Method of Discrete Ordinates IEEE NSREC Vol NS 32 No 6 Dec 1985 R C Little and E Seamon Neutron Induced Photon Production in MCNP Sixth International Conference on Radiation Shielding Vol I p 151 May 1983 H Grady Hughes and Robert G Schrandt Gaussian Sampling of Fission Neutron Multiplicity Los Alamos National Laboratory memorandum X 6 HGH 86 264 1986 J Terrell Distribution of Fission Neutron Numbers Phys Rev C 1 783 1957 J P Lestone Energy and Isotope Dependence of Neutron Multiplicity Distributions submitted to Nucl Sci Eng Los Alamos National Laboratory report LA UR 05 0288 2005 K B hnel The Effect of Multiplication on the Quantitative Determination of Spontaneously Fissioning Isotopes by Neutron Correlation Analysis Nucl Sci Eng 90 75 1985 D Mosteller and C J Werner Reactivity Impact of Delayed Neutron Spectra on MCNP Calculations in Transactions of American Nuclear Society Vol 82 pp 235 236 2000 J S Hendricks E Prael Monte Carlo Next Event Estimates from Thermal Collisions Nucl Sci Eng 109 3 pp 150 157 October 1991 10 3 05 2 203 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS REFERENCES 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 2 204 J S Hendricks E P
233. LA UR 03 1987 Approved for public release distribution is unlimited Title MCNP A General Monte Carlo N Particle Transport Code Version 5 Volume I Overview and Theory Authors X 5 Monte Carlo Team April 24 2003 Revised 10 3 05 Los Alamos NATIONAL LABORATORY Los Alamos National Laboratory an affirmative action equal opportunity employer is operated by the University of California for the U S Department of Energy under contract W 7405 ENG 36 By acceptance of this article the publisher recognizes that the U S Government retains a nonexclusive royalty free license to publish or reproduce the published form of this contribution or to allow others to do so for U S Government purposes Los Alamos National Laboratory requests that the publisher identify this article as work performed under the auspices of the U S Department of Energy Los Alamos National Laboratory strongly supports academic freedom and a researcher s right to publish as an institution however the Laboratory does not endorse the viewpoint of a publication or guarantee its technical correctness Form 836 8 00 MCNP MCNPS and Version 5 are trademarks of the Regents of the University of California Los Alamos National Laboratory COPYRIGHT NOTICE amp DISCLAIMER This material was prepared by the University of California University under Contract W 7405 ENG 36 with the U S Department of Energy DOE rights in the material
234. MCNP are energy cutoff and time cutoff Population Control Methods use particle splitting and Russian roulette to control the number of samples taken in various regions of phase space In important regions many samples of low weight are tracked while in unimportant regions few samples of high weight are tracked A weight adjustment is made to ensure that the problem solution remains unbiased Specific population control methods available in MCNP are geometry splitting and Russian roulette energy splitting roulette time splitting roulette weight cutoff and weight windows Modified Sampling Methods alter the statistical sampling of a problem to increase the number of tallies per particle For any Monte Carlo event it is possible to sample from any arbitrary distribution rather than the physical probability as long as the particle weights are then adjusted to compensate Thus with modified sampling methods sampling is done from distributions that send particles in desired directions or into other desired regions of phase space such as time or energy or change the location or type of collisions Modified sampling methods in MCNP include the exponential transform implicit capture forced collisions source biasing and neutron induced photon production biasing Partially Deterministic Methods are the most complicated class of variance reduction methods They circumvent the normal random walk process by using deterministic like techniques such as ne
235. Maintained by X 5 Eval Date 1992 1992 1992 1978 1978 1984 1984 1990 1990 1990 2003 1992 1988 1988 1978 1995 1992 1978 1978 1992 1978 1978 1978 1978 1978 1978 1978 1978 1978 1993 1993 1993 1993 1993 1993 1993 1992 1993 1976 1976 10 3 05 Temp Length words CK 300 0 300 0 300 0 293 6 293 6 293 6 293 6 293 6 293 6 293 6 293 6 300 0 293 6 293 6 293 6 293 6 300 0 293 6 293 6 300 0 300 0 293 6 293 6 293 6 293 6 293 6 293 6 3000 1 293 6 77 0 400 0 500 0 600 0 800 0 900 0 1200 0 300 0 300 0 293 6 293 6 17717 13464 31966 63223 5267 20484 32558 105150 110048 255036 255036 13445 7406 17349 33448 25187 17284 3524 10982 30572 41814 5404 18763 6067 5404 29054 33952 50571 58875 568756 418556 395964 377116 350292 338236 312572 93878 595005 12631 74049 NE MeV GPD 660 179 2477 8519 263 263 1682 7218 7218 18967 18967 165 562 1087 4610 1537 279 257 718 2177 5337 263 2301 537 263 3753 3753 4565 5603 62522 43747 40923 38567 35214 33707 30499 6827 64841 263 7809 30 0 30 0 30 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 30 0 20 0 20 0 20 0 20 0 30 0 20 0 20 0 30 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 20 0 30 0 20 0 20 0
236. NP computes heating as specified in Table 2 2 with a heating function H E Q modifying a track length reaction rate tally In other words the average energy deposited for all reactions at the incident particle energy is used in the tally regardless of the actual reaction that might be sampled at the next collision The heating functions are tabulated in the nuclear data by incident energy except for fission Q values Great care should be taken to understand exactly what the heating functions include and how they were computed The functions and Q from Table 2 2 are generally defined and computed for tabulation in the data tables as follows 1 Neutrons The heating number is H E E out E Q E where 1 p E Ooj E oq E probability of reaction i at neutron incident energy E E i out E average exiting neutron energy for reaction i at neutron incident energy E Q Q value of reaction i E YUE average exiting gamma energy for reaction i at neutron incident energy E 2 Photons 3 The heating number is H E E our E where i l incoherent Compton scattering with form factors 2 pair production E E 2mgc 1 022016 MeV is rest mass energy of an electron i 3 photoelectric absorption E out E 0 p E probability of reaction i at gamma incident energy E E i ou E average exiting ga
237. P assigns weight windows inversely proportional to the importances Then MCNP supplies the weight windows in an output file suitable for use as an input file in a subsequent calculation The spatial portion of the phase space is divided using either standard MCNP cells or a superimposed mesh grid which can be either rectangular or cylindrical The energy portion of the phase space is divided using the WWGE card The time portion of the phase space can be divided also The constant of proportionality is specified on the WWG card Limitations of the Weight Window Generator The principal problem encountered when using the generator is bad estimates of the importance function because of the statistical nature of the generator In particular unless a phase space region is sampled adequately there will be either no generator importance estimate or an unreliable one The generator often needs a very crude importance guess just to get any tally that is the generator needs an initial importance function to estimate a we hope better one for subsequent calculations Fortunately in most problems the user can guess some crude importance function sufficient to get enough tallies for the generator to estimate a new set of weight windows Because the weight windows are statistical several iterations usually are required before the optimum importance function is found for a given tally The first set of generated weight windows should be used in a subsequent ca
238. PECTRA The following is a list of recommended parameters for use with the MCNP source fission spectra and the SP input card described in Chapter 3 The constants for neutron induced fission are taken directly from the ENDF B V library For each fissionable isotope constants are given for either the Maxwell spectrum or the Watt spectrum but not both The Watt fission spectrum is preferred to the Maxwell fission spectrum The constants for spontaneously fissioning isotopes are supplied by Madland of Group T 16 If you desire constants for isotopes other than those listed below contact 5 Note that both the Watt and Maxwell fission spectra are approximations A more accurate representation has been developed by Madland in T 16 If you are interested in this spectrum contact 5 A Constants for the Maxwell Fission Spectrum Neutron induced CE exp Ela Incident Neutron Ener MeV a MeV n 233 Thermal 1 3294 1 1 3294 14 1 3294 n 794 Thermal 1 2955 1 1 3086 14 1 4792 5 Thermal 1 2955 1 1 3086 14 1 4792 Thermal 1 2996 1 1 3162 14 1 5063 n 237Np Thermal 1 315 1 1 315 14 1 315 10 3 05 H 1 APPENDIX H FISSION SPECTRA CONSTANTS AND FLUX TO DOSE FACTORS CONSTANTS FOR FISSION SPECTRA n n 2 n n n 2 Am n4 242mpy 243 2 Cm 29Cm n Ener Incident Neutron MeV Thermal 1 14 Thermal 1 14 The
239. Proposed Convergence Criteria for Monte Carlo Solutions Trans Am Nucl Soc 64 305 1991 1 M Hosking and J Wallis Parameter and Quantile Estimation for the Generalized Pareto Distribution Technometrics 29 339 1987 W H Press B P Flannery S A Teukolsky and W T Vetterling Numerical Recipes The Art of Scientific Computing Fortran Version Cambridge University Press 1990 Malvin H Kalos Paula A Whitlock Monte Carlo Methods Volume I Basics John Wiley amp Sons New York 1987 10 3 05 2 207 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS REFERENCES 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 2 208 T E Booth Sample Problem for Variance Reduction in MCNP Los Alamos National Laboratory report LA 10363 MS June 1985 A Forster C Little J Briesmeister and J S Hendricks MCNP Capabilities For Nuclear Well Logging Calculations IEEE Transactions on Nuclear Science 37 3 1378 June 1990 T E Booth and J S Hendricks Importance Estimation in Forward Monte Carlo Calculations Nucl Tech Fusion 5 1984 F Clark Exponential Transform as an Importance Sampling Device A Review ORNL RSIC 14 January 1966 P K Sarkar and M A Prasad Prediction of Statistical Error and Optimization of Biased Monte Carlo Transport Cal
240. Q n cosine of angle between surface normal nand particle trajectory surface area cm and volume cm calculated by the code or input by the user track length cm event transit time x particle velocity probability density function for scattering or starting in the direction Qp towards the point detector Azimuthal symmetry is assumed total number of mean free paths from particle location to detector distance to detector from a source or collision event microscopic total cross section barns microscopic fission cross section barns heating number MeV collision total energy deposited by a history in a detector see subsection D page 2 89 atom density atoms barn cm mass density g cm not used in Table 2 1 but used later in this chapter cell mass g fission heating Q value MeV angular flux familiar from nuclear reactor 14115 E t vn f Q E t Where n is the particle density particles cm Me V steradian and v is velocity in cm sh Thus the units of y particles cm sh MeV steradian total not net current crossing a surface average flux on a surface average flux in a cell volume flux at a point point at which is estimated location of point detector total energy deposition in a cell MeV g total fission energy deposition in a cell MeV g 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS TALLIES Adding an asterisk Fn cha
241. Re 185 75185 32 75185 42 75185 50 75185 504 75185 60 75185 65 75185 66 Re 187 75187 32 75187 42 75187 50 75187 50 75187 60 75187 65 75187 66 G 30 Continuous Energy and Discrete Neutron Data Libraries Maintained by X 5 AWR 181 3800 181 3800 181 3800 181 3800 181 3800 181 3800 181 3800 181 3800 181 3800 181 3800 181 3800 181 3800 181 3800 182 3700 182 3700 182 3700 182 3700 182 3700 182 3700 182 3700 182 3700 182 3700 182 3700 182 3700 182 3700 182 3700 184 3600 184 3600 184 3600 184 3600 184 3600 184 3600 184 3600 184 3600 184 3600 184 3600 184 3600 184 3600 184 3600 183 3612 183 3641 183 3640 183 3640 183 3640 183 3640 183 3640 185 3539 185 3497 185 3500 185 3500 185 3500 185 3500 185 3500 Library Name lal50n uresa 16 endf5p dre5 drmccs rmccsa endf60 actib actia actib endf66d endf66e endf66b 1 150 16 endf5p dre5 drmccs rmccsa endf60 actib actia actib endf66d endf66e endf66b lal50n uresa 16 dre5 endf5p drmccs rmccsa endf60 actib actia actib endf66d endf66e endf66c Rhenium misc5xs 7 192 rmccsa drmccs endf60 endf66e endf66c misc5xs 7 endl92 rmccsa drmccs endf60 endf66e endf66c Source 6 B VLO 0 0 B V 2 B V 2 0 B VL8 B VL8 B VL8 6 6 6 B VL6 0 0 0 B V
242. SECTION LIBRARIES Table G 2 Cont Continuous Energy and Discrete Neutron Data Libraries Maintained by X 5 Library Eval Temp Length _ ZAID AWR Name Source Date words NE MeV GPD 0 DN UR Cm 247 96247 42c 244 9479 endl92 LLNL 1992 300 0 3997 3256 30 0 yes both no 96247 60c 244 9500 endf60 2 1976 293 6 38800 3679 20 0 yes tot no no 96247 65c 244 9500 endf66e B VI2 1976 3000 1 49949 3849 20 0 yes tot no no yes 96247 66c 244 9500 endf66c B VI2 1976 293 6 64799 5499 20 0 yes tot no no yes Cm 248 96248 42c 245 9413 endl92 LLNL 1992 300 0 40345 3355 30 0 yes both no no no 96248 60c 245 9410 endf60 0 1978 293 6 83452 9706 20 0 yes tot no no 96248 65c 245 9410 endf66e B VLO 1978 3000 1 102038 10383 20 0 yes tot no no yes 96248 66c 245 9410 endf66c B VLO 1978 293 6 130361 13530 20 0 yes tot no no yes Bk 249 97249 42c 246 9353 end192 LLNL lt 1992 300 0 19573 809 30 0 yes both no no no 97249 60c 246 9400 endf60 0 1986 293 6 50503 5268 20 0 both no no no 97249 65c 246 9400 endf66e B VLO 1986 3000 1 65384 5360 20 0 no both no no yes 97249 66c 246 9400 endf66c B VLO 1986 293 6 85568 7883 20 0 no both no no yes 14 240 98249 42c 246 9352 endl92 LLNL 1992 300 0 49615 4554 30 0 yes both no no no 98249 60c 246 9400 endf60 B VL0 X 1989 293 6 41271 4329 20 0 no both no no no 98249 61c 246 9400 0 1989 293 6 46154 4329 20 0 both no yes no
243. T card 3 141 Material Specification Cards 3 117 Material Void VOID card 3 124 Material Mm card 3 118 Mesh Tally FMESH 3 114 Message Block 3 1 MGOPT card 3 125 Mm 3 118 MODE card 3 24 MPLOT card 3 147 Card 3 120 M Tm card 3 134 Multigroup Adjoint Transport Option MGOPT card 3 125 NONU 3 122 NOTRN card 3 137 NPS 3 137 Output Print Tables PRINT card 3 145 3 147 Particle Track Output PTRAC card 3 148 to 3 152 PDn card 3 51 Perturbation PERTn Card 3 152 to 3 156 Photon Weight PW T Card 3 39 Photon Production Bias PIKMT card 3 124 PHYS card 3 127 to 3 132 PIKMT card 3 124 Plot tally while problem is running MPLOT card 3 147 PRDMP card 3 139 Print and Dump Cycle PRDMP card 3 139 PRINT card 3 145 3 147 Problem Type MODE card 3 24 PTRAC card 3 148 to 3 152 PWT card 3 39 RDUM card 3 139 Repeated Structures cards 3 25 to 3 32 Ring detector 3 82 SBn card 3 61 SCn 3 66 SDEF 3 53 SDn card 3 104 10 3 05 Cell Segment Divisor SDn card 3 104 SFn card 3 102 SIn card 3 61 Source Bias SBn card 3 61 Source Comment SCn card 3 66 Source Information SIn card 3 61 Source Points for KCODE Calculation KSRC card 3 77 Source Probability SPn Card 3 61 Special Treatments for Tallies FTn 3 112 SPn card 3 61 SSR 3 71 SSW 3 69 Summary of MCNP Input Cards 3 157 Surface 3 11 to 3 23 Surface Source Read SSR car
244. TL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL 1983 1983 1983 1983 1983 1983 1983 1983 1983 7 80 Mercury K K K K KK K K K K K K K K K KK K 80202 30y 80203 30y 80204 30y 201 97100 202 97300 203 97300 LLNL ACTL LLNL ACTL LLNL ACTL 1983 1983 1983 Z28 Thallium 8 8 8 a k k ak ak k ak 2 ak ak sk ak k ak ak 81202 30y 81203 30y 81204 30y 81205 30y 201 97200 202 97200 203 97400 204 97400 LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL 1983 1983 1983 1983 7 82 ead k kk kkk 82203 30 82204 30 82205 30 82206 30 82207 30 82208 30 82209 30y 82210 30y 202 97300 203 97300 204 97400 205 97400 206 97600 207 97700 208 98100 209 98400 10 3 05 LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL 1983 1983 1983 1983 1983 1983 1983 1983 151 153 123 123 211 157 157 427 129 183 99 209 261 261 265 265 307 265 269 39 381 365 377 375 373 369 257 405 257 347 333 263 279 351 APPENDIX G MCNP DATA LIBRARIES DOSIMETRY DATA ZAID Dosimetry Data Libraries for MCNP Tallies AWR Table 6 Cont
245. TTB is used This model generates electrons but assumes that they are locally slowed to rest Any bremsstrahlung photons produced by the nontransported electrons are then banked for later transport Thus electron induced photons are not neglected but the expensive electron transport step is omitted The TTB production model contains many approximations compared to models used in actual electron transport In particular the bremsstrahlung photons inherit the direction of the parent electron 3 If IDES 1 on the PHYS P card then all electron production is turned off no electron induced photons are created and all electron energy is assumed to be locally deposited The TTB approximation is the default for MODE P problems In MODE P E problems it plays a role when the energy cutoff for electrons is greater than that for photons In this case the TTB model is used in the terminal processing of the electrons to account for the few low energy bremsstrahlung photons that would be produced at the end of the electrons range 1 Simple Physics Treatment The simple physics treatment is intended primarily for higher energy photons It is inadequate for high Z nuclides or deep penetration problems The physical processes treated are photoelectric effect pair production Compton scattering from free electrons and optionally photonuclear interactions described on page 2 64 The photoelectric effect is regarded as an absorption without fluoresce
246. TTTTIT TmT T TTTTTT TTTTTITT T TTITITT TTTITITT T TTT T TTTTIT 10 7 10 6 10 5 10 4 0 001 0 01 0 1 UP 10 100 NON7FRO TAIIY Figure 2 20 10 3 05 2 125 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS ESTIMATION OF THE MONTE CARLO PRECISION FILE EXPR TALLY 4 TALLY FLUCTUATION CHART BIN TALLIES 1 ELLE d LLL MCNP 4A 11 01 93 11 43 TALLY 4 N NPS 10000000 BIN NORMED RUNTPE EXPR DUMP 3 F CELL FLAG DIR USER SEGMENT MULT COSINE 1 10 0 1 TALLY DENSITY 10 8 10 7 10 6 10 5 10 4 0 001 0 01 Laur t trt TT T TTTHIT TTITTT T TTITTT T TTITTT T TTITTT T TTITTT T THTTT T THTTT TTTIT 10 7 10 6 10 5 10 4 0 001 0 01 0 1 15 10 100 1000 7 TAIIY Figure 2 21 Figure 2 21 shows the sampled distance to first collision in a material that has a macroscopic cross section of about 0 1 cm This analytic function is a negative exponential given by fx X gt see page 2 27 with a mean of 10 empirical f x transitions from a constant 0 1 at values of x less than unity to the expected negative exponential behavior 7 Pareto Fit to the Largest History Scores for the TFC Bin The slope n in 1 x of the largest history tallies x must be estimated to determine if and when
247. Table Cont Length 2526 2787 4360 3687 3628 3664 3672 1968 2061 1929 3490 3384 2524 2896 1970 1988 2150 3164 2166 2174 3553 2147 2812 2442 3038 3044 2856 2956 2535 2284 2480 1970 1950 ZAID 67000 01g 73000 01g 74000 01g 75000 01g 78000 01g 79000 01g 82000 01g 83000 01g 90000 01g 91000 01g 92000 01g 93000 01g 94000 01g 2 2 Photon transport data are not provided for 7594 10 3 05 MGXSNP A Coupled Neutron Photon Multigroup Data Library Photon AWR 163 513493 179 393456 182 269548 184 607108 193 404225 195 274513 205 436151 207 185136 230 044724 229 051160 235 984125 235 011799 241 967559 Length 583 583 583 583 557 583 583 583 583 479 583 479 583 APPENDIX G MCNP DATA LIBRARIES PHOTOATOMIC DATA V PHOTOATOMIC DATA There are four photon transport libraries maintained by X 5 and distributed with MCNP MCPLIB MCPLIB02 MCPLIBO3 and MCPLIBOA Their lineage is summarized below The official version of MCPLIB is unchanged since 1982 7 Versions of MCPLIB existed prior to 1982 MCPLIB contains data from several sources For Z equal 1 to 94 excluding Z equal 84 85 87 88 89 01 93 the cross section data for incident energies from 1 keV to 100 MeV and all form factor data are from the ENDF B IV evaluation which is available from RSICC as data package DLC 7e The excluded elements are tabulated only on the energy range from 1 keV to
248. The SLOPE is not allowed to exceed a value of 10 a perfect score which would indicate an essentially negative exponential decrease If the 100 largest history scores all have values with a spread of less than 196 an upper limit is assumed to have been reached and the SLOPE is set to 10 The SLOPE should be greater than 3 to satisfy the second moment existence requirement of the CLT Then f x will appear to be completely sampled and hence N will appear to have approached infinity A printed plot of f x is automatically generated in the OUTP file if the SLOPE is less than 3 or if any of the other statistical checks described in the next section do not pass If 0 SLOPE 10 several 575 appear on the printed plot to indicate the Pareto fit allowing the quality of the fit to the largest history scores to be assessed visually If the largest scores are not Pareto in shape the SLOPE value may not reflect the best estimate of the largest history score decrease A new SLOPE can be estimated graphically A blank or 162 on the PRINT card also will cause printed plots of the first two cumulative moments of the empirical f x to be made Graphical plots of various f x quantities can be made using the z plot option MCPLOT with the TFC plot command These plots should be examined for unusual behavior in the empirical f x including holes or spikes in the tail MCNP tries to assess both conditions and prints a message if either condi
249. This Russian roulette is so powerful that it is one of two MCNP variance reduction options that is turned on by default The default value of k is 0 1 The other default variance reduction option is implicit capture The DD card Russian roulette game is almost foolproof Performance is relatively insensitive to the input value of k For most applications the default value of k 2 0 1 is adequate Usually choose so that there are 1 5 transmissions pseudoparticle contributions per source history If k is too large too few pseudoparticles are sampled thus 1 is a fatal error Because a random number is used for the Russian roulette game invoked by k gt 0 the addition of a detector tally affects the random walk tracking processes Detectors are the only tallies that affect results If any other tally type is added to a problem the original problem tallies remain unchanged Because detectors use the default DD card Russian roulette game and that game affects the random number sequence the whole problem will track differently and the original tallies will agree only to within statistics Because of this tracking difference it is recommended that k 0 be used once a good guess at w can be made This is especially important if a problem needs to be debugged by starting at some history past the first one Also k 0 makes the first 200 histories run faster There are two cases when it is beneficial to turn off the DD card Russian roulette g
250. V ENDF B V LLNL ACTL LLNL ACTL ENDF B V ENDF B V LLNL ACTL LLNL ACTL ENDF B V ENDF B V LLNL ACTL LLNL ACTL LLNL ACTL lt 1983 1979 1978 lt 1983 lt 1983 1978 1978 lt 1983 lt 1983 1979 1979 lt 1983 lt 1983 lt 1983 7 27 Cobalt 27057 30y 27058 30y 27058 31y 27059 30y 27060 30y 27060 31y 27061 30y 27062 30y 27062 31y 27063 30y G 64 56 93630 57 93580 57 93580 58 93320 59 93380 59 93380 60 93250 61 93400 61 93400 62 93360 Idos 10 3 05 LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL 1983 1983 1983 1983 1983 1983 1983 1983 1983 1983 Length 3T 7405 435 377 417 425 461 419 297 629 531 569 657 435 499 613 463 519 339 ZAID 27064 30y 7 28 Nickel 28057 30 28058 24 28058 26 28058 30 28059 30 28060 24 28060 26 28060 30y 28061 30y 28062 26y 8062 30y 28063 30y 28064 30y 28065 30y Z 2209 Copper 29062 30 29063 24 29063 26 29063 30y 29064 30y 29065 24y 29065 26y 29065 30y 29066 30y 2 20
251. V 0 1976 293 6 20649 263 20 0 yes 82000 50c 205 4300 rmccs B V 0 1976 293 6 37633 1346 20 0 yes 10 3 05 no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no yes yes yes yes yes yes yes no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no yes yes yes yes yes yes no no no no no no no no no no no no no no no no no no no no no no no no G 31 APPENDIX G MCNP DATA LIBRARIES NEUTRON CROSS SECTION LIBRARIES Continuous Energy and Discrete Neutron Data Libraries Maintained by X 5 Table G 2 Cont E max NE MeV GPD Library Eval Temp Length ZAID AWR Name Source Date words 206 82206 24c 204 2000 lal50n B VI 6 1996 293 6 424548 30415 82206 60c 204 2000 endf60 0 1989 293 6 148815 12872 82206 66c 204 2000 endf66c 6 1997 2936 420901 30414 pbp 207 5 82207 24c 205 2000 lal50n B VI 6 1996 293 6 280309 10689 82207 60c 205 2000 endf60 1991 293 6 111750 7524 82207 66c 205 2000 endf66c 6 1997 2936 276136 10689 pbp 208 82208 25c 206 1900 lal50n LANL 1996 293 6 344772 6633 82208 60c 206 1900 endf60 0 1989 293 6
252. a B VL8 2000 293 6 69562 3239 200 yes no no 11023 66c 22 7920 endf66a B VI 1 1977 293 6 64249 3239 200 yes no no G 14 10 3 05 no no no no no no no no no no no no no no no no ZAID AWR Mg nat 12000 42c 24 0962 12000 50d 24 0963 12000 50c 24 0963 12000 51c 24 0963 12000 51d 24 0963 12000 60c 24 0963 12000 61c 24 0963 12000 62c 24 0963 12000 64c 24 0963 12000 66c 24 0963 Library Name endl92 dre5 endfSu rmccs drmccs endf60 actib actia endf66d endf66a Z2 3 Aluminum 27 13027 21c 13027 24c 13027 42c 13027 50d 13027 50c 13027 60c 13027 61c 13027 62c 13027 64c 13027 66c 13027 91c 13027 92c 7 14 k 26 7498 26 7497 26 7498 26 7500 26 7500 26 7500 26 7497 26 7497 26 7497 26 7497 26 7497 26 7497 Si nat 14000 21 14000 42c 14000 50c 14000 50d 14000 51c 14000 51d 14000 60c Si 28 14028 24c 14028 61c 14028 62c 14028 64c 14028 66c 61 29 14029 24 14029 61c 14029 62c 14029 64c 14029 66c Si 30 14030 24c 14030 61c 14030 62c 14030 64c 14030 66c 27 8440 27 8442 27 8440 27 8440 27 8440 27 8440 27 8440 27 7370 27 7370 27 7370 27 7370 27 7370 28 7280 28 7280 28 7280 28 7280 28 7280 29 7160 29 7160 29 7160 29 7160 29 7160 100xs 3 lal50n endl92 drmccs rmccs endf60 actib actia endf66d endf66a actib 6 actia 6 100xs 3 endl92 e
253. a and very poorly on highly scattering media For neutron penetration of concrete or earth experience indicates that a transform parameter p 0 7 is about optimal For photon penetration of high Z material even higher values such as p 0 9 are justified The following explains what happens with an exponential transform without a weight window For simplicity consider a slab of thickness with constant 2 Let the tally be a simple count F1 tally of the weight penetrating the slab and let the exponential transform be the only nonanalog technique used Suppose for a given penetrating history that there are k flights that collide and n that do not collide The penetrating weight is thus However the particle s penetration of the slab means that 10 3 05 2 149 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VARIANCE REDUCTION k 2 ws and hence 1 1 m w e Ta pup r The only variation in w is because of the 1 factors that arise only from collisions For a perfectly absorbing medium every particle that penetrates scores exactly pU If a particle has only a few collisions the weight variation will be small compared to a particle that has many collisions The weight window splits the particle whenever the weight gets too large depriving the particle of getting a whole series of weight multiplications upon collision that are substantially greater than one By setting p and u 1 so that amp
254. ack in the energy bin In an experimental configuration suppose a source emits 100 photons at 10 MeV and ten of these get to the detector cell Further suppose that the first photon and any of its progeny created in the cell deposits 1 keV in the detector before escaping the second deposits 2 keV and so on up to the tenth photon which deposits 10 keV Then the pulse height measurement at the detector would be one pulse in the 1 keV energy bin 1 pulse in the 2 keV energy bin and so on up to 1 pulse in the 10 keV bin In the analogous MCNP pulse height tally the source cell is credited with the energy times the weight of the source particle When a particle crosses a surface the energy times the weight of the particle is subtracted from the account of the cell that it is leaving and is added to the account of the cell that it is entering The energy is the kinetic energy of the particle plus 2m c 1 022016 if the particle is a positron At the end of the history the account in each tally cell is divided by the source weight The resulting energy determines which energy bin the score is put in The value of the score is the source weight for an F8 tally and the source weight times the energy in the account for a F8 tally The value of the score is zero if no track entered the cell during the history The pulse height tally depends on sampling the joint density of all particles exiting a collision event MCNP does not currently sample this joi
255. add multiples of 10 to the tally number For example F11 F21 F981 F991 are all type F1 tallies Particle type is specified by appending a colon and the particle designator For example F11 N and F96 N are neutron tallies and F2 P and F25 P are photon tallies F6 tallies can be for both neutrons and photons for example F16 N P AII F8 tallies except F8 N are for both photons and electrons that is F8 P F8 E and 8 are all identical Jt should be noted that although F8 N is also allowed it is not advised because MCNP neutron transport does not currently sample joint collision exit densities in an analog for example energy conserving way The units of each tally are derived from the units of the source If the source has units of particles per unit time current tallies are particles per unit time and flux tallies are particles per unit time per unit area When the source has units of particles current tallies have units of particles and flux tallies actually represent fluences with units of particles per unit area A steady state flux solution can be obtained by having a source with units of particles per unit time and integrating the tally over all time that is omitting the Tn card The average flux in a time bin can be obtained from the fluence tally for a time dependent source by dividing the tally by the time bin width in shakes These tallies can all be made per unit energy by dividing each energy bin by the energy bin
256. age to DXTRAN is the extra time consumed following DXTRAN particles with low weights Three special games can control this problem 1 DXTRAN weight cutoffs 2 DXC games and 3 DD game Particles inside a DXTRAN sphere are not subject to the normal MCNP weight cutoff or weight window game Instead DXTRAN spheres have their own weight cutoffs allowing the user to roulette DXTRAN particles that for one reason or another do not have enough weight to be worth following Sometimes low weighted DXTRAN particles occur because of collisions many free paths from the DXTRAN sphere The exponential attenuation causes these particles to have extremely small weights The DXTRAN weight cutoff will roulette these particles only after much effort has been spent producing them The DXC cards are cell dependent and allow DXTRAN contributions to be taken only some fraction of the time They work just like the PD cards for detectors see page 2 102 The user specifies a probability p that a DXTRAN particle will be produced at a given collision or source sampling in cell i The DXTRAN result remains unbiased because when a DXTRAN particle is produced its weight is multiplied by p The non DXTRAN particle is treated exactly as before unaffected unless it enters the DXTRAN sphere whereupon it 15 killed To see the utility suppose that the DXTRAN weight cutoff was immediately killing 99 of the DXTRAN particles from cell Only 1 of the DXTRAN particles su
257. al BCD format Type 1 format If desired an auxiliary processing code MAKXSF converts these files into unformatted binary files Type 2 format allowing faster access of the data during execution of MCNP and reduced disk space for storing the files The data contained on a table are independent of how they are stored The format for each class of ACE table is given in full detail in Appendix F This appendix may be useful for users making extensive modifications to MCNP involving cross sections or for users debugging MCNP at a fairly high level The available data tables are listed in Appendix G Each data table is identified by a ZAID The general form of a ZAID is ZZZAAA nnX where ZZZ is the atomic number AAA is the atomic mass number nn is the unique evaluation identifier and X indicates the class of data For elemental evaluations AAA 000 Data tables are selected by the user with the Mn MPNn and MTn cards In the remainder of this section we describe several characteristics of each class of data such as evaluated sources processing tools and differences between data on the original evaluation and on the MCNP data tables The means of accessing each class of data through MCNP input will be detailed and some hints will be provided on how to select the appropriate data tables 10 3 05 2 15 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CROSS SECTIONS A Neutron Interaction Data Continuous Energy and Discrete Reaction I
258. al and elastic cross sections from the data library are G 4 thermally adjusted by MCNP to the temperature of the problem if that temperature is different from the temperature at which the cross section set was processed see page 2 29 If different cells have different temperatures the cross sections first are adjusted to zero degrees and adjusted again to the appropriate cell temperatures during transport The cross section plot will never display the transport adjustment Therefore for plotting reactions 1 and 1 are equivalent and reactions 2 and 3 are equivalent But for the FM card reactions 1 and 3 will use the zero degree data and reactions 1 and 2 will use the transport adjusted data For example if a library evaluated at 300 is used in a problem with cells at 400 and 500 the cross section plotter and MT 1 and MT 3 options on the FM card will use 0 data The MT 1 and MT 2 options the FM card will use 400 and 500 data The user looking for total production of p d t and should be warned that in some evaluations such processes are represented using reactions with MT or R numbers other than the standard ones given in the above list This is of particular importance with the so called pseudolevel representation of certain reactions which take place in light isotopes For example the ENDF B V evaluation of carbon includes cross sections for the n n 3a reaction in MT 52 to 58 The
259. ally give fairly complete information for example flux throughout the phase space of the problem Monte Carlo supplies information only about specific tallies requested by the user When Monte Carlo and discrete ordinates methods are compared it is often said that Monte Carlo solves the integral transport equation whereas discrete ordinates solves the integro differential transport equation Two things are misleading about this statement First the integral and integro differential transport equations are two different forms of the same equation if one is solved the other is solved Second Monte Carlo solves a transport problem by simulating particle histories A transport equation need not be written to solve a problem by Monte Carlo Nonetheless one can derive an equation that describes the probability density of particles in phase space this equation turns out to be the same as the integral transport equation Without deriving the integral transport equation it is instructive to investigate why the discrete ordinates method is associated with the integro differential equation and Monte Carlo with the integral equation The discrete ordinates method visualizes the phase space to be divided into many small boxes and the particles move from one box to another In the limit as the boxes get progressively smaller particles moving from box to box take a differential amount of time to move a differential distance in space In the limit t
260. ame by setting 0 First when looking at the tail of a spectrum or some other low probability event the DD card roulette game will preferentially eliminate small scores and thus eliminate the very phenomenon of interest For example if energy bias is used to preferentially produce high energy particles these biased particles will have a lower weight and thus preferentially will be rouletted by the DD card game Second in very deep penetration problems pseudoparticles will sometimes go a long way before being rouletted In this rare case it is wasteful to roulette a pseudoparticle after a great deal of time has been spent following it and perhaps a fractional PD card should be used or if possible a cell or surface tally d Coincident detectors Because tracking pseudoparticles is very expensive MCNP uses a single pseudoparticle for multiple detectors known as coincident detectors that must be identical in geometric location particle type that is neutron or photon upper time bin limit 10 3 05 2 103 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS TALLIES DD card Russian Roulette control parameter and PD card entries if any Energy bins time bins tally multipliers response functions fictitious sphere radii user supplied modifications TALLY X etc can all be different Coincident detectors require little additional computational effort because most detector time is spent in tracking a pseudoparticle Mult
261. amined to see whether and how it should be plotted A point near the center of the segment is transformed back to the x y z coordinate system All cells immediately adjacent to the surface at that point are found If there is exactly one cell on each side of the surface and those cells are the same the segment is not plotted If there is exactly one cell on each side and those cells are different the segment is plotted as a solid line If anything else is found the segment is plotted as a dotted line which indicates either that there is an error in the problem geometry or that some other surface of the problem also intersects the plot plane along the segment If acurve to be plotted is not a straight line it is plotted as a sequence of short straight lines between selected points on the curve The points are selected according to the criterion that the middle of the line drawn between points must not lie farther from the nearest point on the true curve than the nominal resolution of the picture The nominal resolution is fixed at 1 3000 of a side of the 2 190 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS RANDOM NUMBERS viewport This is a bit coarse for the best plotting devices and is quite a bit too fine for the worst ones but it produces adequate pictures at reasonable cost XI RANDOM NUMBERS Like any other Monte Carlo program MCNP uses a sequence of random numbers to sample from probability distributions MCNP has al
262. amos Fermi invented a mechanical device called FERMIAC to trace neutron movements through fissionable materials by the Monte Carlo Method By 1948 Stan Ulam was able to report to the Atomic Energy Commission that not only was the Monte Carlo method being successfully used on problems pertaining to thermonuclear as well as fission devices but also it was being applied to cosmic ray showers and the study of partial differential equations o In the late 1940s and early 1950s there was a surge of papers describing the Monte Carlo method and how it could solve problems in radiation or particle transport and other 2 3 14 Many of the methods described in these papers are still used in Monte Carlo today including the method of generating random numbersP used in MCNP Much of the interest 2 2 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS INTRODUCTION was based on continued development of computers such as the Los Alamos MANIAC Mechanical Analyzer Numerical Integrator and Computer in March 1952 The Atomic Energy Act of 1946 created the Atomic Energy Commission to succeed the Manhattan Project In 1953 the United States embarked upon the Atoms for Peace program with the intent of developing nuclear energy for peaceful applications such as nuclear power generation Meanwhile computers were advancing rapidly These factors led to greater interest in the Monte Carlo method In 1954 the first comprehensive review of t
263. an be changed by the 5th entry on the PRDMP card The FOM is a very important statistic about a tally bin and should be studied by the user It is a tally reliability indicator in the sense that if the tally is well behaved the FOM should be approximately a constant with the possible exception of statistical fluctuations very early in the problem An order of magnitude estimate of the expected fractional statistical fluctuations in the FOM is 2R This result assumes that both the relative statistical uncertainty in the relative error is of the order of the relative error itself and the relative error is small compared to unity The user should always examine the tally fluctuation charts at the end of the problem to check that the FOMs are approximately constant as a function of the number of histories for each tally The numerical value of the FOM can be better appreciated by considering the relation 1 FOM T 2 24b Table 2 6 shows the expected value of R that would be produced in a one minute problem T 1 as a function of the value of the FOM It is clearly advantageous to have a large FOM for a problem because the computer time required to reach a desired level of precision is proportionally reduced Examination of Eq 2 21b shows that doubling the FOM for a problem will reduce the computer time required to achieve the same R by a factor of two Table 2 6 R Values as a Function of the FOM for T 1 Minute FOM 1 10 100 1000 10000
264. an be either a fraction of the average of previous DXTRAN particle weights or a user input reference weight Recall that a DXTRAN particle s weight is computed by multiplying the exit weight of the non DXTRAN particle by a weight factor having to do with the scattering probability and the negative exponential of the optical path between the collision site and DXTRAN sphere The optical path is computed by tracking a pseudoparticle from collision to the DXTRAN sphere The weight of the pseudoparticle is monotonically decreasing so the DD game compares the pseudoparticle s weight at the collision site and upon exiting each cell against the reference weight A roulette game is played when the pseudoparticle s weight falls below the reference weight The DD card stops tracking a pseudoparticle as soon as the weight becomes inconsequential saving time by eliminating subsequent tracking Final Comments a DXTRAN should be used carefully in optically thick problems Do not rely on DXTRAN to do penetration b Ifthe source is user supplied some provision must be made for obtaining the source contribution to particles on the DXTRAN sphere c Extreme care must be taken when more than one DXTRAN sphere is in a problem Cross talk between spheres can result in extremely low weights and an excessive growth in the number of particle tracks d Never put a zero on the DXC card A zero will bias the calculation by not creating DXTRAN particles but still kill
265. an would be needed by most histories see page 2 191 MCNP does not provide an estimate of the error in the difference Reference 133 shows how the error in the difference between two correlated runs can be estimated A postprocessor code would have to be written to do this Correlated sampling should not be confused with more elaborate Monte Carlo perturbation schemes that calculate differences and their variances directly MCNP also has a sophisticated perturbation capability VIII CRITICALITY CALCULATIONS Nuclear criticality the ability to sustain a chain reaction by fission neutrons is characterized by the eigenvalue to the neutron transport equation In reactor theory kepis thought of as the ratio between the number of neutrons in successive generations with the fission process regarded as the birth event that separates generations of neutrons 139 For critical systems kep 1 and the chain reaction will just sustain itself For subcritical systems kep lt 1 and the chain reaction will not sustain itself For supercritical systems gt 1 and the number of fissions in the chain reaction will increase with time In addition to the geometry description and material cards all that is required to run a criticality problem is a KCODE card described below and an initial spatial distribution of fission points using either the KSRC card the SDEF card or an SRCTP file Calculating k consists of estimating the mean number of fissi
266. ance reduction techniques are working cooperatively that is one is not destructively interfering with another 3 the FOM table is not erratic which would indicate poor sampling and 4 there is nothing that looks obviously ridiculous Unfortunately analyzing the output information requires considerable thought and experience Reference 133 shows in detail strategies and analysis for a particular problem After ascertaining that the techniques are improving the calculation the user makes a few more short runs to refine the parameters until the sampling no longer improves The weight window generator can also be turned on to supply information about the importance function in different regions of the phase space This rather complex subject is described on page 2 146 5 Erratic Error Estimates Erratic error estimates are sometimes observed in MCNP calculations In fact the primary reason for the Tally Fluctuation Chart TFC table in the MCNP output is to allow the user to monitor the 10 3 05 2 137 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VARIANCE REDUCTION FOM and the relative error as a function of the number of histories With few exceptions such as an analog point detector embedded in a scattering medium with Ro 0 a practice highly discouraged MCNP tallies are finite variance tallies For finite variance tallies the relative error should decrease roughly as so the FOM should be roughly constant and the ten
267. ant sampling of a tally that is N has tended to infinity then X 8 E x x Sc 68 of the time and 2 21a K 28 lt E x lt 25 95 of the time 2 21b from standard tables for the normal distribution function Eq 2 18a is a68 confidence interval and Eq 2 18b is a 95 confidence interval The key point about the validity of these confidence intervals is that the physical phase space must be adequately sampled by the Monte Carlo process If an important path in the geometry or a window in the cross sections for example has not been well sampled both x and 5 will be unknowingly incorrect and the results will be wrong usually tending to be too small The user must take great care to be certain that adequate sampling of the source transport and any tally response functions have indeed taken place Additional statistical quantities to aid in the assessment of proper confidence intervals are described in later portions of this section beginning on page 2 127 D Estimated Relative Errors in MCNP standard MCNP tallies are normalized to be per starting particle history except for some criticality calculations and are printed in the output with a second number which is the estimated relative error defined as 2 22 The relative error is a convenient number because it represents statistical precision as a fractional result with respect to the estimated mean Combining Eqs 2 15 2 16 and 2 1
268. are reserved by DOE on behalf of the Government and the University pursuant to the contract This report was prepared as an account of work sponsored by an agency of the United States Government Neither the United States Government nor any agency thereof nor any of their employees makes any warranty express or implied or assumes any legal liability or responsibility for the accuracy completeness or usefulness of any information apparatus product or process disclosed or represents that its use would not infringe privately owned rights Reference herein to any specific commercial product process or service by trade name trademark manufacturer or otherwise does not necessarily constitute or imply its endorsement recommendation or favoring by the United States Government or any agency thereof The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States government or any agency thereof ii 10 3 05 FOREWORD This manual is a practical guide for the use of the general purpose Monte Carlo code MCNP The previous version of the manual LA 13709 M March 2000 has been corrected and updated to include the new features found in MCNP Version 5 MCNP5 The manual has also been split into 3 volumes Volume I MCNP Overview and Theory Chapters 1 2 and Appendices Volume MCNP User s Guide Chapters 1 3 4 5 and Appendices A B I J Volume III MCNP Developer s Guide Appendices
269. arlo problem are 1 history scoring efficiency 2 dispersions in nonzero history scores and 3 computer time per history three factors are included in the FOM The first two factors control the value of the third is T The relative error can be separated into two components the nonzero history scoring efficiency component A and the intrinsic spread of the nonzero x scores amp Defining to be the fraction of histories producing nonzero x s Eq 2 19b can be rewritten as N 2 2 2 1 1 1 1 4 2 252 2 2 2 Zi 1x i X 0 0 X 20 24 NEU Note by Eq 2 19b that the first two terms are the relative error of the qN nonzero scores Thus defining 2 118 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS ESTIMATION OF THE MONTE CARLO PRECISION 2 2 Xi 1 and 2 25b Qi ug wm Reg 1 q qN yields 2 25c 2 art 2 254 For identical nonzero is zero and for a 100 scoring efficiency is Zero It is usually possible to increase q for most problems using one or more of the MCNP variance reduction techniques These techniques alter the random walk sampling to favor those particles that produce a nonzero tally The particle weights are then adjusted appropriately so that the expected tally is preserved This topic is described in Section VII Variance Reduction beginning on page 2 134 The sum of the two terms of Eq 2 22d produces
270. at not enough inactive cycles were skipped The table of combined k 4 by number of cycles skipped should be examined to determine if enough inactive cycles were skipped It is assumed that is large enough so that the collection of active cycle k j estimates for each estimator will be normally distributed if the fundamental spatial mode has been achieved in cycles and maintained for the rest of the calculation To test this assumption MCNP performs normality checks on each of the three keg estimator cycle data at the 95 and 99 confidence levels A WARNING message is issued if an individual set does not appear to be normally distributed at the 9990 confidence level This condition will happen to good data about 1 of the time Unless there is a high positive correlation among the three estimators it is expected to be rare that all three estimators will not appear normally distributed at the 99 confidence level when the normal spatial mode has been achieved and maintained When the condition that all three sets of k estimators do not appear to be normal at the 99 confidence level occurs the box with the final not be printed The final confidence interval results are available elsewhere in the output Examine the calculation carefully to see if the normal mode was achieved before the active cycles began The normality checks are also made for the batched amp and k by cycles skipped tables so that normality behavior ca
271. ata is associated with the energy transition E E gt j 1 The data consist of sets of equally probable discrete cosines for k 1 v with v typically 4 or 8 An index is selected with probability 1 and u is obtained by the relation 1 1 2 The data consist of bin boundaries of equally probable cosine bins In this case random linear interpolation is used to select one set or the other with p being the probability of selecting the set corresponding to incident energy E The subsequent procedure consists of sampling for one of the equally probable bins and then choosing uniformly in the bin 2 54 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS For elastic scattering the above two angular representations are allowed for data derived by an incoherent approximation In this case one set of angular data appears for each incident energy and is used with the interpolation procedures on incident energy described above For elastic scattering when the data have been derived in the coherent approximation a completely different representation occurs In this case the data actually stored are the set of parameters where D E for E lt E lt E o 0 for E lt Ep and are Bragg energies derived from the lattice parameters For incident energy E such that S ES D D for 1 k represents a discrete cumula
272. atio is approximated by performing two calculations one with the original data and one with the perturbed data This approach is useful even when the magnitude of the perturbation becomes very small In Monte Carlo methods however this approach fails as the magnitude of the perturbation becomes small because of the uncertainty associated with the response For this reason the differential operator technique was developed The differential operator perturbation technique as applied in the Monte Carlo method was introduced by Olhoeft gt in the early 1960s Nearly a decade after its introduction this technique was applied to geometric perturbations by Takahashi A decade later the method was generalized for perturbations in cross section data by Hall and later Rief 6 A rudimentary implementation into MCNP followed shortly thereafter 162 With an enhancement of the user interface and the addition of second order effects this implementation has evolved into a standard MCNP feature A Derivation of the Operator In the differential operator approach a change in the Monte Carlo response c due to changes in a related data set represented by the parameter v is given by a Taylor series expansion 2 n Ac e Ayers E dv 2 dv dv n Av c where the n order coefficient is This can be written as 2 192 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PERTURBATIONS yw beB heH
273. atment 2 57 Production Bias PIKMT card 3 124 Production Method 30 x 20 2 33 Expanded 2 33 Scattering 2 33 Spectra F 20 Weight Card 3 39 Photon Physics Treatment Detailed 2 59 Simple 2 57 Photonuclear Data 4th entry on PHYS card 2 66 Nuclide Selector 3 120 Photonuclear Physics 2 64 PHYS 3 127 PHYS Card 2 57 2 59 3 127 to 3 132 Electrons 3 130 to 3 132 Neutrons 3 127 to 3 128 Photons 3 128 to 3 129 PIKMT card 3 124 Pinhole Camera Flux Tally 3 83 Pinhole Image Tally FIP 2 98 Plot tally while problem is running MPLOT Card 3 147 Plotting 2 188 to 2 191 3 8 3 9 3 10 3 140 3 148 Plus 3 11 3 81 3 86 Point detectors 2 91 3 82 Cautions 2 64 Contributions NOTRN Card 3 137 Index 8 Response function 3 85 3 96 3 99 3 100 Power law source distribution 3 65 PRDMP card 3 139 Precision 2 108 2 110 Factors Affecting 2 111 Print and Dump Cycle PRDMP card 3 139 PRINT Card 3 145 Print cycle 3 139 Problem Cutoff Cards 3 135 to 3 138 Title card 3 2 Type MODE card 3 24 Prompt v 3 74 3 122 PTRAC card 3 148 to 3 152 Pulse Height Tallies 2 89 Pulse Height Tally Variance Reduction 3 87 Weight 2 26 F8 3 85 PWT card 2 31 2 32 3 39 Q Quasi deuteron photon absorption 2 65 R Radiograph Image Tallies FIC 2 97 FIR 2 97 Radiography Tallies 2 97 3 82 RAND Card 3 141 RCC 3 19 3 22 RDUM array 3 138 RDUM card 3 139 Reflecting surface 2 12 3 11 3
274. average over all e ow histories if there is precisely one active cycle but then neither nor is printed out because there too few cycles The cycle average does not precisely equal the history average 1 because they are ratios l and are the average time to escape and capture that is printed in the problem summary table for all neutron and photon problems ir Ws ly W and lyw are the weight lost to escape capture nOn and fission in the problem summary table The fractions F printed out below the lifespan in the KCODE summary table are for x e c f orr F W EW 2W W The prompt lifetimes for the various reactions are then op NEN o DdVdt C A T used Note again that the A Both t and the covariance weighted combined estimator slight differences between similar quantities are because and are averaged over all active 4 C A T us histories whereas and averaged within each active cycle and then the final values are the averages of the cycle values i e history averages vs batch averages The prompt removal lifetime can also be calculated using the F4 track length tally with the 1 v multiplier option on the FM card and using the volume divided by the average source weight as the multiplicative constant The standard track length tally is then converted from
275. because the source volume is half of the original volume Without the normalization 2 12 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS GEOMETRY the full weight of source particles is started in only half the volume These normalization factors are problem dependent and should be derived very carefully Another way to view this problem is that the tally surface has doubled because of the reflecting surface two scores are being made across the tally surface when one is made across each of two opposite surfaces in the nonreflecting problem The detector has doubled too except that the contributions to it from beyond the reflecting surface are not being made see page 2 101 4 White Boundaries A surface can be designated a white boundary surface by preceding its number on the surface card with a plus A particle hitting a white boundary is reflected with a cosine distribution p u relative to the surface normal that is 5 where is a random number White boundary surfaces are useful for comparing MCNP results with other codes that have white boundary conditions They also can be used to approximate a boundary with an infinite scatterer They make absolutely no sense in problems with next event estimators such as detectors or DXTRAN see page 2 101 and should always be used with caution 5 Periodic Boundaries Periodic boundary conditions can be applied to pairs of planes to simulate an infinite lattice Al
276. behavior if other sources of error are not minimized Factors affecting accuracy were discussed in Section VI beginning on page 2 108 2 134 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VARIANCE REDUCTION 2 Two Choices That Affect Efficiency The efficiency of a Monte Carlo calculation is affected by two choices tally type and random walk sampling The tally choice for example point detector flux tally vs surface crossing flux tally amounts to trying to obtain the best results from the random walks sampled The chosen random walk sampling amounts to preferentially sampling important random walks at the expense of unimportant random walks A random walk is important if it has a large affect on a tally These two choices usually affect the time per history and the history variance as described in the next section on page 2 136 MCNP estimates tallies of the form ar y DT y t by sampling particle histories that statistically produce the correct particle density N t The tally function 7 V 1 is zero except where a tally is required For example for a surface crossing tally F1 T will be one on the surface and zero elsewhere MCNP variance reduction techniques allow the user to try to produce better statistical estimates of N where T is large usually at the expense of poorer estimates where T is zero or small There are many ways to statistically produce 7
277. both a library and a format The US effort to create a national evaluated nuclear data library led to formation of the Cross Section Evaluation Working Group CSEWG in the 1960s This body standardized the ENDF format which is used to store evaluated nuclear data files and created the US ENDF B library that contains the set of data evaluations currently recommended by CSEWG Each update of the ENDF B library receives a unique identifier discussed below While ENDF began as a US effort over time other data centers have adopted the ENDF storage format for their own use this international standardization has encouraged and facilitated many collaborations Today the ENDF 6 format note that the Arabic number 6 indicates the ENDF format version has become the international standard for storing evaluated nuclear data and is used by data centers in Europe Japan China Russia Korea and elsewhere The user should be aware that there are many evaluated nuclear data libraries of which ENDF B is only one It is worth discussing the ENDF B library for a moment The US based CSEWG meets once a year to discuss and approve changes to the ENDF B library In order to track the updates to the ENDF B library the following notation has been adopted The in ENDF B is used to indicate the US data library as recommended by CSEWG There was at one time an ENDF A that was a repository for other possibly useful data However this is no longer used The
278. butions of these DXTRAN particles on the outer sphere within the cone defined by the inner sphere The weight of the DXTRAN particle is adjusted to account for the probability of scattering in the direction of the point on the outer sphere and traversing the distance with no further collision 10 3 05 2 159 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VARIANCE REDUCTION 2 160 The steps in sampling the DXTRAN particles are outlined 1 2 n cos0 L R L 1 2 no cos0g 12 RS L Sample n 1 1 n p uniformly in 9 1 with probability Q 1 n y Q 1 np n no and with probability nr noMQu n nol sample n N N 7 n uniformly in N 0 1 The quantity Q equal to 5 in MCNP is a factor that measures the importance assigned to scattering in the inner cone relative to the outer cone Therefore Q is also the ratio of weights for particles put in the two different cones With cos chosen a new direction u v w is computed by considering the rotation through the polar angle and a uniform azimuthal angle from the reference direction 202 L L L The particle is advanced in the direction u v to the surface of the sphere of radius The new DXTRAN particle with appropriate direction and coordinates is banked The weight of the DXTRAN particle is determined by multiplying the weight of the particle at collision by f o s d
279. c that is useful in assessing the quality of confidence intervals from Monte Carlo calculations Consider a generic Monte Carlo problem with difficult to sample but extremely important large history scores This type of problem produces three possible scenarios The first and obviously desired case is a correctly converged result that produces a statistically correct confidence interval The second case is the sampling of an infrequent but very large history score that causes the mean and R to increase and the FOM to decrease significantly This case is easily detectable by observing the behavior of the FOM and the R in the TFCs The third and most troublesome case yields an answer that appears statistically converged based on the accepted guidelines described previously but in fact may be substantially smaller than the correct result because the large history tallies were not well sampled This situation of too few large history tallies is difficult to detect The following sections discuss the use of the empirical history score PDF to gain insight into the TFC bin result A pathological example to illustrate the third case follows 2 History Score Probability Density Function f x A history score posted to a tally bin can be thought of as having been sampled from an underlying and generally unknown history score PDF f x where the random variable x is the score from one complete particle history to a tally bin The history s
280. care must be taken with the weight cutoff game page 2 143 the weight window game page 2 144 and subsequent collisions of the particle within the cell The weight window game is not played on the surface of a forced collision cell that the particle is entering For collisions inside the cell the user has two options Option 1 negative entry for the cell on the forced collision card After the forced collision subsequent collisions of the particle are sampled normally The weight cutoff game is turned off and detector contributions and DXTRAN particles are made before the weight window game is played If weight windows are used they should be set to the weight of the collided particle weight or set to zero if detector contributions or DXTRAN particles are desired Option 2 positive entry for the cell on the forced collision card After the forced collision detector contributions or DXTRAN particles are made and either the weight cutoff or weight window game is played Surviving collided particles undergo subsequent forced collisions If weight windows are used they should bracket the weight of particles entering the cell 10 Source Variable Biasing Provision is made for biasing the MCNP sources in any or all of the source variables specified MCNP s source biasing although not completely general allows the production of more source particles with suitably reduced weights in the more important regimes of each variable For example o
281. cay after a pulsed source can now be modeled with MCNP because the delay in neutron emission following fission is properly accounted for In this treatment a natural sampling of prompt and delayed neutrons is implemented as the default and an additional delayed neutron biasing control is available to the user via the PHYS N card The biasing allows the number of delayed neutrons produced to be increased artificially because of the low probability of a delayed neutron occurrence The delayed neutron treatment is intended to be used with the TOTNU option in MCNP giving the user the flexibility to use the time dependent treatment of delayed neutrons whenever the delayed data are available The impact of sampling delayed neutron energy spectra on reactivity calculations has been studied As expected most of the reactivity impacts are very small although changes of 0 1 0 2 10 3 05 2 53 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS were observed for certain cases Overall inclusion of delayed neutron spectra be expected to produce small positive reactivity changes for systems with significant fast neutron leakage and small negative changes for some systems in which a significant fraction of the fissions occurs in isotopes with an effective fission threshold e g 2297 and 7 Pu 6 5 Treatment The 5 8 thermal scattering treatment is a complete representation of thermal neutron scattering by m
282. ce a as well as that of each of its other bounding surfaces A particle in cell 1 cannot have the same sense relative to surface a as does a particle in cell 2 More than one ambiguity surface may be required to define a particular cell A second example may help to clarify the significance of ambiguity surfaces We would like to describe the geometry of Figure 2 3a Without the use of an ambiguity surface the result will be Figure 2 3b Surfaces 1 and 3 are spheres about the origin and surface 2 is a cylinder around the y axis Cell 1 is both the center and outside world of the geometry connected by the region interior to surface 2 a b Figure 2 3 At first glance it may appear that cell 1 can easily be specified by 1 2 3 whereas cell 2 is simply 1 This results in Figure 2 3b in which cell 1 is everything in the universe interior to surface 1 plus everything in the universe interior to surface 2 remember the cylinder goes to plus and minus infinity plus everything in the universe exterior to surface 3 10 3 05 2 11 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS GEOMETRY An ambiguity surface plane 4 at y 0 will solve the problem Everything in the universe to the right of the ambiguity surface intersected with everything in the universe interior to the cylinder is cylindrical region that goes to plus infinity but terminates at y 0 Therefore 1 4 2 3 defines cell 1 as desired in Figure 2 3a The
283. cess is sampled exactly by Kahn s method below 1 5 MeV and by Koblinger s method above 1 5 MeV as analyzed and recommended by Blomquist and Gelbard For next event estimators such as detectors and DXTRAN the probability density for scattering toward the detector point must be calculated 2 58 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS p u 2 where 652 is the total Klein Nishina cross section obtained by integrating over all angles for energy a This is a difficult integration so the empirical formula of Hastings is used 2 3 o1 Z nr 3 7 41 d d where 1 222037a cl 1 651035 c2 9 340220 c3 8 325004 41 12 501332 d2 14 200407 and 43 1 699075 Thus 2 9 y 1 n din 4 S CA a m cin t Above 100 MeV where the Hastings fit is no longer valid the approximation of Z 6 Z a Z made so that 2 Detailed Physics Treatment The detailed physics treatment includes coherent Thomson scattering and accounts for fluorescent photons after photoelectric absorption Again photonuclear interactions may optionally be included see page 2 64 Form factors are used with coherent and incoherent scattering to account for electron binding effects Photo neutron reactions can also be included for select isotopes Analog capture is always used as described below under ph
284. condary particle undergoing transport Based on this ratio an integer number of emission particles are sampled If weight games i e weight cut offs or weight windows are being used these secondary particles are subjected to splitting or roulette to ensure that the sampled particles will be of an appropriate weight The emission parameters for each secondary particle are then sampled independently from the reaction laws provided in the data Last tallies and summary information are appropriately updated applicable variance reduction games are performed and the emitted particle is banked for further transport Note that photonuclear physics was implemented in the traditional Monte Carlo style as a purely statistical based process This means that photons undergoing a photonuclear interaction produce an average number of emission particles For multiple particle emission the particles may not be sampled from the same reaction for example if two neutrons are sampled one may be from the g 2n distributions and the second from the g np distributions Note that the photonuclear data use the same energy angle distributions that have been used for neutrons and the same internal 2 66 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS coding for sampling See Nonfission Inelastic Scattering and Emission Laws on page 2 41 This generalized particle production method is statistically correct for large sampling populations and
285. core can be either positive or negative The quantity f x dx is the probability of selecting a history score between x and x dx for tally bin Each tally bin will have its own f x The most general form for expressing f x mathematically is 2 122 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS ESTIMATION OF THE MONTE CARLO PRECISION n Kx fa pl x 1 where f x is the continuous nonzero part and na 1 9 x represents the n different discrete components occurring at x with probability p An f x could be composed of either or both parts of the distribution A history score of zero is included in f x as the discrete component 0 By the definition of a PDF f x dx 1 As discussed on page 2 109 f x is used to estimate the mean variance and higher moment quantities such as the VOV 3 The Central Limit Theorem and f x As discussed on page 2 112 the Central Limit Theorem CLT states that the estimated mean will appear to be sampled from a normal distribution with a known standard deviation o N when N approaches infinity In practice o is NOT known and must be approximated by the estimated standard deviation S The major difficulty in applying the CLT correctly to a Monte Carlo result to form a confidence interval is knowing when N has approached infinity The CLT requires the first two moments of f x to exist Nearly all MCNP tally estimators except point dete
286. core probability density function Carefully check tally results and the associated tables in the tally fluctuation charts to ensure a well behaved and properly converged tally 2 108 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS ESTIMATION OF THE MONTE CARLO PRECISION Monte Carlo Means Variances and Standard Deviations Monte Carlo results are obtained by sampling possible random walks and assigning a score x for example x energy deposited by the i random walk to each random walk Random walks typically will produce a range of scores depending on the tally selected and the variance reduction chosen Suppose f x is the history score probability density function for selecting a random walk that scores x to the tally being estimated The true answer or mean is the expected value of x E x where E x true mean The function f x is seldom explicitly known thus f x is implicitly sampled by the Monte Carlo random walk process The true mean then is estimated by the sample mean x where o 2 18 where x is the value of x selected from f x for the history and N is the number of histories calculated in the problem The Monte Carlo mean x is the average value of the scores x for all the histories calculated in the problem The relationship between E x and x is given by the Strong Law of Large Numbers that states that if E x is finite x tends to the limit E x as approache
287. creened Nuclei and Orbital Electrons of Neutral Atoms with Z 1 to 100 Atom Data and Nuc Data Tables 35 1986 345 E Rutherford The Scattering of a and Particles by Matter and the Structure of the Atom Philos Mag 21 1911 669 W B rsch Supan the Evaluation of the Function 4 o gea for Real Values of J Res National Bureau of Standards 65B 1961 245 J A Halbleib R P Kensek T A Mehlhorn G D Valdez S M Seltzer and M J Berger ITS Version 3 0 The Integrated TIGER Series of Coupled Electron Photon Monte Carlo Transport Codes Sandia National Laboratories report SAND91 1634 March 1992 O Blunck Westphal Zum Energieverlust energiereicher Elektronen in d nnen Schichten Z Physik 130 1951 641 V Chechin and V C Ermilova The Ionization Loss Distribution at Very Small Absorber Thickness Nucl Instr Meth 136 1976 551 10 3 05 2 205 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS REFERENCES 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 2 206 Stephen M Seltzer Electron Photon Monte Carlo Calculations The ETRAN Code Appl Radiat Isot Vol 42 No 10 1991 pp 917 941 D R Schaart J T M Jansen J Zoetelief and P F A de Leege A Comparison of MCNPAC Electron Transport with ITS 3 0 and Experiment at Incident En
288. cs endf60 actia endf66a endl92 drmccs rmccs endf5mt 1 endf60 endf66a endl92 dre5 endf5p drmccs rmccsa newxsd newxs endf60 endf66a lal50n drmccs rmccs endf60 endf66a 100xs 3 192 drmecs 5 rmccs 5 endl92 LLNL LANL T X LANL B V 0 B V 0 0 B VL8 B VLO LLNL B V 0 B V 0 B V 0 B VI 1 B VI 1 LLNL 0 B V 0 B V 0 T B V 0 T LANL T LANL T B VLO 0 6 B V 0 B V 0 B VI 1 6 LLNL 0 0 LLNL 1992 1989 1989 1976 1976 1986 2000 1986 1992 1977 1977 1977 1989 1989 1992 1974 1974 1971 4 1971 4 1986 1986 1989 1989 1996 1977 1977 1989 1989 1989 1992 1977 1977 1992 300 0 300 0 293 6 293 6 293 6 293 6 293 6 293 6 300 0 293 6 293 6 587 2 293 6 293 6 300 0 293 6 293 6 293 6 293 6 293 6 293 6 293 6 293 6 293 6 293 6 293 6 293 6 293 6 300 0 300 0 293 6 293 6 300 0 1544 28964 68468 8886 8756 64410 115407 113907 4733 12322 20200 23676 27957 51569 4285 2812 4344 7106 12254 17348 56929 108351 149785 79070 16844 23326 22422 79070 28809 6229 16844 23326 5993 7 7 Nitrogen 7014 24c 7014 42c 7014 50c 7014 504 7014 60c 7014 62c 7014 66c 13 8827 13 8828 13 8830 13 8830 13 8828 13 8828 13 8828 1 150 19
289. cted weight executing any given random walk is preserved For example a particle can be split into two identical pieces and the tallies of each piece are weighted by 1 2 of what the tallies would have been without the split Such nonanalog or variance reduction techniques can often decrease the relative error by sampling naturally rare events with an unnaturally high frequency and weighting the tallies appropriately 3 Variance Reduction Tools in MCNP There are four classes of variance reduction techniques that range from the trivial to the esoteric Truncation Methods the simplest of variance reduction methods They speed up calculations by truncating parts of phase space that do not contribute significantly to the solution The simplest example is geometry truncation in which unimportant parts of the geometry are simply not modeled Specific truncation methods available in MCNP are the energy cutoff and time cutoff Population Control Methods use particle splitting and Russian roulette to control the number of samples taken in various regions of phase space In important regions many samples of low weight are tracked while in unimportant regions few samples of high weight are tracked A weight adjustment is made to ensure that the problem solution remains unbiased Specific population 10 3 05 1 9 CHAPTER 1 MCNP OVERVIEW INTRODUCTION TO MCNP FEATURES control methods available in MCNP are geometry splitting and Russian roule
290. ction algorithm averaged over u is 68 and approaches 100 as either the incident neutron energy approaches zero or becomes much larger than KT 3 Optional Generation of Photons Photons are generated if the problem is a combined neutron photon run and if the collision nuclide has a nonzero photon production cross section The number of photons produced is a function of neutron weight neutron source weight photon weight limits entries on the PWT card photon production cross section neutron total cross section cell importance and the importance of the neutron source cell No more than 10 photons may be born from any neutron collision In a KCODE calculation secondary photon production from neutrons is turned off during the inactive cycles 10 3 05 2 31 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS Because of the many low weight photons typically created by neutron collisions Russian roulette is played for particles with weight below the bounds specified on the PWT card resulting in fewer particles each having a larger weight The created photon weight before Russian roulette is where W photon weight W neutron weight photon production cross section total neutron cross section Both and are evaluated at the incoming neutron energy without the effects of the thermal free gas treatment because nonelastic cross sections are assumed independent of temperature The Russian roule
291. ction of the fission source points enter a cell with a fissionable material As a result one of two error messages can be printed 1 no new source points were generated or 2 the new source has overrun the old source The second message occurs when the MCNP storage for the fission source points is exceeded because the small results from a poor initial source causes to become very large The fission energy of next cycle neutron is sampled separately for each source point and stored for the next cycle It is sampled from the same distributions as fissions would be sampled in the random walk based on the incident neutron energy and fissionable isotope The geometric coordinates and cell of the fission site are also stored 4 collision nuclide and reaction are sampled after steps 1 2 and 3 but the fission reaction is not allowed to occur because fission is treated as capture The fission neutrons 10 3 05 2 165 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CRITICALITY CALCULATIONS that would have been created are accrued by three different methods to estimate k for this cycle The three estimators are a collision estimator an absorption estimator and a track length estimator as discussed in subsection B on page 2 167 3 Cycle Termination At the end of each k cycle a new set of M source particles has been written from fissions in that cycle The number M varies from cycle to cycle but the total
292. ctors with zero neighborhoods in a scattering material and some exponential transform problems satisfy this requirement Therefore the history score PDF f x also exists One can also examine the behavior of f x for large history scores to assess if f x appears to have been completely sampled If complete sampling has occurred the largest values of the sampled x s should reached the upper bound if such a bound exists or should decrease faster than 1 3 so that E x x exists is assumed to be finite in the CLT Otherwise is assumed not to have approached infinity in the sense of the CLT This is the basis for the use of the empirical f x to assess Monte Carlo tally convergence The argument should be made ln since 5 must be a good estimate of c the expected value of the fourth history score moment x Hdx should exist It will be assumed that only the second moment needs to exist so that the f x convergence criterion will be relaxed somewhat Nevertheless this point should be kept in mind 4 Analytic Study of f x for Two State Monte Carlo Problems Booth 6 examined the distribution of history scores analytically for both an analog two state splitting problem and two exponential transform problems This work provided the theoretical 10 3 05 2 123 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS ESTIMATION OF THE MONTE CARLO PRECISION foundation for statistical studies o
293. ctron of energy E is assigned to the group A The electron attempts to traverse substeps each of which is assigned the energy loss A m If m substeps are completed the process starts over with the assignment of a new energy group n such that gt EZ E A straggled energy loss is sampled from L E n Sn However if the electron crosses a cell boundary or if the electron energy falls below the current group the loop over m is abandoned even if fewer than m substeps have been completed and the energy group is reassigned Since the straggling parameters are pre computed at the midpoints of the energy groups this algorithm does succeed in assigning to each substep a straggled energy loss based on parameters that are as close as possible to the beginning energy of the substep However there are two problems with the current MCNP approach First there is a high probability that the electron will not actually complete the expected range s for which the energy loss was sampled in which case the energy loss relies on a linear interpolation in a theory that is clearly nonlinear Second the final substep of each sequence using the sampled energy loss from L E s A will frequently fall partially in the next lower energy group 1 but no substep using the sample from LUE p Sp will ever be partially in higher group n 1 This results in a small but potentially significant systematic error See for example the inves
294. ctuating around the fundamental eigenmode solution It is recommended that the user make an initial run with a relatively small number of source particles per generation perhaps 500 or 1000 and generously allow a large enough number of cycles so that the eigenvalue appears to be fluctuating about a constant value The user should examine the results and continue the calculation if any trends in the eigenvalue are noticeable The SRCTP file from the last cycle of the initial run can then be used as the source for the final production run to be made with a larger number of histories per cycle This convergence procedure can be extended for very slowly convergent problems typically large thermal low leakage systems where a convergence run might be made with 500 or 1000 histories per cycle Then a second convergence run would be made with 1000 histories per cycle using the SRCTP file from the first run as an initial fission source guess If the results from the second run appear satisfactory then a final run might be made using 5000 or 10000 particles per cycle with the SRCTP file from the second run as an initial fission source guess In the final run only a few cycles should need to be skipped The bottom line is this skip enough cycles so that the normal spatial mode is achieved The second potential problem arises from the fact that the criticality algorithm produces a very small negative bias in the estimated eigenvalue The bias depends up
295. culation The tallies are for one fission neutron generation Biases may exist in these criticality results but appear to be smaller than statistical uncertainties These tallied quantities are accumulated only after the 7 inactive cycles are finished The tally normalization is per active source weight w where w T 1 and N is the nominal source size from the KCODE card J is the total number of cycles in the problem and Z is the number of inactive cycles from KCODE card The number w is appropriately adjusted if the last cycle is only partially completed If the tally normalization flag on the KCODE card is turned on the tally normalization is the actual number of starting particles during the active cycles rather than the nominal weight above Bear in mind however that the source particle weights are 2 180 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CRITICALITY CALCULATIONS all set to W 2 N M so that the source normalization is based upon the nominal source size N for each cycle An MCNP tally in a criticality calculation is for one fission neutron being born in the system at the start of a cycle The tally results must be scaled either by the total number of neutrons in a burst or by the neutron birth rate to produce respectively either the total result or the result per unit time of the source The scaling factor is entered on the Fm card The statistical errors that are calculated for the tall
296. culations Nucl Sci Eng 70 243 261 1979 J S Hendricks Construction of Equiprobable Bins for Monte Carlo Calculation Trans Am Nucl Soc 35 247 1980 G Bell and S Glasstone Nuclear Reactor Theory Litton Educational Publishing Inc 1970 T J Urbatsch R A Forster R E Prael and R J Beckman Estimation and Interpretation of kep Confidence Intervals in MCNP Los Alamos National Laboratory report LA 12658 November 1995 D Harmon II D Busch J F Briesmeister and A Forster Criticality Calculations with MCNP A Primer Nuclear Criticality Safety Group University of New Mexico Los Alamos National Laboratory December 1993 F B Brown Fundamentals of Monte Carlo Particle Transport Los Alamos National Laboratory report LA UR 05 4983 2005 S Nakamura Computational Methods in Engineering and Science R E Krieger Publishing Company Malabar FL 1986 T Ueki and F B Brown Stationarity Diagnostics Using Shannon Entropy in Monte Carlo Criticality Calculation I F Test Trans Am Nuc 87 156 2002 and Los Alamos National Laboratory report LA UR 02 3783 2002 T Ueki and B Brown Stationarity and Source Convergence Diagnostics in Monte Carlo Criticality Calculation M amp C 2003 ANS Topical Meeting Gatlinburg Tennessee April 2003 and Los Alamos National Laboratory report LA UR 02 6228 2002 E Gelbard and Prael Computations of Standard Deviation
297. d 3 71 Surface Source Write SSW card 3 69 Surface Flagging SFn card 3 102 5 Material MTm card 3 134 Tally Cards Tally Comment FCn card 3 91 Tally Energy card En 3 92 Tally Fluctuation TFn card 3 107 Tally Multiplier FMn card 3 95 Tally Segment FSn card 3 102 Tally Specification 3 79 Tally Time Tn card 3 92 Tally Fna cards 3 80 TALLYX FUn Input card 3 105 TALNP card 3 147 TFn 3 107 Thermal Times THTME card 3 133 THTME card 3 133 Time Multiplier TMn card 3 100 Title 3 2 TMn card 3 100 card 3 132 Tn 3 92 Total Fission TOTNU card 3 122 TRCL 3 28 TRn 3 30 to 3 32 TSPLT card 3 37 Vector Input VECT card 3 42 VOID card 3 124 VOL 3 24 Weight Window Generator WWG 3 47 WWG 3 47 10 3 05 MCNP MANUAL INDEX Continuous biasing 2 153 X 3 15 XSn Card 3 123 Y 3 15 Z 3 15 Cell Ambiguities 2 10 Bins 3 81 Complement 2 8 Flux F4 tally 3 80 Tally 3 80 Cell Based Weight Window Bounds WWN 3 44 Cell cards 3 2 3 9 to 3 11 Cell Importance IMP card 3 34 Cell Transformation TRCL card 3 28 Cell Volume VOL card 3 24 Shorthand Cell Specification 3 11 Cell by cell Energy Cutoff ELPT Card 3 136 Cell Flagging Card 3 101 Central Limit Theorem 2 112 CFn Card 3 101 Change current tally reference vector 2 106 Characteristic X rays 2 78 Charge Deposition Tally 3 80 CMn Card 3 101 Cn card 3 93 Code development 3 132 Coherent photon sca
298. d Monte Carlo multigroup transport code as discussed by Sloan Unfortunately a first order treatment is not adequate for many applications Morel et al have addressed this difficulty by developing a hybrid multigroup continuous energy algorithm for charged particles that retains the standard multigroup treatment for large angle scattering but treats exactly the CSDA operator As with standard multigroup algorithms adjoint calculations are performed readily with the hybrid scheme 12 The process for performing an MCNP MGBFP calculation for electron photon transport problems involves executing three codes First the CEPXS code is used to generate coupled electron photon multigroup cross sections Next the CRSRD code casts these cross sections into a form suitable for use in MCNP by adjusting the discrete ordinate moments into a Radau quadrature form that can be used by a Monte Carlo code CRSRD also generates a set of multigroup response functions for dose or charge deposition that can be used for response estimates for a forward calculation or for sources in an adjoint calculation Finally MCNP is executed using these adjusted multigroup cross sections Some applications of this capability for electron photon transport have been presented in Ref 113 V TALLIES MCNP automatically creates standard summary information that gives the user a better insight into the physics of the problem and the adequacy of the Monte Carlo simulation includi
299. d by other biasing techniques by requiring all particles in a cell to have weight W lt W lt Wy The geometry splitting will preserve any weight fluctuations because it is weight independent f Intherare case where no other weight modification schemes are present importances will cause all particles in a given cell to have the same weight Weight windows will merely bound the weight g The weight windows be turned off for a given cell or energy regime by specifying a zero lower bound This is useful in long or large regions where no single importance function applies Care should be used because when the weight window is turned off at collisions the weight cutoff game is turned on sometimes causing too many particles to be killed h For repeated structures the geometry splitting uses the product of the importances at the different levels No product is used for the weight windows The Weight Window Generator The generator is a method that automatically generates weight window importance functions gt The task of choosing importances by guessing intuition experience or trial and error is simplified and insight into the Monte Carlo calculation is provided Although the window generator has proved very useful two caveats are appropriate The generator is by no means a panacea for all importance sampling problems and certainly is not a substitute for thinking on the user s part In fact in most instances the user will hav
300. d in centimeters and if lt the point detector estimation inside is assumed to be the average flux uniformly distributed in volume f DdV O R lt R dV Wp u d 57 XR Wp u l e 2 10 3 05 2 93 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS TALLIES If x 0 the detector is not in a scattering medium no collision can occur and Wp u R 2 31h O R R X 0 If the fictitious sphere radius is specified in mean free paths A thenA X R and 2 Wp u 1l e X 3750 The choice of R may require some experimentation For a detector in a void region or a region with very few collisions such as air can be set to zero For a typical problem setting R to a mean free path or some fraction thereof is usually adequate If is in centimeters it should correspond to the mean free path for some average energy in the sphere Be certain when defining R that the sphere it defines does not encompass more than one material unless you understand the consequences This is especially true when defining R in terms of mean free path because R becomes a function of energy and can vary widely In particular if R is defined in terms of mean free paths and if a detector is on a surface that bounds a void on one side and a material on the other the contribution to the detector from the direction of the void will be zero even though the importance of the void is non
301. d of them Forced collisions A particle can be forced to undergo a collision each time it enters a designated cell that is almost transparent to it The particle and its weight are appropriately split into two parts collided and uncollided Forced collisions are often used to generate contributions to point detectors ring detectors or DXTRAN spheres Source variable biasing Source particles with phase space variables of more importance are emitted with a higher frequency but with a compensating lower weight than are less important source particles This technique can be used with pulse height tallies Point and ring detectors When the user wishes to tally a flux related quantity at a point in space the probability of transporting a particle precisely to that point is vanishingly small Therefore pseudoparticles are directed to the point instead Every time a particle history is born in the source or undergoes a collision the user may require that a pseudoparticle be tallied at a specified point in space In this way many pseudoparticles of low weight reach the detector which is the point of interest even though no particle histories could ever reach the detector For problems with rotational symmetry the point may be represented by a ring to enhance the efficiency of the calculation 10 3 05 1 11 CHAPTER 1 MCNP OVERVIEW MCNP GEOMETRY 13 DXTRAN DXTRAN which stands for deterministic transport improves sampling in the vicinity
302. d on page 2 36 The energy of each fission neutron is determined from the appropriate emission law These laws are discussed in the preceding section MCNP then models the transport of the first neutron out after storing all other neutrons in the bank f Prompt and Delayed Neutron Emission If 1 MCNP is using 2 the data for the collision isotope includes delayed neutron spectra and 3 the use of detailed delayed neutron data has not been preempted on the PHYS N card then each fission neutron is first determined by MCNP to be either a prompt fission neutron or a delayed fission neutron Assuming analog 2 52 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS sampling the type of emitted neutron is determined from the ratio of delayed v E to total v E n as 45 lt vq4 E produce a delayed neutron or Vg Ein Ein produce a prompt neutron to where v is the expected number of delayed neutrons If the neutron is determined to be a prompt fission neutron it is emitted instantaneously and the emission laws angle and energy specified for prompt fission are sampled If the neutron is determined to be a delayed fission neutron then MCNP first samples for the decay group by using the specified abundances Then the time delay is sampled from the exponential density with decay constant specified for the sampled decay group Finally the emission laws angle and energ
303. d when using the el library except to make finer energy bins over which the distribution is calculated MCNP addresses the sampling of bremsstrahlung photons at each electron substep The tables of production probabilities are used to determine whether a bremsstrahlung photon will be created For data from the el03 library the bremsstrahlung production is sampled according to a Poisson distribution along the step so that none one or more photons could be produced the el library allows for either none or one bremsstrahlung photon in a substep If a photon is produced the new photon energy is sampled from the energy distribution tables By default the angular deflection of the photon from the direction of the electron is also sampled from the tabular data The direction of the electron is unaffected by the generation of the photon because the angular deflection of the electron is controlled by the multiple scattering theory However the energy of the electron at the end of the substep is reduced by the energy of the sampled photon because the treatment of electron energy loss with or without straggling is based only on nonradiative processes There is an alternative to the use of tabular data for the angular distribution of bremsstrahlung photons If the fourth entry on the PHYS E card is 1 then the simple material independent probability distribution 2 e du 2 15 2 1 where u cos and wc will be used to sample for the a
304. dary electrons with gt is given by 1 do c d amp 2 17 At each electron substep MCNP uses o to determine randomly whether knock on electrons will be generated If so the distribution of Eq 2 14 is used to sample the energy of each secondary electron Once an energy has been sampled the angle between the primary direction and the direction of the newly generated secondary particle is determined by momentum conservation This angular deflection is used for the subsequent transport of the secondary electron However neither the energy nor the direction of the primary electron is altered by the sampling of the secondary particle On the average both the energy loss and the angular deflection of the primary electron have been taken into account by the multiple scattering theories 10 Multigroup Boltzmann Fokker Planck Electron Transport The electron physics described above can be implemented into a multigroup form using a hybrid multigroup continuous energy method for solving the Boltzmann Fokker Planck equation as 10 3 05 2 79 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS TALLIES described by Morel The multigroup formalism for performing charged particle transport was pioneered by Morel and Lorence for use in deterministic transport codes With a first order treatment for the continuous slowing down approximation CSDA operator this formalism is equally applicable to a standar
305. data are calculated using the scheme developed by Everett and Cashwell Photonuclear data are stored on ACE tables that use ZAIDs with the form ZZZAAA nnU New to MCNPS photon interactions can include photonuclear events However the current data distribution includes tables for only 13 nuclides Because of this photonuclear physics must be explicitly turned on If on a table must be provided for each nuclide of every material or a fatal error will occur and the simulation will not run This situation should improve sometime relatively 10 3 05 2 21 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CROSS SECTIONS soon More than 150 other photonuclear data evaluations exist these were created as part of an IAEA collaboration These evaluations have been processed and are available for beta testing use through the nuclear data website at Los Alamos National Laboratory see http t2 lanl gov and click on photonuclear These files need peer review and validation testing before becoming part of the official MCNP data package Photonuclear interaction data describe nuclear events with specific isotopes The reaction descriptions use the same ENDF 6 format as used for neutron data Their processing storage as ACE tables and sampling in a simulation are completely analogous to what is done for neutrons See the previous discussion of the neutron data for more details Note that the photonuclear data available so far are complete in the se
306. df5 tmccs hwtr 04t endf5 tmccs hwtr 05t endf5 tmccs hwtr 60t endf6 3 sab2002 hwtr 61t endf6 3 sab2002 hwtr 62t endf6 3 sab2002 hwtr 63t endf6 3 sab2002 hwtr 64t endf6 3 sab2002 Hydrogen in Liquid Methane 1001 Imeth 01t 89 therxs Imeth 60t endf6 3 sab2002 Hydrogen in Light Water 1001 Iwtr O1t endf5 tmccs Iwtr O2t endf5 tmccs lwtr 03t endf5 tmccs lwtr 04t endf5 tmccs Iwtr O5t endf5 tmccs lwtr 60t endf6 3 sab2002 Iwtr 61t endf6 3 sab2002 lwtr 62t endf6 3 sab2002 lwtr 63t endf6 3 sab2002 lwtr 64t endf6 3 sab2002 Hydrogen in Polyethylene 1001 poly 01t endf5 tmccs poly 60t endf6 3 sab2002 Hydrogen in Solid Methane 1001 smeth 01t lanl89 therxs smeth 60t endf6 3 sab2002 Date of Processing 03 03 89 06 14 00 06 13 00 06 14 00 06 14 00 06 14 00 06 14 00 06 14 00 10 22 85 10 22 85 10 22 85 10 22 85 10 22 85 09 14 99 01 20 03 09 14 99 09 14 99 01 20 03 04 10 88 09 17 99 10 22 85 10 22 85 10 22 85 10 22 85 10 22 85 09 13 99 09 13 99 09 13 99 09 13 99 01 21 03 10 22 85 09 14 99 04 10 88 09 17 99 10 3 05 Temp CK 300 400 500 600 800 294 400 600 800 1000 100 100 300 400 500 600 800 294 400 600 800 1000 300 294 22 22 Numof Numof Elastic Angles Energies Data none none none none none none none none none none none none none none none none none none none none none none none none none none none none n
307. df66b 0 1976 293 6 47405 5652 20 0 no no no no 41093 24c 92 1051 la150n LANL 1997 293 6 375888 23213 150 0 yes no yes no no 41093 42c 92 1083 endl92 LLNL 1992 300 0 73324 927 30 0 yes no no no no 41093 50c 92 1051 endf5p 0 1974 293 6 128960 17279 200 yes no no no 41093 50d 92 1051 dre5 0 1974 293 6 10332 263 20 0 yes no no no no 41093 51 92 1051 rmccs B V 0 1974 293 6 14675 963 20 0 yes no no no no 41093 51d 92 1051 drmccs B V 0 1974 293 6 10332 263 20 0 yes no no no no 41093 60c 92 1051 endf60 B VI 1 1990 293 6 110269 10678 20 0 yes no no no no 41093 66c 92 1051 endf66b 6 1997 293 6 367638 23063 150 0 yes no yes no no Mo nat 42000 42c 95 1158 endl92 LLNL 1992 300 0 9293 442 30 0 yes no no no no 42000 50d 95 1160 dre5 0 1979 293 6 7154 263 20 0 yes no no no no 42000 50c 95 1160 endf5u 0 1979 293 6 35634 4260 20 0 yes no no no no 42000 51 95 1160 rmccs B V 0 1979 293 6 10139 618 20 0 yes no no no no 42000 51d 95 1160 drmccs B V 0 1979 293 6 7754 263 20 0 42000 60 95 1160 endf60 B VLO 1979 293 6 45573 5466 20 0 yes no no no no 42000 66c 95 1160 endf66b 0 1979 293 6 68710 7680 200 yes no no no no 95 42095 50c 94 0906 kidman B V 0 1980 293 6 15411 2256 200 no no no no no 99 43099 50c 98 1500 kidman B V 0 1978 293 6 12152 1640 20 0 no no no no no 43099 60c 98 1500 endf60 B VLO 1978 293 6 54262 8565 20 0 no no no no 430
308. dius of the ring is very large compared to the dimensions of the scattering media such that the detector sees essentially a point source in a vacuum the ring detector is still more efficient than a point detector The reason for this unexpected behavior is that the individual scores to the ring detector for a specific history have a mean closer to the true mean than to the regular point detector contributions That is the point detector contributions from one history will tend to cluster about the wrong mean because the history will not have collisions uniformly in volume throughout the problem whereas the ring detector will sample many paths through the problem geometry to get to different points on the ring 2 96 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS TALLIES 3 Flux Image Detectors Flux image detector tallies are an array of point detectors close enough to one another to generate an image based on the point detector fluxes Each detector point represents one pixel of the flux image The source need not be embedded in the object The particle creating the image does not have source particle type Three types of neutral particle flux image tallies can be made Flux Image Radiograph FIR a flux image radiograph on a planar image surface Flux Image on a Cylinder FIC a flux image on a cylindrical image surface and Flux Image by Pinhole FIP a flux image by pinhole on a planar image surface Wh
309. dom number parameters MCNP prints a WARNING and counts the number of histories for which the stride S is exceeded MCNP also prints a WARNING if the period P is exceeded Exceeding the stride or the period does 10 3 05 2 191 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PERTURBATIONS not result in wrong answers but may result in an underestimate of the variance However because the random numbers are used for very different purposes MCNP seems quite insensitive to overrunning either the stride or the period 156 Sometimes users wish to know how much of the variation between problems is purely statistical and the variance is insufficient to provide this information In correlated sampling see page 2 163 and criticality problems the variances can be underestimated because of correlation between histories In this case rerun the problems with a different random number sequence either by starting with a new random number or by changing the random number stride or multiplier on the RAND card MCNP checks for and does not allow invalid choices such as an even numbered initial random number that after a few random numbers would result in all subsequent random numbers being zero XII PERTURBATIONS The evaluation of response or tally sensitivities to cross section data involves finding the ratio of the change in a tally to the infinitesimal change in the data as given by the Taylor series expansion In deterministic methods this r
310. e 2 156 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VARIANCE REDUCTION The Russian roulette game is played by sampling particle 1 normally and keeping it only if it does not enter on its next flight the DXTRAN sphere that is particle 1 survives by definition of p4 with probability Similarly the Russian roulette game is lost if particle enters on its next flight the DXTRAN sphere that is particle 1 loses the roulette with probability p To restate this idea with probability particle 1 has weight wg and does not enter the DXTRAN sphere and with probability p the particle enters the DXTRAN sphere and is killed Thus the expected weight not entering the DXTRAN sphere is wo p 0 p wy as desired So far this discussion has concentrated on the non DXTRAN particle and ignored exactly what happens to the DXTRAN particle The sampling of the DXTRAN particle will be discussed after a second viewpoint on the non DXTRAN particle 2 DXTRAN Viewpoint 2 This second way of viewing DXTRAN does not see DXTRAN as a splitting process but as an accounting process in which weight is both created and destroyed on the surface of the DXTRAN sphere In this view DXTRAN estimates the weight that should go to the DXTRAN sphere upon collision and creates this weight on the sphere as DXTRAN particles If the non DXTRAN particle does not enter the sphere its next flight will proceed exactly as it would have withou
311. e distribution is isotropic SIn 1v1l 1 v 1 7 SPn 0 2 5 0 The direction cosine relative to the reference direction say is sampled uniformly within the cone lt lt 1 with probability and within 1 lt v lt v with the complementary probability The weights assigned W 1 v 2p5 W 1 v 2p respectively Note that for a very small cone defined by v and a high probability gt gt p for being within the cone the few source particles generated outside the cone will have a very high weight that can severely perturb a tally b Covering Cylinder Extent Biasing This biasing prescription for the SDEF EXT variable allows the automatic spatial biasing of source particles in a cylindrical source covering volume along the axis of the cylinder Such biasing can aid in the escape of source particles from optically thick source regions and thus represents a variance reduction technique Covering Cylinder or Sphere Radial Biasing This biasing prescription for the SDEF RAD variable allows for the radial spatial biasing of source particles in either a spherical or cylindrical source covering volume Like the previous example of extent biasing this biasing can be used to aid in the escape of source particles from optically thick source regions 3 Standard Analytic Source Functions The preceding examples discuss the biasing of source variables by either input of
312. e active cycles is proportional to N 1 1 and the standard deviation in the estimated eigenvalue is proportional to 1 N 7 From the results of the convergence run the total number of histories needed to achieve the desired standard deviation can be estimated It is recommended that 200 to 1000 active cycles be used This large number of cycles will provide large batch sizes of cycles for example 40 batches of 10 cycles each for 400 active cycles to compare estimated standard deviations with those obtained for a batch size of one cycle For example for 400 active cycles 40 batches of 10 k values are created and analyzed for a new average k and a new estimated standard deviation The behavior of the average amp by a larger number of cycles can also be observed to ensure a good normal spatial mode Fewer than 30 active cycles is not recommended because trends in the average k may not have enough cycles to develop 3 Analysis of Criticality Problem Results The goal of the calculation is to produce k confidence interval that includes the true result the desired fraction of the time Check all WARNING messages Understand their significance to the calculation Study the results of the checks that MCNP makes that were described starting on page 2 178 The criticality problem output contains a lot of useful information Study it to make sure that 1 the problem terminated properly 2 enough cycles were skipped to en
313. e cell Particles here split A U Upper weight bound specified as a constani Cy times Wi Particles within The constants C window do are for nothing the entire problem 5 Asurvival weight specified as a constani Cs times Wy L Increasing Fee weight bound Weight specified for each space energy cell Particles here play roulette kill or move to Figure 2 23 Figure 2 24 1 W the lower weight bound 2 Ws the survival weight for particles playing roulette and 3 Wy the upper weight bound The user specifies W for each phase space cell on WWN cards W and Wy are calculated using two problem wide constants and Cy entries on the WWP card as and Wy Thus all cells have an upper weight bound Cy times the lower weight bound and a survival weight times the lower weight bound 2 144 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VARIANCE REDUCTION Although the weight window can be effective when used alone it was designed for use with other biasing techniques that introduce a large variation in particle weight In particular a particle may have several unpreferred samplings each of which will cause the particle weight to be multiplied by a weight factor substantially larger than one Any of these weight multiplications by itself is usually not serious but the cumulative weight multiplications can seriously degrade calculational ef
314. e contributed Furthermore as N oo the apparent error will go to zero and therefore mislead the unwary Serious consideration should be given to two techniques discussed later energy roulette and space energy weight window that are always unbiased The energy cutoff has one advantage not directly related to variance reduction A lower energy cutoff requires more cross sections so that computer memory requirements go up and interactive computing with a timesharing system is degraded 2 Time Cutoff The time cutoff in MCNP is a single user supplied problem wide time value Particles are terminated when their time exceeds the time cutoff The time cutoff terminates tracks and thus decreases the computer time per history A time cutoff is like a Russian roulette game with zero survival probability The time cutoff should only be used in time dependent problems where the last time bin will be earlier than the cutoff Although the energy and time cutoffs are similar more caution must be exercised with the energy cutoff because low energy particles can produce high energy particles whereas a late time particle cannot produce an early time particle 3 Geometry Splitting with Russian Roulette Geometry splitting Russian roulette is one of the oldest and most widely used variance reducing techniques in Monte Carlo codes When used judiciously it can save substantial computer time As particles migrate in an important direction they are increas
315. e first order perturbation with 0 be m Pi gt 0 J k and let the second order perturbation with 0 be m 2 J N20 Then the Taylor series expansion for Rj 0 is 1 2 2 If Ri z 0 then 1 2 s Ro 1 2 2 2 That is the R 0 case is just a correction to the Ry 0 case In MCNP P and P5 are accumulated along every track length through a perturbed cell perturbed tallies are multiplied by 1 2 2 and then if 0 the tally is further corrected by Av Py Ry Av 2 198 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PERTURBATIONS R jis the fraction of the reaction rate tally involved in the perturbation 0 for F1 F2 F4 tallies without FM cards and F4 tallies with FM cards with positive multiplicative constants B Limitations Although it is always a high priority to minimize the limitations of any MCNP feature the perturbation technique has the limitations given below Chapter 3 page 3 154 has examples you can refer to 1 A fatal error is generated if a PERT card attempts to unvoid a region The simple solution is to include the material in the unperturbed problem and void the region of interest with the PERT card See Appendix B of Ref 165 2 fatal error is generated if a PERT card attempts to alter a material composition in such a way as to introduce a new nuclide The solution is to set up the unperturbed problem wi
316. e in the summary table of the output file Implicit capture is not possible 2 One fluorescent photon of energy greater than keV is emitted The photon energy is the difference in incident photon energy E less the ejected electron kinetic energy less a residual excitation energy e that is ultimately dissipated by further Auger processes This dissipation leads to additional electrons or photons of still lower energy The ejected electron and any Auger electrons can be transported or treated with the TTB approximation In general E E e e e e These primary transactions are taken to have the full fluorescent yield from all possible upper levels but are apportioned among the x ray lines L4 K Koo La gt K KB mean kB meanN gt 3 Two fluorescence photons can occur if the residual excitation e of process 2 exceeds 1 keV An electron of binding energy can fill the orbit of binding energy emitting a second fluorescent photon of energy E As before the residual excitation is dissipated by further Auger events and electron production that can be modeled with electron transport in Mode P E calculations approximated with the TTB model or assumed to deposit all energy locally These secondary transitions come from all upper shells and go to L shells Thus the primary transitions must be Ka or to leave an L shell vacancy Each fluore
317. e introduced 1 nuclear data and reactions 2 source specifications 3 tallies and output 4 estimation of errors and 5 variance reduction The third section explains MCNP geometry setup including the concept of cells and surfaces I MCNP AND THE MONTE CARLO METHOD MCNP is a general purpose continuous energy generalized geometry time dependent coupled neutron photon electron Monte Carlo transport code It can be used in several transport modes neutron only photon only electron only combined neutron photon transport where the photons are produced by neutron interactions neutron photon electron photon electron or electron photon The neutron energy regime is from 1071 MeV to 20 MeV for all isotopes and up to 150 MeV for some isotopes the photon energy regime is from 1 keV to 100 GeV and the electron energy regime is from KeV to 1 GeV The capability to calculate k eigenvalues for fissile systems is also a standard feature The user creates an input file that is subsequently read by MCNP This file contains information about the problem in areas such as the geometry specification the description of materials and selection of cross section evaluations the location and characteristics of the neutron photon or electron source the type of answers or tallies desired and any variance reduction techniques used to improve efficiency Each area will be discussed in the primer by use of a sample problem Remember five
318. e nearly perfect point of intersection if the common point is used in the surface specification It is frequently difficult to get complicated surfaces to meet at one point if the surfaces are specified by the equation coefficients Failure to achieve such a meeting can result in the unwanted loss of particles There are however restrictions that must be observed when specifying surfaces by points that do not exist when specifying surfaces by coefficients Surfaces described by points must be either skew planes or surfaces rotationally symmetric about the x y or z axes They must be unique real and continuous For example points specified on both sheets of a hyperboloid are not allowed because the surface is not continuous However it is valid to specify points that are all on one sheet of the hyperboloid See the X Y Z and P input card descriptions on page 3 15 for additional explanation 1 18 10 3 05 CHAPTER 1 MCNP OVERVIEW REFERENCES IV REFERENCES 10 11 12 13 14 Rose Compiler and Editor ENDF 201 ENDF B VI Summary Documentation BNL NCS 17541 Brookhaven National Laboratory October 1991 S Frankle C Reedy and Young ACTI An MCNP Data Library for Prompt Gamma ray Spectroscopy 12th Biennial Radiation Protection and Shielding Topical Meeting Santa Fe NM April 15 19 2002 R J Howerton D E Cullen R C Haight M H MacGregor S T Perkins and E F Plec
319. e of the largest history scores fluctuate as a function of the number of histories run tally results except for mesh tallies can be displayed graphically either while the code is running or in a separate postprocessing mode D Estimation of Monte Carlo Errors MCNP tallies are normalized to be per starting particle and are printed in the output accompanied by a second number which is the estimated relative error defined to be one estimated standard deviation of the mean 5 divided by the estimated mean In MCNP the quantities required for this error estimate the tally and its second moment are computed after each complete Monte Carlo history which accounts for the fact that the various contributions to a tally from the same history are correlated For a well behaved tally will be proportional to 1 where N is the number of histories Thus to halve R we must increase the total number of histories fourfold For a poorly behaved tally R may increase as the number of histories increases The estimated relative error can be used to form confidence intervals about the estimated mean allowing one to make a statement about what the true result is The Central Limit Theorem states that as N approaches infinity there is a 68 chance that the true result will bein the range x 1 R and a 95 chance in the range x 1 2R It is extremely important to note that these confidence statements refer only to the precision of the Mon
320. e often not compact The very complex processing codes used for this purpose include NJOY for evaluated data in ENDF 5 and ENDF 6 format and MCPOINT for evaluated data in the ENDL format Data on the MCNP neutron interaction tables include cross sections and emission distributions for secondary particles Cross sections for all reactions given in the evaluated data are specified For a particular table the cross sections for each reaction are given on one energy grid that is sufficiently dense that linear linear interpolation between points reproduces the evaluated cross sections within a specified tolerance Over the years this tolerance has been tightened as computer memory has increased In general the tables currently available have cross sections that are reproduced to a tolerance of 1 or less although many recent tables have been created with tolerances of 0 1 Depending primarily on the number of resolved resonances for each isotope the resulting energy grid may contain up to 100 000 points see Appendix for information about specific tables Angular distributions for neutron and photonuclear collisions are given in each table for all reactions emitting neutrons or photons note that older neutron tables may not include photon distributions The distributions are typically given in the center of mass system for elastic scattering and discrete level inelastic scattering Other distributions may be given in either the center of mass
321. e other hand the weight window generator will also fail if the phase space is too finely subdivided and subdivisions are not adequately sampled Adequate sampling of the important regions of phase space is always key to accurate Monte Carlo calculations and the weight window generator is a tool to help the user determine the important phase space regions When using the mesh based weight window generator resist the temptation to create mesh cells that are too small 10 3 05 2 147 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VARIANCE REDUCTION 7 Exponential Transform The exponential transform samples the distance to collision from a nonanalog probability density function Although many impressive results are claimed for the exponential transform it should be remembered that these results are usually obtained for one dimensional geometries and quite often energy independent problems A review article by Clark gives theoretical background and sample results for the exponential transform Sarkar and Prasad have done purely analytical analysis for the optimum transform parameter for an infinite slab and one energy group The exponential transform allows particle walks to move in a preferred direction by artificially reducing the macroscopic cross section in the preferred direction and increasing the cross section in the opposite direction according to X 1 d where x fictitious transformed cross sect
322. e plots of Shannon entropy vs cycle are easier to interpret and assess than are 2 D or 3 D plots of the source distribution vs cycle 10 3 05 2 179 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CRITICALITY CALCULATIONS To compute it is necessary to superimpose 3 D grid on a problem encompassing all of the fissionable regions and then to tally the number of fission sites in a cycle that fall into each of the grid boxes These tallies may then be used to form a discretized estimate of the source distribution J 1 N where N is the number of grid boxes in the superimposed mesh and number of source sites in J grid box total number of source sites Then the Shannon entropy of the discretized source distribution for that cycle is given by N S HQ Pj 151 src Varies between for a point distribution to In5 N for a uniform distribution Also note that as P approaches 0 In Pj approaches 0 MCNP prints for each cycle of a KCODE calculation Plots of H vs cycle can also be obtained during or after a calculation using the z option and requesting plots for kcode 6 The user may specify a particular grid to use in determining by means of the HSRC input card If the HSRC card is provided users should specify a small number of grid boxes e g 5 10 in each of the XYZ directions chosen according to the symmetry of the problem and layout of the fuel regions If t
323. e ratio of the atomic mass of the nuclide to a neutron This is the AWR that is contained in the original evaluation and that was used in the NJOY processing of the evaluation Name of the library that contains the data file for that ZAID The number in brackets following a file name refers to one of the special notes at the end of Table G 2 Indicates the originating evaluation for that data file ENDF B V or ENDF B VI such as B V 0 and B VI 1 are the Evaluated Nuclear Data Files a US effort coordinated by the National Nuclear Data Center at Brookhaven National Laboratory The evaluations are updated periodically by evaluators from all over the world and the release number of the evaluation is given This is not necessarily the same as the ENDF revision number for that evaluation 10 3 05 APPENDIX MCNP DATA LIBRARIES NEUTRON CROSS SECTION LIBRARIES Evaluation Date Temperature Length Number of Energies For example Pu 243 is noted as ENDF B VI 2 as it was first released with Release 2 of ENDF B VI but it is Revision 1 of that evaluation LLNL evaluated nuclear data libraries compiled by the Nuclear Data Group at Lawrence Livermore National Laboratory The number in the library name indicates the year the library was produced or received LANL evaluations from the Nuclear Physics Group T 16 at Los Alamos National Laboratory X the original evaluation has been modified by the Los Alamos Nat
324. e required for a complete representation of thermal neutron scattering by molecules and crystalline solids The source of 5 data is a special set of tapes The THERMR and ACER modules of the NJOY system have been used to process the evaluated thermal data into a format appropriate for MCNP Data are for neutron energies generally less than 4 eV Cross sections are tabulated on table dependent energy grids inelastic scattering cross sections are always given and elastic scattering cross sections are sometimes given Correlated energy angle distributions are provided for inelastically scattered neutrons A set of equally probable final energies is tabulated for each of several initial energies Further a set of equally probable cosines or cosine bins is tabulated for each combination of initial and final energies Elastic scattering data can be derived from either an incoherent or a coherent approximation In the incoherent case equally probable cosines or cosine bins are tabulated for each of several incident neutron energies In the coherent case scattering cosines are determined from a set of Bragg energies derived from the lattice parameters During processing approximations to the evaluated data are made when constructing equally probable energy and cosine distributions ZAIDs for the thermal tables are entered on an MTn card that is associated with an existing Mn card The thermal table generally will provide data for one comp
325. e to decide when the generator s results look reasonable and when they do not After these disclaimers one might wonder what use to make of a generator that produces both good and bad results use the generator effectively it is necessary to remember that the generated parameters are only statistical estimates and that these estimates can be subject to considerable error Nonetheless practical experience indicates that a user can learn to use the generator effectively to solve some very difficult transport problems Examples of the weight window generator are given in Refs 133 and 135 and should be examined before using the generator Note that this importance estimation scheme works regardless of what other variance reduction techniques are used in a calculation Theory The importance of a particle at a point P in phase space equals the expected score a unit weight particle will generate Imagine dividing the phase space into a number of phase space cells or regions The importance of a cell then can be defined as the expected score generated by a unit weight particle after entering the cell Thus with a little bookkeeping the cell s importance can be estimated as total score because of particles and Importance their progeny entering the cell expected score total weight entering the cell 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VARIANCE REDUCTION After the importances have been generated MCN
326. e with a flat weighting function This is not a multigroup representation the cross sections are simply given as histograms rather than as continuous curves The remaining data angular distributions energy distributions 0 etc are identical in discrete reaction and continuous energy neutron tables Discrete reaction tables have been provided in the past as a method of shrinking the required data storage to enhance the ability to run MCNP on small machines or in a time sharing environment Given the advances in computing speed and storage they are no longer necessary and should not be used There original purpose was for preliminary scoping studies They were never recommended as a substitute for the continuous energy tables when performing final calculations The matter of how to select the appropriate neutron interaction tables for your calculation is now discussed Multiple tables for the same isotope are differentiated by the nn evaluation identifier portion of the ZAID The easiest choice for the user is not to enter the nn at all If no identifier nn 2 18 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CROSS SECTIONS is entered MCNP will select the first match found in the directory file XSDIR The XSDIR file provided as part of the MCNP package contains the evaluations in the recommended by the nuclear data team at LANL order Thus the user can select the currently recommended table by entering only the ZZZAAA po
327. ea calculations by MCNP See page 4 15 for an example The complement operator can be easily abused if it is used indiscriminately A simple example can best illustrate the problems Figure 2 1 consists of two concentric spheres inside a box Cell 4 can be described using the complement operator as 4 0 933432141 Although cells 1 and 2 do not touch cell 4 to omit them would be incorrect If they were omitted the description of cell 4 would be everything in the universe that is not in cell 3 Since cells 1 and 2 are not part of cell 3 they would be included in cell 4 Even though surfaces 1 and 2 do not physically bound cell 4 using the complement operator as in this example causes MCNP to think that all surfaces involved with the complement do bound the cell Even though this specification is correct and required by MCNP the disadvantage is that when a particle enters cell 4 or has a collision in cell 4 MCNP must calculate the intersection of the particle s trajectory with all real 2 8 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS GEOMETRY bounding surfaces of cell 4 plus any extraneous ones brought in by the complement operator This intersection calculation is very expensive and can add significantly to the required computer time 3 9 2 Figure 2 1 A better description of cell 4 would be to complement the description of cell 3 omitting surface 2 by reversing the senses and interchanging union and intersec
328. eceives a large amount of energy from the absorption mechanism and escapes the binding force of the nucleus after at least one but very few interactions with other nuclei This is in contrast to a direct emission where the emission particle escapes the nucleus without any interactions Typically this occurs from QD absorption of the photon where the incident energy is initially split between the neutron proton pair Particles emitted by this process tend to be characterized by higher emission energies and forward peaked angular distributions Equilibrium emission can be conceptualized as particle evaporation This process typically occurs after the available energy has been generally distributed among the nucleons In the classical sense particles boil out of the nucleus as they penetrate the nuclear potential barrier The barrier may contain contributions from coulomb potential for charged particles and effects of angular momentum conservation It should be noted that for heavy elements evaporation neutrons are emitted preferentially as they are not subject to the coulomb barrier Particles emitted by this process tend to be characterized by isotropic angular emission and evaporation energy spectra Several references are available on the general emission process after photoabsorption 169 67 For all of the emission reactions discussed thus far the nucleus will most probably be left in an excited state It will subsequently relax to the ground
329. ecommendations for Making a Good Criticality Calculation 183 VOLUMES AND AREAS a 185 Rotationally Symmetric Volumes and Areas 186 Polyhedron Volumes and 186 Stochastic Volume and Area Calculation 187 Rr 188 RANDOM NUMBERS 2 5 at UH YOUR THEN DUNS ANDRE 191 PERTURBATIONS E HN 192 Derivation Ol the Operon aman uentis 192 Limitations OH e P 199 Me 199 REFERENCES 201 APPENDIX MCNP DATA LIBRARIES eese eene eene enne tn sas tn aeos tasa tasses 1 ENDF B REACTION TX PES ben abe enam Ed Ius ihe 1 S a B DATA FOR USE WITH THE MTn CARD 5 NEUTRON CROSS SECTION LIBRARIES 2 9 MULTIGROUP DATA 40 PETE POA TOC IDs UA aded Ruta ed 43 PHOTONUCLEAR DATA 58 DOSIMETRY DATA 60 REFERENCES M
330. ed in number to provide better sampling but if they head in an unimportant direction they are killed in an unbiased manner to avoid wasting time on them Oversplitting however can substantially waste computer time Splitting generally decreases the history variance but increases the time per history whereas Russian roulette generally increases the history variance but decreases the time per history Each cell in the problem geometry setup is assigned an importance J by the user on the IMP input card The number 7 should be proportional to the estimated value that particles in the cell have for the quantity being scored When a particle of weight W passes from a cell of importance to one of higher importance the particle is split into a number of identical particles of lower weight according to the following recipe If 7 is an integer n n gt 2 the particle is split into identical particles each weighing W n Weight is preserved in the integer splitting process If 7 7 is not an integer but still greater than 1 splitting is done probabilistically so that the expected number of splits is equal to the importance ratio Denoting n T to be the largest integer in 7 2 140 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VARIANCE REDUCTION p 1 is defined Then with probability p n 1 particles are used and with probability 1 p n particles are used For example if 7 7 is 2 75 75 of the time spli
331. egative energy pulse height scores These scores will be caught in the 0 energy bin If they are a large fraction of the total F8 tally then the tally is invalid because of nonanalog events Another situation is differentiating zero contributions from particles not entering the cell and particles entering the cell but not depositing any energy These are differentiated in MCNP by 2 90 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS TALLIES causing an arbitrary 1 e 12 energy loss for particles just passing through the cell These will appear in the O epsilon bin E Flux at a Detector The neutral particle flux can be estimated at a point or ring using the point or ring detector next event estimator Neutral particle flux images using an array of point detectors one detector for each pixel can also be estimated Detectors can yield anomalous statistics and must be used with caution Detectors also have special variance reduction features such as a highly advantageous DD card Russian roulette game Whenever a user supplied source is specified a user supplied source angle probability density function must also be provided 1 Point Detector A point detector is a deterministic estimate from the current event point of the flux at a point in space Contributions to the point detector tally are made at source and collision events throughout the random walk The point detector tally F5 may be considered a limiting case o
332. eight windows have a ratio greater than 4 PRINT TABLE 120 in the OUTP file lists the affected cells and ratios Generally in a deep penetration shielding problem the sample size number of particles diminishes to almost nothing in an analog simulation but splitting helps keep the size built up A good rule is to keep the population of tracks traveling in the desired direction more or less constant that is approximately equal to the number of particles started from the source good initial approach is to split the particles 2 for 1 wherever the track population drops by a factor of 2 Near optimum splitting usually can be achieved with only a few iterations and additional iterations show strongly diminishing returns Note that in a combined neutron photon problem importances will probably have to be set individually for neutrons and for photons MCNP never splits into a void although Russian roulette can be played entering a void Splitting into a void accomplishes nothing except extra tracking because all the split particles must be tracked across the void and they all make it to the next surface The split should be done according to the importance ratio of the last nonvoid cell departed and the first nonvoid cell entered Note four more items 1 Geometry splitting Russian roulette works well only in problems that do not have extreme angular dependence In the extreme case splitting Russian roulette can be useless if no particles ever en
333. em as necessary Law 66 N body phase space distribution ENDF law 6 The phase space distribution for particle in the center of mass coordinate system is 3n 2 4 Pik where all energies and angles also in the center of mass system and p is the maximum possible energy for particle i and T T is used for calculating The normalization constants for n 3 4 5 are M pps 1 105 WE 82087 256 5 lAn E i is a fraction of the energy available E pe Mami where M is the total mass of the n particles being treated m is the mass of particle i and T E 0 3 where is the target mass and is the projectile mass For neutrons 10 3 05 2 47 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS 1 and for a total mass ratio M m Thus max ae A The total mass and the number of particles in the reaction provided in data library The outgoing energy is sampled as follows Let i 1 9 be random numbers on the unit interval Then from rejection technique R28 from the Monte Carlo Sampler accept and if mo and accept 6 and 4 if Then let p 6 ifn 3 556 ifn 4 and 55665758 ifn 5 and let 2 2 _ ln 6i 62 61 5 2 31 5
334. en these flux image tallies are used with FSn and Cn cards to construct a virtual image grid millions of point detectors can be created one detector for each pixel to produce a flux image The FSn card is used to define the image pixels along the s axis The Cn card defines the pixels along the t axis The relationship of the s axis t axis and reference direction for the planar image grid is defined by the right hand rule Since the orientation of the s axis and the f axis is dependent on the reference direction in the geometry coordinate system the MCNP tally output should be examined to see the direction cosines of these two planar image grid axes The image grid SHOULD NOT be in a scattering material because the point detector average flux neighborhood is not used for flux image tallies a Radiograph Image Tallies FIR and FIC Both the FIR and FIC tallies act like film for an x ray type image that is a transmitted image for neutrons or photons The diagram in Figure 2 11 shows how the FIR planar rectangular grid image is defined for a source particle passing through an object and scattering in an object An FIC cylindrical surface grid generates an image on a cylinder as shown in Figure 2 12 for the particles generated inside the object FIR Planar Image Grid Object Geometry Source Contribution Source Geometry Reference Uu Particle P ad Transport Particle Sampled Source Point Scatter
335. ence no matter what the previous i 1 particles did in their random walks MCNP GEOMETRY We will present here only basic introductory information about geometry setup surface specification and cell and surface card input Areas of further interest would be the complement operator use of parentheses and repeated structure and lattice definitions found in Chapter 2 Chapter 4 contains geometry examples and is recommended as a next step Chapter 3 has detailed information about the format and entries on cell and surface cards and discusses macrobodies The geometry of MCNP treats an arbitrary 3 dimensional configuration of user defined materials in geometric cells bounded by first and second degree surfaces and fourth degree elliptical tori The cells are defined by the intersections unions and complements of the regions bounded by the surfaces Surfaces are defined by supplying coefficients to the analytic surface equations or for certain types of surfaces known points on the surfaces MCNP also provides a macrobody capability where basic shapes such as spheres boxes cylinders etc may be combined using boolean operators This capability is essentially the same as the combinatorial geometry provided by other codes such as MORSE KENO and VIM MCNP has a more general geometry than is available in most combinatorial geometry codes In addition to the capability of combining several predefined geometrical bodies as in a combina
336. ength Estimate of Cell Flux F4 2 85 Transformation 3 28 TRCL card 3 28 TRn card 3 30 to 3 32 TSPLT card 3 37 U Universe 3 25 Universe U card 3 26 Unresolved neutron resonances 2 55 Unresolved Resonance Data G 11 URAN 3 32 User Data Arrays 3 138 to 3 139 User modification 2 108 10 3 05 Variance Reduction 2 134 to 2 163 V Variance Reduction 2 134 to 2 163 and Accuracy 2 134 and Efficiency 2 135 DXTRAN 2 156 Energy Cutoff 2 139 3 135 Energy roulette 2 142 Energy splitting 2 142 Exponential transform 3 10 3 40 Forced collisions 2 151 to 2 152 3 42 Geometry splitting 2 140 Introduction 2 134 Modified Sampling Methods 2 139 Partially Deterministic Methods 2 139 Population Control Methods 2 139 Russian roulette 2 140 Schemes for detectors 2 102 Techniques 2 139 Time cutoff 2 140 3 135 Truncation Methods 2 139 Weight cutoff 3 135 Variance Reduction Cards 3 34 to 3 52 BBREM 3 52 Detector Contribution PDn card 3 51 DXC 3 51 DXTRAN DXT card 3 110 ESPLT 3 35 EXT 3 40 FCL 3 42 IMP 3 34 MESH 3 48 PDn 3 51 PWT 3 39 Weight Window Cards 3 43 to 3 47 Weight Window Generation Cards 3 46 to 3 51 WWE 3 44 WWG 3 47 WWGE 3 47 WWN 3 44 WWP 3 45 Vector Input VECT card 3 42 Velocity sampling 2 29 Vertical Input Format 3 5 VOID card 3 124 VOL card 3 24 10 3 05 MCNP MANUAL INDEX ZZZAAA also see ZAID 2 15 Warning Messages 3 7 Watt fissi
337. ent and photonuclear cross sections Detailed physics includes the additional coherent cross section in this sum The toggle for turning on and off photonuclear physics is also used to select biased or unbiased photonuclear collisions For the unbiased option the type of collision is sampled as either photonuclear or photoatomic based on the ratio of the partial cross sections The biased option is similar to forced collisions At the collision site the particle is split into two parts one forced to undergo photoatomic interaction and the other photonuclear The weight of each particle is adjusted by the ratio of their actual collision probability The photoatomic sampling routines as described in sections 1 and 2 above are used to sample the emission characteristics for secondary electrons and photons from a photoatomic collision The emission characteristics for secondary particles from photonuclear collisions are handled independently Once it has been determined that a photon will undergo a photonuclear collision the emission particles are sampled as follows First the appropriate collision isotope is selected based on the ratio of the total photonuclear cross section from each relevant table Note that photoatomic collisions are sampled from a set of elemental tables whereas photonuclear collisions are sampled from a set of isotopic tables Next the code computes the ratio of the production cross section to the total cross section for each se
338. ented in Section IV E beginning on page 2 67 of this chapter The hierarchy rules for electron cross sections require that each material must use the same electron library If a specific ZAID is selected a material card such as specifying ZZZ000 01E that choice of library will be used as the default for all elements in that material Alternatively the default electron library for a given material can be chosen by specifying ELIB nnE on the M card Under no circumstances should data tables from different libraries be specified for use in the same material e g m6 12000 01e 1 20000 03e 1 should not be used This will result in a fatal error as reported at run time Overriding this error with a FATAL option will result in unreliable results In the absence of any specification MCNP will use the first electron data table listed in the XSDIR cross section directory file for the relevant element D Neutron Dosimetry Cross Sections Dosimetry cross section tables cannot be used for transport through material These incomplete cross section sets provide energy dependent neutron cross sections to MCNP for use as response functions with the FM tally feature e g they may be used in the calculation of a reaction rate ZAIDs for dosimetry tables are of the form ZZZAAA nnY Remember dosimetry cross section tables have no effect on the particle transport of a problem The available dosimetry cross sections are from three sources ENDF B V Dosimet
339. eometries a source point in any one cell that is repeated will satisfy this test For example assume a problem with a cylinder and a cube that are both filled with the same universe namely a sphere of uranium and the space outside the sphere If a source point is placed in the sphere inside the cylinder but not in the sphere inside the cube the test will be satisfied One basic assumption that is made for a good criticality calculation is that the normal spatial mode for the fission source has been achieved after cycles were skipped MCNP attempts to assess this condition in several ways The estimated combined its estimated standard deviation for the first and second active cycle halves of the problem are compared A WARNING message is issued if either the difference of the two values of combined col abs track length k does not appear to 2 178 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CRITICALITY CALCULATIONS be zero or the ratio of the larger to the smaller estimated standard deviations of the two col abs track length k is larger than expected Failure of either or both checks implies that the two active halves of the problem do not appear to be the same and the output from the calculation should be inspected carefully MCNP checks to determine which number of cycles skipped produces the minimum estimated standard deviation for the combined k estimator If this number is larger than Z it may indicate th
340. er lies outside of a confidence interval Reference 141 is an introduction to using MCNP for criticality calculations focusing on the unique aspects of setting up and running a criticality problem and interpreting the results A quickstart chapter gets the new MCNP user on the computer running a simple criticality problem as quickly as possible A Criticality Program Flow Because the calculation of entails running successive fission cycles criticality calculations have a different program flow than MCNP fixed source problems They require a special criticality source that is incompatible with the surface source and user supplied sources Unlike fixed source problems where the source being sampled throughout the problem never changes the criticality source changes from cycle to cycle 1 Cuiticality Problem Definition To set up a criticality calculation the user initially supplies an INP file that includes the KCODE card with the following information the nominal number of source histories N per keff cycle an initial guess of 1 2 3 the number of source cycles I to skip before keff accumulation and 4 the total number of cycles in the problem Other KCODE entries are discussed in Chapter 3 page 3 76 The initial spatial distribution of fission neutrons can be entered by using 1 the KSRC card with sets of x y z point locations 2 the SDEF card to define points uniformly in volume or 3 a file SRCTP from
341. ergies Between 100 keV and 20 MeV Influence of Voxel Size Substeps and Energy Indexing Algorithm Phys Med Biol 47 pp 1459 1484 2002 Grady Hughes Improved Logic for Sampling Landau Straggling in MCNP5 American Nuclear Society 2005 Mathematics and Computation Topical Meeting Los Alamos National Laboratory report LA UR 05 4404 2005 M E Riley C J MacCallum and F Biggs Theoretical Electron Atom Elastic Scattering Cross Sections Selected Elements 1 keV to 256 keV Atom Data and Nucl Data Tables 15 1975 443 F Mott The Scattering of Fast Electrons by Atomic Nuclei Proc Roy Soc London A124 1929 425 Moliere Theorie der Streuung schneller geladener Teilchen II Mehrfach und Vielfachstreuung Z Naturforsch 3a 1948 78 Bethe and W Heitler Stopping of Fast Particles and on the Creation of Positive Electrons Proc Roy Soc London A146 1934 83 W Koch and J Motz Bremsstrahlung Cross Section Formulas and Related Data Rev Mod Phys 31 1959 920 Martin J Berger and Stephen M Seltzer Bremsstrahlung and Photoneutrons from Thick Tungsten and Tantalum Targets Phys Rev C2 1970 621 Pratt Tseng C M Lee Kissel C MacCallum and M Riley Bremsstrahlung Energy Spectra from Electrons of Kinetic Energy 1 keV lt T lt 2000 keV Incident on Neutral Atoms 2 lt Z lt 92 Atom Data and Nuc Data Tables 20 1977
342. ergies E probability density functions p cumulative density functions precompound fractions and angular distribution slope values The secondary emission energy is found exactly as stated in the Law 4 description on page 2 42 Unlike Law 4 Law 44 includes a correlated angular distribution associated 10 3 05 2 45 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS with each incident energy as given by the Kalbach parameters and Thus the sampled emission angle is dependent on the sampled emission energy The sampled values for R and A are interpolated on both the incident and outgoing energy grids For discrete spectra 4 k and R Rik For continuous spectra with histogram interpolation and R Rik For continuous spectra with linear linear interpolation A kt Ap ky 17 Aj GR 1 and R Rikt Ri k17 DE The outgoing neutron center of mass scattering angle is sampled from the Kalbach density function A E p in using the random numbers 3 and 54 on the unit interval as follows If 3 gt then let T 2 amp 4 1 sinh A and u n T 4T 1 A or if lt R then In Ie e 1 Ege As with Law 4 the emission energy and angle are transformed from the center of mass to the laboratory system as necessary
343. ering or an inelastic reaction including fission is selected and the new energy and direction of the outgoing track s are determined 6 if the energy of the neutron is low enough and an appropriate S table is present the collision is modeled by the S treatment instead of by step 5 1 Selection of Collision Nuclide If there are n different nuclides forming the material in which the collision occurred and if amp is a random number on the unit interval 0 1 then the k nuclide is chosen as the collision nuclide if k 1 n k Y SS Zus E 1 i21 where z is the macroscopic total cross section of nuclide If the energy of the neutron is low enough below about 4 eV and the appropriate s o p table is present the total cross section is the sum of the capture cross section from the regular cross section table and the elastic and inelastic scattering cross sections from the s o p table Otherwise the total cross section is taken from the regular cross section table and is adjusted for thermal effects as described below 2 Free Gas Thermal Treatment A collision between a neutron and an atom is affected by the thermal motion of the atom and in most cases the collision is also affected by the presence of other atoms nearby The thermal motion cannot be ignored in many applications of MCNP without serious error The effects of nearby atoms are also important in some applications MCNP uses a thermal
344. es such as those discussed in Section VII of this chapter beginning on page 2 134 B Precision and Accuracy There is an extremely important difference between precision and accuracy of a Monte Carlo calculation As illustrated in Figure 2 16 precision is the uncertainty in X caused by the statistical SYSTEMATIC ERROR Sx Figure 2 16 fluctuations of the x s for the portion of physical phase space sampled by the Monte Carlo process Important portions of physical phase space might not be sampled because of problem cutoffs in time or energy inappropriate use of variance reduction techniques or an insufficient sampling of important low probability events Accuracy is a measure of how close the expected value of x E x is to the true physical quantity being estimated The difference between this true value and E x is called the systematic error which is seldom known Error or uncertainty estimates for the results of Monte Carlo calculations refer only to the precision of the result and not to the accuracy It is quite possible to calculate a highly precise result that is far from the physical truth because nature has not been modeled faithfully 2 110 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS ESTIMATION OF THE MONTE CARLO PRECISION 1 Factors Affecting Problem Accuracy Three factors affect the accuracy of a Monte Carlo result 1 the code 2 problem modeling and 3 the user C
345. f a surface flux tally F2 as will be shown below Consider the point detector to be a sphere whose radius is shrinking to zero Figure 2 9 shows the details r source or collision point rp detector point Figure 2 9 Let be in the direction to the center of the sphere i e in the direction rp Let dQ be the solid angle subtended by the sphere from r and let dA be defined by the intersection of an arbitrary plane passing through the detector point and the collapsing cone 10 3 05 2 91 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS TALLIES In order to contribute to a flux tally upon crossing dA the particle has to do two things First the particle must scatter toward dA i e into solid angle this occurs with probability p 9 40 Second the particle must have a collisionless free flight for the distance R p r along to the sphere this occurs with probability R E X s ds e o where 2 5 is the total macroscopic cross section at a distance s along from the source or collision point The probability that these two events both occur is A X s ds p Define y to be the cosine of the angle between the particle direction and the unit normal n to area dA If a particle of weight w reaches dA it will contribute w 7 dA to the flux compare F2 tally on page 2 86 As the sphere shrinks to a point the solid angle subtended by dA is dQ
346. f cycles skipped This information can provide insight into fission source spatial convergence normality of the amp data sets and changes in the 95 and 9946 confidence intervals If concern persists a problem could be run that tallies the track length estimator k using an F4 n tally and an FM card using the 6 and 7 reaction multipliers see Chapter 4 for an example In the most drastic cases several independent calculations can be made and the variance of the k values and any other tallies could be computed from the individual values If a conservative too large k confidence interval is desired the results from the largest occurring on the next cycle table can be used This situation could occur with a maximum probability of 1 1 1 for highly positively correlated k values to 1 7 Ly for no correlation Finally keep in mind the discussion starting on page 2 180 For large systems with a dominance ratio close to one the estimated standard deviations for tallies could be much smaller than the true standard deviation The cycle to cycle correlations in the fission sources are not taken into account especially for any tallies that are not made over the entire problem The only way to obtain the correct statistical errors in this situation is to run a series of independent problems using different random number sequences and analyze the sampled tally results to estimate the statistical uncertainties IX VOLUMES
347. f surface 6 Cell 2 is described similarly Cell 3 cannot be specified with the intersection operator The following section about the union operator is needed to describe cell 3 2 Cells Defined by Unions of Regions of Space The union operator signified by a colon on the cell cards allows concave corners in cells and also cells that are completely disjoint The intersection and union operators are binary Boolean operators so their use follows Boolean algebra methodology unions and intersections can be used in combination in any cell description Spaces on either side of the union operator are irrelevant but remember that a space without the colon signifies an intersection In the hierarchy of operations intersections are performed first and then unions There is no left to right ordering Parentheses can be used to clarify operations and in some cases are required to force a certain order of operations Innermost parentheses are cleared first Spaces are optional on either side of a parenthesis A parenthesis is equivalent to a space and signifies an intersection For example let A and B be two regions of space The region containing points that belong to both A and B is called the intersection of A and B The region containing points that belong to A alone or to B alone or to both A and B is called the union of A and B The shaded area in Figure 1 5a represents the union of A and B or A B and the shaded area in Figure 1 5b represe
348. f the correlation is zero the two estimators appear statistically independent and the combined estimated standard deviation should be significantly less than either If the correlation is negative one even more information is available because the second estimator will tend to be low relative to the expected value when the first estimator is high and vice versa Even larger improvements in the combined standard deviation should occur correlation The combined average estimator X or and the estimated standard deviation of all three estimators are based on the method of Halperin and is much more complicated than the two combination case The improvements to the standard deviation of the three combined estimator 2 176 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CRITICALITY CALCULATIONS will depend on the magnitude and sign of the correlations as discussed above The details and analysis of this method are given in Ref 140 For many problems all three estimators are positively correlated The correlation will depend on what variance reduction for example implicit or analog capture is used Occasionally the absorption estimator may be only weakly correlated with either the collision or track length estimator Itis possible for the absorption estimator to be significantly anticorrelated with the other two estimators for some fast reactor compositions and large thermal systems Except in the most heterogeneou
349. fSu endf66e endf66b uresa drmccs rmccs newxsd newxs endf60 endf66e endf66b uresa endfSu dre5 endf66e endf66b kidman endf66b rmccsa drmccs endfSu dre5 misc5xs 7 14 endf60 endf66e endf66b dre5 endfSu misc5xs 7 14 endf60 endf66e endf66b Source LLNL LLNL LLNL 0 0 0 LANL T LANL T B VLO 0 0 0 0 0 0 0 0 0 0 LANL T LANL T 0 B VLO B VLO 0 0 0 B VLO 0 0 B VI 1 LLNL LLNL B V 0 B V 0 B V 0 T 0 4 4 0 B V 0 B V 0 T 0 4 4 APPENDIX MCNP DATA LIBRARIES NEUTRON CROSS SECTION LIBRARIES Table G 2 Cont Continuous Energy and Discrete Neutron Data Libraries Maintained by X 5 Eval Date 1985 1985 1992 1986 1977 1977 1986 1986 1986 1986 1986 1988 1973 1973 1988 1988 1986 1978 1978 1986 1986 1986 1986 1986 1989 1973 1973 1989 1989 1974 1988 1985 1985 1977 1977 1986 1977 1994 1994 1977 1977 1986 1977 1994 1994 10 3 05 Temp Length words CK yes yes 300 0 300 0 293 6 293 6 293 6 293 6 293 6 3000 1 293 6 300 0 293 6 293 6 3000 1 293 6 300 0 293 6 293 6 293 6 293 6 293 6 3000 1 293 6 300 0 293 6 293 6 3000 1 293 6 293 6 293 6 yes yes 293 6 293 6 293 6 293 6 3
350. face 1 reenters on the right side surface 2 If the surfaces were reflecting the reentering particle would miss the cylinder shown by the dotted line In a fully specified lattice and in the periodic geometry the reentering particle will hit the cylinder as it should Much more complicated examples are possible particularly hexagonal prism lattices In all cases MCNP checks that the periodic surface pair matches properly and performs all the necessary surface rotations and translations to put the particle in the proper place on the corresponding periodic plane The following limitations apply Periodic boundaries cannot be used with next event estimators such as detectors or DXTRAN see page 2 101 periodic surfaces must be planes Periodic planes cannot also have a surface transformation The periodic cells may be infinite or bounded by planes on the top or bottom that must be reflecting or white boundaries but not periodic Periodic planes can only bound other periodic planes or top and bottom planes A single zero importance cell must be on one side of each periodic plane All periodic planes must have a common rotational vector normal to the geometry top and bottom CROSS SECTIONS The MCNP code package is incomplete without the associated nuclear data tables The kinds of tables available and their general features are outlined in this section The manner in which information contained on nuclear da
351. ficiency Worse the error estimates may be misleading until enough extremely high weight particles have been sampled Monte Carlo novices are prone to be misled because they do not have enough experience reading and interpreting the summary information on the sampling supplied by MCNP Hence a novice may put more faith in an answer than is justified Although it is impossible to eliminate all pathologies in Monte Carlo calculations a properly specified weight window goes far toward eliminating the pathology referred to in the preceding paragraph As soon as the weight gets above the weight window the particle is split and subsequent weight multiplications will thus be multiplying only a fraction of the particle s weight before splitting Thus it is hard for the tally to be severely perturbed by a particle of extremely large weight In addition low weight particles are rouletted so time is not wasted following particles of trivial weight One cannot ensure that every history contributes the same score a zero variance solution but by using a window inversely proportional to the importance one can ensure that the mean score from any track in the problem is roughly constant A weight window generator exists to estimate these importance reciprocals see page 2 146 In other words the window is chosen so that the track weight times the mean score for unit track weight is approximately constant Under these conditions the variance is due mostly
352. ficult to converge 10 3 05 2 107 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS ESTIMATION OF THE MONTE CARLO PRECISION 2 Segregate electrons and positrons into separate bins plus a total bin There will be three bins positron electron and total all with positive scores The total bin will be the same as the single tally bin without the ELC option 3 Segregate electrons and positrons into separate bins plus a total bin with the electron bin scores being all negative to reflect their charge The bins will be for positrons positive scores electrons negative scores and total The total bin will be the same as the single bin with the first ELC option above usually with negative scores because there are more electrons than positrons 5 User Modification If the above capabilities do not provide exactly what is desired tallies can be modified by a user supplied subroutine FU card As with user supplied SOURCE subroutine which lets the users provide their own specialized source the TALLYX subroutine lets the user modify any tally with all the programming changes conveniently located in a single subroutine 6 Tally Output Format Not only can users change the contents of MCNP tallies the output format can be modified as well Any desired descriptive comment can be added to the tally title by the tally comment FC card The printing order can be changed FQ card so that instead of for instance get
353. for all elements from Z 1 through Z 100 The data in the photon interaction tables allow MCNP to account for coherent and incoherent scattering photoelectric absorption with the possibility of fluorescent emission and pair production Scattering angular distributions are modified by atomic form factors and incoherent scattering functions Cross sections for nearly 2000 dosimetry or activation reactions involving over 400 target nuclei in ground and excited states are part of the MCNP data package These cross sections can be used as energy dependent response functions in MCNP to determine reaction rates but cannot be used as transport cross sections Thermal data tables are appropriate for use with the S o scattering treatment in MCNP The data include chemical molecular binding and crystalline effects that become important as the neutron s energy becomes sufficiently low Data at various temperatures are available for light and heavy water beryllium metal beryllium oxide benzene graphite polyethylene and zirconium and hydrogen in zirconium hydride 1 4 10 3 05 CHAPTER 1 MCNP OVERVIEW INTRODUCTION TO MCNP FEATURES B Source Specification MCNP s generalized user input source capability allows the user to specify a wide variety of source conditions without having to make a code modification Independent probability distributions may be specified for the source variables of energy time position and direction and for othe
354. for the F2 F4 and F5 tallies can be recast as F2 al aaa E t F4 1 and 5 Lae tp E t The range of integration over energy and time can be tailored by E and T cards If no E card is present the integration limits are the same as the limits for the corresponding cross sections used The F4 cell flux and F2 surface flux tallies are discussed in this section The F5 detector flux tally is discussed on page 2 89 1 Track Length Estimate of Cell Flux F4 10 3 05 2 85 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS TALLIES The average particle flux in a cell from Table 2 2 can be written II v aE a avjao w t Q E n v a av ao far vn f Q E t vN 1 E t where N E t Q E t is the density of particles regardless of their trajectories at a point Defining ds to be the differential unit of track length and noting that ds vdt yields v a av as M t E t The quantity N E t ds may be thought of as a track length density thus the average flux can be estimated by summing track lengths MCNP estimates by summing WT V for all particle tracks in the cell Time and energy dependent subdivisions of are made by binning the track lengths in appropriate time and energy bins The track length estimator is generally quite reliable because there are frequently many tracks in a cell compared to the
355. formation TRCL 3 28 Cell Volume VOL 3 24 Cell by cell energy cutoff ELPT 3 136 Cell flagging CFn 3 101 CFn 3 101 CMn 3 101 Cn 3 93 Comment 3 4 Computer time cutoff 3 138 Coordinate Transformation TRn 3 30 to 3 32 Cosine Cn 3 93 Criticality Source KCODE 3 76 Cross Section File XSn Card 3 123 Index 1 MCNP MANUAL INDEX Cards CTME 3 138 CUT 3 135 DCBN 3 142 DDn 3 108 DE 3 99 DE DF H 3 Debug Information DBCN card 3 142 Defaults 3 7 3 157 Designators 3 7 Detector Contribution PDn card 3 51 Detector Diagnostics DDn 3 108 Detector F5 3 82 DF 3 99 Dose 3 99 DRXS 3 121 DSn 3 65 DXC DXTRAN Contribution card 3 51 DXTRAN DXT 3 110 ELPT 3 136 En 3 92 Energy Multiplier EMn 3 100 Energy Physics Cutoff PHYS card 3 127 to 3 132 Energy Splitting and Roulette ESPLT card 3 35 Energy normed tally plots B 27 Exponential Transform EXT card 3 40 FCn 3 91 File creation FILES card 3 144 FILES 3 144 FILL 3 29 Fission Turnoff NONU card 3 122 Floating Point Array RDUM card 3 139 FMESH card 3 114 FMn 3 95 Fna 3 80 Forced collision card FCL 3 42 Free Gas Thermal Temperature TMP card 3 132 FSn 3 102 FTn 3 112 FUn 3 105 General Source SDEF card 3 53 History Cutoff NPS card 3 137 IDUM card 3 138 IMP 3 34 Integer Array IDUM card 3 138 Index 2 Cards KCODE card 3 76 KSRC 3 77 Lattice LAT card 3 28 Lost Particle LOS
356. g neutrons and one photon One neutron and the photon are banked for later analysis The first fission neutron is captured at event 3 and terminated The banked neutron is now retrieved and by random sampling leaks out of the slab at event 4 The fission produced photon has a collision at event 5 and leaks out at event 6 The remaining photon generated at event 1 is now followed with a capture at event 7 Note that MCNP retrieves banked particles such that the last particle stored in the bank is the first particle taken out This neutron history is now complete As more and more such histories are followed the neutron and photon distributions become better known The quantities of interest whatever the user requests are tallied along with estimates of the statistical precision uncertainty of the results 10 3 05 1 3 CHAPTER 1 MCNP OVERVIEW INTRODUCTION TO MCNP FEATURES INTRODUCTION TO MCNP FEATURES Various features concepts and capabilities of MCNP are summarized in this section More detail concerning each topic is available in later chapters or appendices A Nuclear Data and Reactions MCNP uses continuous energy nuclear and atomic data libraries The primary sources of nuclear data are evaluations from the Evaluated Nuclear Data File ENDE system Advanced Computational Technology Initiative ACTI the Evaluated Nuclear Data Library Evaluated Photon Data Library EPDL the Activation Library ACTL compilatio
357. g numbers MeV collision nubar prompt or total fission Q in print table 98 but not plots 10 3 05 S a B MT 1 2 4 APPENDIX G MCNP DATA LIBRARIES Microscopic Cross Section Description Total cross section Elastic scattering cross section Inelastic scattering cross section Neutron and Photon Multigroup MT 1 18 101 202 301 318 401 Photoatomic Data MT 501 504 502 522 516 301 Electrons see Note 3 MT FM 1 Microscopic Cross Section Description Total cross section Fission cross section Nubar data Fission chi data Absorption cross section Stopping powers Momentum transfers Edit reaction n Photon production Heating number Fission Q Heating number times total cross section Microscopic Cross Section Description Total Incoherent Compton Form Factor Coherent Thomson Form Factor Photoelectric with fluorescence Pair production Heating number Microscopic Cross Section Description de dx electron collision stopping power de dx electron radiative stopping power de dx total electron stopping power electron range electron radiation yield relativistic stopping power density correction ratio of rad col stopping powers drange dyield 10 3 05 ENDF B REACTION TYPES APPENDIX G MCNP DATA LIBRARIES ENDF B REACTION TYPES 11 rng array values 12 qav array values 13 ear array values Notes 1 At the time they are loaded the tot
358. gher importance to a region of lower importance where they will probably contribute little to the desired problem result undergo Russian roulette that is some of those particles will be killed a certain fraction of the time but survivors will be counted more by increasing their weight the remaining fraction of the time In this way unimportant particles are followed less often yet the problem solution remains undistorted On the other hand if a particle is transported to a region of higher importance where it will likely contribute 1 10 10 3 05 10 11 12 CHAPTER 1 MCNP OVERVIEW INTRODUCTION TO MCNP FEATURES to the desired problem result it may be split into two or more particles or tracks each with less weight and therefore counting less In this way important particles are followed more often yet the solution is undistorted because on average total weight is conserved Energy splitting Russian roulette Particles can be split or rouletted upon entering various user supplied energy ranges Thus important energy ranges can be sampled more frequently by splitting the weight among several particles and less important energy ranges can be sampled less frequently by rouletting particles Time splitting Russian roulette Like energy splitting roulette but based on time Weight cutoff Russian roulette If a particle weight becomes so low that the particle becomes insignificant it undergoes Russian roulette Most partic
359. ght side As with rotationally symmetric cells the area of a surface is determined cell by cell twice once for each side The area of a surface on one side is the sum over all facets on that side The volume of a polyhedron is computed by using an arbitrary reference plane Prisms are projected from each facet normal to the reference plane and the volume of each prism is V 2 da cos 0 where d distance from reference plane to facet centroid facet area and angle between the external normal of the facet and the positive normal of the reference plane The sum of the prism volumes is the polyhedron cell volume Stochastic Volume and Area Calculation MCNP cannot calculate the volumes and areas of asymmetric nonpolyhedral or infinite cells Also in very rare cases the volume and area calculation can fail because of roundoff errors For these cases a stochastic estimation is possible by ray tracing The procedure is as follows 1 Void out all materials in the problem VOID card Set all nonzero importances to one and all positive weight windows to zero Use a planar source with a source weight equal to the surface area to flood the geometry with particles This will cause the particle flux throughout the geometry to statistically approach unity Perhaps the best way to do a stochastic volume estimation is to use an inward directed biased cosine source on a spherical surface with weight equal to x2 Use the cell flux
360. ght w is then put on the cell boundary The collision site of the collided particle of weight w is selected from a conditional distance to collision probability density the condition being that the particle must collide in the cell This technique preserves the expected weight colliding at any point in the cell as well as the expected weight not colliding A little simple mathematics is required to demonstrate this technique Russian roulette takes a particle at 7 V t of weight wp and turns it into a particle of weight gt Wo With probability and kills it that is weight 0 with probability 1 wo w The expected weight at 7 V t is wy wo wj 1 w w1 0 Wo the same as in the analog game Some techniques use a combination of these basic games and DXTRAN uses all three 3 Efficiency Time per History and History Variance Recall from page 2 116 that the measure of efficiency for MCNP calculations is the FOM FOM 1 R T where R sample relative standard deviation of the mean and T computer time for the calculation in minutes Recall from Eqns 2 17 and 2 19a that R 5 where S sample history variance number of particles and X sample mean Generally we are interested in obtaining the smallest R in a given time The equation above indicates that to decrease R it is desirable to 1 decrease 5 and 2 increase N that is decrease the time per particle histo
361. gy such that lt Ej and Ej Ejtr E 4 Ej 1 A random number on the unit interval 0 1 is used to sample a cosine bin k from the cumulative density function C kSS CL ku where i if gt i 1 if lt and 5is random number on the unit interval For histogram interpolation the sampled cosine is For linear linear interpolation the sampled cosine is 2 PLk fan PLk 1 PLk LM ket M and If the emitted angular distribution for some incident neutron energy is isotropic is chosen from u 6 where amp is a random number on the interval 1 1 Strictly in MCNP random numbers are always furnished the interval 0 1 Thus to compute amp on 1 1 we calculate 5 2 1 where amp is a random number on 0 1 The ENDF 6 format also has various formalisms to describe correlated secondary energy angle spectra These are discussed later in this chapter 10 3 05 2 37 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS For elastic scattering inelastic level scattering and some ENDF 6 inelastic reactions the scattering cosine is chosen in the center of mass system Conversion must then be made to the cosine in the target at rest system For other inelastic reactions the scattering cosine is sampled directly in the target at rest system The incident particle direction cosines
362. haty The LLL Evaluated Nuclear Data Library ENDL Evaluation Techniques Reaction Index and Descriptions of Individual Reactions Lawrence Livermore National Laboratory report UCRL 50400 Vol 15 Part A September 1975 D E Cullen M H Chen J H Hubbell S T Perkins E F Plechaty J A Rathkopf and J H Scofield Tables and Graphs of Photon Interaction Cross Sections from 10 eV to 100 GeV Derived from the LLNL Evaluated Photon Data Library EPDL Lawrence Livermore National Laboratory report UCRL 50400 Volume 6 Rev 4 Part A Z 1 to 50 and Part B 7 51 to 100 1989 M A Gardner R J Howerton ACTL Evaluated Neutron Activation Cross Section Library Evaluation Techniques and Reaction Index Lawrence Livermore National Laboratory report UCRL 50400 Vol 18 October 1978 E D Arthur and P Young Evaluated Neutron Induced Cross Sections for 9496Ee to 40 MeV Los Alamos Scientific Laboratory report LA 8626 MS ENDF 304 December 1980 D Foster Jr and E D Arthur Average Neutronic Properties of Prompt Fission Products Los Alamos National Laboratory report LA 9168 MS February 1982 E D Arthur Young A Smith and C A Philis New Tungsten Isotope Evaluations for Neutron Energies Between 0 1 and 20 MeV Trans Am Nucl Soc 39 793 1981 R E MacFarlane and D W Muir The NJOY Nuclear Data Processing System Version 91 Los Alamos National Laboratory repor
363. he HSRC card is not provided MCNP will automatically determine a grid that encloses all of the fission sites for the cycle The number of grid boxes will be determined by dividing the number of histories per cycle by 20 and then finding the nearest integer for each direction that will produce this number of equal sized grid boxes although not fewer than 4x4x4 will be used Upon completion of the problem MCNP will compute the average value of H for the last half of the active cycles as well as its population standard deviation MCNP will then report the first cycle found active or inactive where falls within one standard deviation of its average for the last half of the cycles along with a recommendation that at least that many cycles should be inactive Plots of H vs cycle should be examined to further verify that the number of inactive cycles is adequate for fission source convergence When running criticality calculations with MCNP it is essential that users examine the convergence of both the fission source distribution using Shannon entropy If either or the fission source distribution is not converged prior to starting the active cycles then results from the calculations will not be correct 9 Normalization of Standard Tallies in a Criticality Calculation Track length fluxes surface currents surface fluxes heating and detectors all the standard MCNP tallies can be made during a criticality cal
364. he Monte Carlo method was published by Herman Kahn and the first book was published by Cashwell and Everett in 1959 At Los Alamos Monte Carlo computer codes developed along with computers The first Monte Carlo code was the simple 19 step computing sheet in John von Neumann s letter to Richtmyer But as computers became more sophisticated so did the codes At first the codes were written in machine language and each code would solve a specific problem In the early 1960s better computers and the standardization of programming languages such as Fortran made possible more general codes The first Los Alamos general purpose particle transport Monte Carlo code was MCS 9 written in 1963 Scientists who were not necessarily experts in computers and Monte Carlo mathematical techniques now could take advantage of the Monte Carlo method for radiation transport They could run the MCS code to solve modest problems without having to do either the programming or the mathematical analysis themselves MCS was followed by MCN in 1965 MCN could solve the problem of neutrons interacting with matter in a three dimensional geometry and used physics data stored in separate highly developed libraries In 1973 MCN was merged with MCG a Monte Carlo gamma code that treated higher energy photons to form MCNG a coupled neutron gamma code In 1977 MCNG was merged with MCP a Monte Carlo Photon code with detailed physics treatment down to 1 keV to accurately
365. he combined average keg and which for multivariate normality is the almost minimum variance estimate It is almost because the covariance matrix is not known exactly and must be estimated The three combined k and estimators are the best final estimates from an MCNP calculation 9 This method of combining estimators can exhibit one feature that is disconcerting sometimes usually with highly positively correlated estimators the combined estimate will lie outside the interval defined by the two or three individual average estimates Statisticians at Los Alamos have shown that this is the best estimate to use for a final kep and value Reference 140 shows the results of one study of 500 samples from three highly positively correlated normal distributions all with a mean of zero In 319 samples all three estimators fell on the same side of the expected value This type of behavior occurs with high positive correlation because if one estimator is above or below the expected value the others have a good probability of being on the same side of the expected value The advantage of the three combined estimator is that the Halperin algorithm correctly predicts that the true value will lie outside of the range 6 Error Estimation and Estimator Combination After the first Z inactive cycles during which the fission source spatial distribution is allowed to come into spatial equilibrium MCNP begins to accumulate the estimates of k
366. he detector The 200 million history point detector result is 5 41 x 10 n cm 5 R 0 035 VOV 0 60 slope 2 4 FOM 0 060 The point detector f x slope is increasing but still is not yet completely sampled This tally did not pass 6 of 10 checks with 200 million histories The result is about 1 5 estimated standard deviations below the correct answer It is important to note that calculating a large number of histories DOES NOT guarantee a precise result The more compact empirical ring f x for 20 million histories appears to be completely sampled because of the large slope The results for 1 billion histories are shown in Ref 121 For difficult to sample problems such as this example it is possible that an even larger history score could occur that would cause the VOV and possibly the slope to have unacceptable values The mean and RE will be much less affected than the VOV The additional running time required to reach acceptable values for the VOV and the slope could be prohibitive The large history score should NEVER be discarded from the tally result It is important that the cause for the large history score be completely understood If the score was created by a poorly sampled region of phase space the problem should be modified to provide improved phase space sampling It is also possible that the large score was created by an extremely unlikely set of circumstances that occurred early in the calculation In this situation if the RE i
367. he general effect of CN Z Z is to decrease the Thomson cross section more extremely for backward scattering for high E and low Z This effect is opposite in these respects to the effect of 10 3 05 2 61 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS I Z v Z on K o u in incoherent Compton scattering For a given Z C Z v decreases from C Z 0 Z to C Z 0 For example C Z is a rapidly decreasing function of u as u varies from 1 to 1 and therefore the coherent cross section is peaked in the forward direction At high energies of the incoming photon coherent scattering is strongly forward and can be ignored The parameter v is the inverse length v sin 0 2 A 1 where 10 m c h 2 29 1445cm 1 The maximum value of v is Unax A 2 41 2166a at 1 The square of the maximum value is 1 1698 8038o The qualitative features of C Z v are shown in Figure 2 6 V max TE 1 0 aon Q 0 0 1 2 d 4 5 6 Figure 2 6 For next event estimators one must evaluate the probability density function nr wc 2 for given Here Z a is the integrated coherent cross section The value of C 2 v atv ka 1 mustbe interpolated in the original C Z v tables separately stored on the cross section library for this purpose Note that at high energies coherent scattering is virtually straight ahead with no energy los
368. he method of 32 equiprobable cosine bins accurately represents high probability regions of the scattering probability however it can be a very crude approximation in low probability regions For example it accurately represents the forward scattering in a highly forward peaked distribution but may represent all the back angle scattering using only one or a few bins 2 36 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS A new more rigorous angular distribution representation was implemented in MCNP 4C This new representation features a tabulation of the probability density function PDF as a function of the cosine of the scattering angle Interpolation of the PDF between cosine values may be either by histogram or linear linear interpolation The new tabulated angular distribution allows more accurate representations of original evaluated distributions typically given as a set of Legendre polynomials in both high probability and low probability regions Tabular angular distributions are equivalent to tabular energy distribution as defined using ENDF law 4 except that the sampled value is the cosine of the scattering angle and discrete lines are not allowed For each incident neutron energy there is a pointer to a table of cosines probability density functions p and cumulative density functions The index i and the interpolation fraction are found on the incident energy grid for the incident ener
369. he object of this example A surface flux estimator would have been over a factor of 150 to 30 000 times more efficient than ring and point detectors respectively Figure 2 22 shows MCNP plots of the estimated mean R VOV and slope of the history score PDF as a function of N values of 20 000 left column and 5 million right column The ring detector results are shown as the solid line and the point detector result is the dashed line Column 1 shows the results as a function of N for 20 000 histories The point detector result at 14 000 histories not shown was 1 41 x 10 P cm s R 0 041 The FOM varied somewhat randomly between about 800 and 1160 for the last half of the problem With no other information this result could be accepted by even a careful Monte Carlo practitioner However the VOV never gets close to the required 0 1 value and the slope of the unbounded is less than 1 4 This slope could not continue indefinitely because even the mean of f x would not exist Therefore a 10 3 05 2 131 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS ESTIMATION OF THE MONTE CARLO PRECISION confidence interval should not be formed for this tally At 20 000 histories R increases substantially and the FOM crashes indicating serious problems with the result The ring detector result i is having problems of its own The ring detector result for 14 000 histories was 4 60 x 10 n em s R 0 17 VOV 0 35 slope 2 1 FOM 67 None
370. he population changes in accordance with kg N Noe where is the adjoint weighted removal lifetime MCNP calculates the nonadjoint weighted prompt removal lifetime t that can be significantly different in a multiplying system In a nonmultiplying system 0 and the population decays as t 1 n noe where the nonadjoint weighted removal lifetime 7 15 also the relaxation time Noting that the flux is defined as where is the speed the MCNP nonadjoint weighted prompt removal lifetime 7 is defined as B f pV aided V JdVdtdEdQ p 0 o 6 dVdtdEdO V O E O T oo V O E O The prompt removal lifetime is a fundamental quantity in the nuclear engineering point kinetics equation It is also useful in nuclear well logging calculations and other pulsed source problems because it gives the population time decay constant 10 3 05 2 169 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CRITICALITY CALCULATIONS 1 Collision Estimators The collision estimate for k for any active cycle is ie ly yw In 2 USOT where i is summed over all collisions in a cycle where fission is possible k is summed over all nuclides of the material involved in the collision total microscopic cross section microscopic fission cross section average number of prompt or total neutrons produced per fissi
371. he simulation of particle transport from one place to another is deterministically short circuited Transport from the source or collision point to the detector is replaced by a deterministic estimate of the potential contribution to the detector This transport between the source or collision point and the detector can be thought of as being via pseudoparticles Pseudoparticles undergo no further collisions These particles do not reduce the weight or otherwise affect the random walk of the particles that produced them They are merely estimates of a potential contribution The only resemblance to Monte Carlo particles is that the quantity they 2 100 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS TALLIES estimate requires an attenuation term that must be summed over the trajectory from the source or collision to the detector Thus most of the machinery for transporting particles can also be used for the pseudoparticles No records for example tracks entering are kept about pseudoparticle passage Because detectors rely on pseudoparticles rather than particle simulation by random walk they should be considered only as a very useful last resort Detectors are unbiased estimators but their use can be tricky misleading and occasionally unreliable Consider the problem illustrated in Figure 2 14 Scattering Region Monoenergetic Detector isotropic source Figure 2 14
372. he thick target bremsstrahlung approximation default for MODE P problems IDES 0 on the PHYS P card or they may undergo full electron transport default for MODE P E problems IDES 0 on the PHYS P card Multigroup or multigroup adjoint photons are treated separately After the surface crossing or collision is processed transport continues by calculating the distance to cell boundary and so on Or if the particle involved in the collision was killed by capture or variance reduction the bank is checked for any remaining progeny and if none exists the history is terminated Appropriate summary information is incremented the tallies of this particular history are added to the total tally data the history is terminated and a return is made For each history checks are made to see if output is required or if the job should be terminated because enough histories have been run or too little time remains to continue For continuation HSTORY is called again Otherwise a return is made to MCRUN and the summary information and tally data are printed GEOMETRY The basic MCNP geometry concepts discussed in Chapter 1 include the sense of a cell the intersection and union operators and surface specification Covered in this section are the complement operator the repeated structure capability an explanation of two surfaces the cone and the torus and a description of ambiguity reflecting white and periodic boundary surfaces 10 3 05 2
373. hechin and Ermilova investigated the Landau Blunck Leisegang theory and derived an estimate for the relative error E Boe caused by the neglect of higher order moments Based on this work Seltzer describes and recommendis a correction to the Blunck Westphal variance _ l 3 eg This value for the variance of the Gaussian is used in MCNP Examination of the asymptotic form for AX shows that unrestricted sampling of A will not result in a finite mean energy loss Therefore a material and energy dependent cutoff imposed on the sampling of A In the initiation phase of an MCNP calculation the code makes use of two preset arrays flam mlanc and avIm mlanc with mlanc 1591 The array flam contains candidate values for the range 4 lt Ac lt 50000 the array avim contains the corresponding expected mean values for the sampling of For each material and electron energy the code uses the known mean collisional energy loss A interpolating this tabular function to select a suitable value for which is then stored in the dynamically allocated array flc During the transport phase of the calculation the value of flc applicable to the current material and electron energy is used as an upper limit and any sampled value of greater than the limit is rejected In this way the correct mean energy loss is preserved 5 Logic for Sampling Energy Straggling The Landau theory described in the previou
374. here are several problems associated with 30 x 20 photon production data The 30 x 20 matrix is an inadequate representation of the actual spectrum of photons produced In particular discrete photon lines are not well represented and the high energy tail of a photon continuum energy distribution is not well sampled Also the multigroup representation is not consistent with the continuous energy nature of MCNP Finally not all photons should be produced isotropically None of these problems exists for data processed into the expanded photon production format 4 Absorption Absorption is treated in one of two ways analog or implicit Either way the incident incoming neutron energy does not include the relative velocity of the target nucleus from the free gas thermal treatment because nonelastic reaction cross sections are assumed to be nearly independent of temperature That is only the scattering cross section is affected by the free gas thermal treatment The terms absorption and capture are used interchangeably for non fissile nuclides both meaning For fissile nuclides absorption includes both capture and fission reactions a Analog Absorption In analog absorption the particle is killed with probability o o7 where o and are the absorption and total cross sections of the collision nuclide at the incoming neutron energy The absorption cross section is specially defined for MCNP as the sum of all cro
375. his approaches the integro differential transport equation which has derivatives in space and time By contrast Monte Carlo transports particles between events for example collisions that are separated in space and time Neither differential space nor time are inherent parameters of Monte Carlo transport The integral equation does not have terms involving time or space derivatives Monte Carlo is well suited to solving complicated three dimensional time dependent problems Because the Monte Carlo method does not use phase space boxes there are no averaging approximations required in space energy and time This is especially important in allowing detailed representation of all aspects of physical data B The Monte Carlo Method Monte Carlo can be used to duplicate theoretically a statistical process such as the interaction of nuclear particles with materials and is particularly useful for complex problems that cannot be modeled by computer codes that use deterministic methods The individual probabilistic events that comprise a process are simulated sequentially The probability distributions governing these 1 2 10 3 05 CHAPTER 1 MCNP OVERVIEW MCNP AND THE MONTE CARLO METHOD events are statistically sampled to describe the total phenomenon In general the simulation is performed on a digital computer because the number of trials necessary to adequately describe the phenomenon is usually quite large The statistical sampling process
376. hlung production models were integrated into MCNP 4C l Electron Steps and Substeps The condensed random walk for electrons can be considered in terms of a sequence of sets of values 0 Eo 1 51 5 E tU r where 5 Ep tp Up and r are the total path length energy time direction and position of the electron at the end of n steps On the average the energy and path length are related by E Sn dE Bs qub ag d E gt 2 6 where dE ds is the total stopping power in energy per unit length This quantity depends on energy and on the material in which the electron is moving ETRAN based codes customarily choose the sequence of path lengths 5 such that 2 7 1 for constant k The most commonly used value is k 2 5 loss per step of 8 3 Which results in an average energy Electron steps with energy dependent path lengths s s 5 determined by Eqs 2 3 2 4 are called major steps or energy steps The condensed random walk for electrons is structured in terms of these energy steps For example all precalculated and tabulated data for electrons are stored on an energy grid whose consecutive energy values obey the ratio in Eq 2 4 In addition the Landau and Blunck Leisegang theories for energy straggling are applied once per energy step But see page 2 74 below for a more detailed option For a single step the angular scattering could also be calculated with
377. hysics treatment 2 59 Inelastic Scattering 2 35 2 39 Initiate run 3 1 3 2 3 3 3 135 INP File 3 1 Card Format 3 4 Continue Run 3 2 to 3 3 Default Values 3 7 Geometry Errors 3 8 Initiate Run 3 2 Input Error Messages 3 7 Message Block 3 1 Particle Designators 3 7 Installation TC 1 Integer Array IDUM card 3 138 Integers 8 byte DBCN 3 142 DBUG 3 142 MPLOT 3 147 NPS 3 137 PRDMP 3 139 PTRAC 3 148 RAND 3 141 Interpolate nI 3 4 IPTAL Array 3 106 E 31 J Jerks g 3 80 Jump nJ 3 5 KCODE card 3 76 Klein Nishina 2 58 2 59 2 60 KSRC card 3 77 10 3 05 Lattice card 3 28 Lattice card 3 28 Lattice Tally 3 81 3 85 Lattice Tally Enhancements 3 116 Lethargy normed tally plots B 27 Lost Particle LOST card 3 141 Lost particles 3 9 3 141 M Macrobodies 3 18 BOX 3 18 3 21 Facets 3 21 HEX 3 19 3 22 RCC 3 19 3 22 RHP 3 19 3 22 RPP 3 18 3 21 SPH 3 19 3 22 Mass Atomic 3 118 Density 3 95 B 7 Material Card Fraction 3 118 ZAID 3 118 Material number 3 9 3 10 3 95 3 96 3 97 3 118 3 124 3 149 3 152 Material Specification Card 3 117 Material Void VOID card 3 124 Material Mm card 3 118 Maxwell fission energy spectrum 3 64 MCNP Input 3 1 MCNP Structure 2 4 D 6 Means Variances Standard Deviations 2 109 MESH Card 3 48 Mesh Tally 2 83 Mesh tally FMESH 3 114 Mesh Based Weight Window MESH card 3 48 Message Block INP File
378. i 10 3 05 Table of Contents Volume I Overview and Theory CHAPTER 1 MCNP OVERVIEW ee taria OR ed TR EDU UE 1 MCNP AND THE MONTE CARLO METHOD essere enne 1 Monte Carlo Method vs Deterministic Method 2 The Monte Carlo Method RR aa 2 INTRODUCTION TO MCNP FEATURES a aa 4 ue lear and Reactions eT 4 Source Specification tede Uem ee 3 Tallies and Output Ei 5 Estimation of Monte Carlo Errors Po 6 Varnance Reduction 8 Ret E 12 Cells E 13 Surface Typ SS CNC AUN 2o uda hisdem titu uda ttd Uude 17 Surface Parameter Specification 17 REFERENCES c 19 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS 1 INTRODUCTION a a a CUP DUE 1 a 1 NICINP Structure E 4 History FIOW 5 GEOMETRY Merc
379. i tnb ete gas 2 TOC 4 10 3 05 Table of Contents MCNP Execution Line Options and Useful Combinations 3 MCNP Execution Lines for Various Types of Problems 4 MCNP Physical Units and Tally Units 22 oA En hi bk ncs bano rto 4 MCNP Interrupts press cr after each entry 5 Example of an MCNP Fixed Source INP File Lutetia toii nes oda bre 5 Example of Eigenvalue INP File 6 INPUT INP FILE COMMANDS osise cU Ei en t 7 Input re iile vnica 7 Commands 8 Input Commands by Function sioe ide rv 11 Concise Input Command Descriptions cx rete 14 GEOMETRY PLOTTING COMMANDS 44 Geometry Plotting Command Formats nennen 44 Geometry Plotting 45 Geometry Plotting Commands By Function 6 46 Concise Geometry Plotting Command Descriptions 47 TALLY AND CROSS SECTION
380. iance reduction techniques available to solve the problem If an analog calculation will not suffice to calculate the tally there must be something special about the particles that tally The user should understand the special nature of those particles that tally Perhaps for example only particles that scatter in particular directions can tally After the user understands why the tallying particles are special MCNP techniques can be selected or developed by the user that will increase the number of special particles followed After the MCNP techniques are selected the user typically has to supply appropriate parameters to the variance reduction techniques This is probably more difficult than is the selection of techniques The first guess at appropriate parameters typically comes either from experience with similar problems or from experience with an analog calculation of the current problem It is usually better to err on the conservative side that is too little biasing rather than too much biasing After the user has supplied parameters for the variance reduction techniques a short Monte Carlo run is done so that the effectiveness of the techniques and parameters can be monitored with the MCNP output The MCNP output contains much information to help the user understand the sampling This information should be examined to ensure that 1 the variance reduction techniques are improving the sampling of the particles that tally 2 the vari
381. ib03 2002 1344 84 100 B IV 89 B IV E amp C 26000 04p mcplib04 2002 5718 813 100 B VL8 8 8 Z 27 Cobalt K K K K K K 27000 01p mcplib 1982 417 45 0 1 B IV B IV E amp C 27000 02p mcplib02 1993 651 84 100 B IV 89 E amp C 27000 03p mcplib03 2002 1344 84 100 B IV 89 B IV E amp C 27000 04p mcplib04 2002 5436 766 100 B VL8 8 8 Z 28 Nickel 28000 01p meplib 1982 429 47 0 1 B IV B IV E amp C 28000 02p mcplib02 1993 663 86 100 B IV 89 B IV E amp C 28000 03p mcplib03 2002 1356 86 100 B IV 89 B IV E amp C 28000 04p mcplib04 2002 5826 831 100 B VL8 8 8 Z 29 29000 01p mcplib 1982 429 47 0 1 B IV B IV E amp C 29000 02p mcplib02 1993 663 86 100 B IV 89 B IV E amp C 29000 03p mcplib03 2002 1356 86 100 B IV 89 B IV E amp C 29000 04p mcplib04 2002 5754 819 100 B VL8 8 18 Z 30 Zinc 30000 01p mcplib 1982 453 51 0 1 B IV B IV E amp C 30000 02p meplib02 1993 687 90 100 B IV 89 E amp C 30000 03p mcplib03 2002 1380 90 100 B IV 89 B IV E amp C 30000 04p mcplib04 2002 6288 908 100 B VL8 8 8 Z 31 Gallium 31000 01 meplib 1982 457 51 0 1 B IV B IV E amp C 31000 02p meplib02 1993 691 90 100 B IV 89 E amp C 31000 03p mcplib03 2002 1483 90 100 B IV 89 B IV E amp C 31000 04p mcplib04 2002 6787 974 100 B VL8 8 8 Z 32
382. ic scattering There are three options 1 none no elastic scattering data for this material 2 coh coherent elastic scattering data provided for this material Bragg scattering 3 inco incoherent elastic scattering data provided for this material 10 3 05 G 5 APPENDIX G MCNP DATA LIBRARIES 5 DATA FOR USE WITH THE MTn CARD Table G 1 Thermal S o p Cross Section Libraries Library ZAID Source Name Beryllium Metal 4009 be 01t endf5 tmccs be 04t endf5 tmccs be O5t endf5 tmccs be 06t endf5 tmccs be 60t endf6 3 sab2002 be 61t endf6 3 sab2002 be 62t endf6 3 sab2002 be 63t endf6 3 sab2002 be 64t endf6 3 sab2002 be 65t endf6 3 sab2002 be 69t endf6 3 sab2002 Benzene 1001 6000 6012 benz O1t endf5 tmccs benz 02t endf5 tmccs benz 03t endf5 tmccs benz 04t endf5 tmccs benz 05t endf5 tmccs benz 60t endf6 3 sab2002 benz 61t endf6 3 sab2002 benz 62t endf6 3 sab2002 benz 63t endf6 3 sab2002 Beryllium Oxide 4009 8016 beo 01t endf5 tmccs beo 04t endf5 tmccs beo O5t endf5 tmccs beo 06t endf5 tmccs beo 60t endf6 3 sab2002 beo 61t endf6 3 sab2002 beo 62t endf6 3 sab2002 beo 63t endf6 3 sab2002 beo 64t endf6 3 sab2002 beo 65t endf6 3 sab2002 Ortho Deuterium 1002 dortho O1t lanl89 therxs dortho 60t endf6 3 sab2002 Para Deuterium 1002 dpara 01t 89 therxs dpara 60t endf6 3 sab2002 Date of Processing 10 24 85 10 24 85 10 24 85 10 24 85 09 13 99 09 13 99 09 13 99 09 14 99 09 14 99
383. idence intervals could not be formed via the central limit theorem because the central limit theorem requires a finite variance For this reason MCNP sets u 0 05 when u lt 0 10 because of this approximation the F2 tally is not an exact estimate of the surface flux The SD card can be used to input a new area that divides the tally In other words if is input on the SD card the tally will be divided by A instead of The F2 tally is essential for stochastic calculation of surface areas when the normal analytic procedure fails see page 2 187 C Track Length Cell Energy Deposition Tallies The F6 and F7 cell heating and energy deposition tallies are track length flux tallies modified to tally a reaction rate convolved with an energy dependent heating function or Q op from Table 2 2 instead of a flux The derivation of such modified track length estimators along the lines of the derivation of the track length flux estimator in subsection on page 2 85 is straightforward The heating tallies are merely flux tallies F4 multiplied by an energy dependent multiplier FM card the equivalence is shown in this section The units of the heating tally are MeV g An asterisk F6 and F7 changes the units to jerks g 1 MeV 1 6021910 jerks the asterisk causes the tally to be multiplied by a constant rather than by energy as in the other tallies The SD card can be used to input a new mass that divides the tally In
384. ideuteron Model of Photoabsorption Physical Review C Vol 44 No 2 pp 814 823 1991 J R Wu and C C Chang Pre Equilibrium Particle Decay in the Photonuclear Reactions Physical Review C Vol 16 No 5 pp 1812 1824 1977 M Blann B L Berman and T Komoto Precompound Model Analysis of Photoneutron Reaction Physical Review C Vol 28 No 6 pp 2286 2298 1983 M B Chadwick P G Young and S Chibas Photonuclear Angular Distribution Systematics in the Quasideuteron Regime Journal of Nuclear Science and Technology Vol 32 No 11 pp 1154 1158 1995 Fasso A Ferrari and P Sala Total Giant Resonance Photonuclear Cross Sections for Light Nuclei A Database for the FLUKA Monte Carlo Transport Code Third Specialists Meeting on Shielding Aspects of Accelerators Targets and Irradiation Facilities SATIF 3 Tohoku University Sendai Japan Organization for Economic Cooperation and Development Nuclear Energy Agency Paris France 1997 M C White Development and Implementation of Photonuclear Cross Section Data for Mutually Coupled Neutron Photon Transport Calculations in the Monte Carlo N Particle MCNP Radiation Transport Code Ph D thesis University of Florida 2000 M C White C Little and M B Chadwick Photonuclear Physics in MCNP X ANS Conference on Nuclear Applications of Accelerator Technology Long Beach California November 14 16 1999 D Mostelle
385. ies assume that all the neutron histories are independent They are not independent because of the cycle to cycle correlations that become more significant for large or loosely coupled systems For some very large systems the estimated standard deviation for a tally that involves only a portion of the problem has been observed to be underestimated by a factor of five or more see Ref 149 pages 42 44 This value also is a function of the size of the tally region In the Ref 149 slab reactor example the entire problem that is standard deviation was not underestimated at all An MCNP study 15 of the FFTF fast reactor indicates that 90 coverage rates for flux tallies are good but that 2 out of 300 tallies were beyond four estimated standard deviations Independent runs can be made to study the real eigenfunction distribution that is tallies and the estimated standard deviations for difficult criticality calculations This method is the only way to determine accurately these confidence intervals for large or loosely coupled problems where intergeneration correlation is significant 10 Neutron Tallies and the MCNP Net Multiplication Factor The MCNP net multiplication factor M printed out on the problem summary page differs from the kep from the criticality code We will examine a simple model to illustrate the approximate relationship between these quantities and compare the tallies between standard and criticality calculations Assu
386. ies of the major energy steps The mean ionization potential and density effect correction depend upon the state of the material either gas or solid In the fit of Sternheimer and Peierls the physical state of the material also modifies the density effect calculation In the Sternheimer Berger and Seltzer treatment the calculation of the density effect uses the conduction state of the material to determine the contribution of the outermost conduction electron to the ionization potential The occupation numbers and atomic binding energies used in the calculation are from Carlson 4 b Radiative Stopping Power The radiative stopping power is dE 24 2 2 F 10 7 7 o rad where is the scaled electron nucleus radiative energy loss cross section based upon evaluations by Berger and Seltzer for data from either the el or the e103 library details of the numerical values of the data on the el03 library can be found in Refs 85 86 and 87 1 parameter to account for the effect of electron electron bremsstrahlung it is unity when using data from the el library and when using data from the el03 library it is based upon the work of S Seltzer 85 86 87 can be different from unity a is the fine structure constant mc is the and M Berger mass energy of an electron and r is the classical electron radius The dimensions of the radiative stopping power are the same as the collisional stopping power
387. iffer H 4 10 3 05 APPENDIX H FISSION SPECTRA CONSTANTS AND FLUX TO DOSE FACTORS FLUX TO DOSE CONVERSION FACTORS significantly 22096 below approximately 0 7 MeV Maximum disagreement occurs at 0 06 MeV where the ANSI ANS value is about 2 3 times larger than the ICRP value B Silicon Displacement Kerma Factors Radiation damage to or effects on electronic components are often of interest Of particular interest are the absorbed dose in rads and silicon displacement kerma factors The absorbed dose may be calculated for a specific material by using the FM tally card discussed in Chapter 3 with an appropriate constant C to convert from the MCNP default units to rads The silicon displacement kermas however are given as a function of energy similar to the biological conversion factors Therefore they may be implemented on the DE and DF cards One source of these kerma factors and a discussion of their significance and use can be found in Reference 4 Table H 1 Neutron Flux to Dose Rate Conversion Factors and Quality Factors NCRP 38 AN SI ANS 6 1 1 1977 ICRP 21 Energy E DF E Quality DF E Quality MeV rem hr n em s _ Factor rem hry n cm s Factor 2 5E 08 3 67 06 2 0 3 85E 06 2 3 1 0E 07 3 67 06 2 0 4 17 06 2 0 1 0 06 4 46 06 2 0 4 55 06 2 0 1 0 05 4 54E 06 2 0 4 35E 06 2 0 1 0 04 4 18 06 2 0 4 17E 06 2 0 1 0E 03 3 76 06 2 0 3 70E 06 2 0 1 0E 02 3 56E 06 2 5 3 57E 06 2 0 1 0E 01 2 17E 05 7 5 2 0
388. iformly for positions on the ring to determine the flux at any point on the ring The ring detector efficiency is improved by biasing the selection of point detector locations to favor those near the contributing collision or source point This bias results in the same total 2 94 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS TALLIES number of detector contributions but the large contributions are sampled more frequently reducing the relative error For isotropic scattering in the lab system experience has shown that a good biasing function is proportional to e R where P is the number of mean free paths and R is the distance from the collision point to the detector point For most practical applications using a biasing function involving P presents prohibitive computational complexity except for homogeneous medium problems For air transport problems a biasing function resembling e has been used with good results A biasing function was desired that would be applicable to problems involving dissimilar scattering media and would be effective in reducing variance The function meets these requirements In Figure 2 10 consider a collision point x y z at a distance from a point detector location x y z The point x y z is to be selected from points a ring of radius r that is symmetric about the y axis in this case 0 20 Figure 2 10 To sample a position x y z on the ring with
389. ify in the input file a DXTRAN sphere that encloses the small region Upon collision or exiting the source outside the sphere DXTRAN creates a special DXTRAN particle and deterministically scatters it toward the DXTRAN sphere and deterministically transports it without collision to the surface of the DXTRAN sphere The collision itself is otherwise treated normally producing a non DXTRAN particle that is sampled in the normal way with no reduction in weight However the non DXTRAN particle is killed if it tries to enter the DXTRAN sphere DXTRAN uses a combination of splitting Russian roulette and sampling from a nonanalog probability density function The subtlety about DXTRAN is how the extra weight created for the DXTRAN particles is balanced by the weight killed as non DXTRAN particles cross the DXTRAN sphere The non DXTRAN particle is followed without any weight correction so if the DXTRAN technique is to be unbiased the extra weight put on the DXTRAN sphere by DXTRAN particles must somehow on average balance the weight of non DXTRAN particles killed on the sphere 1 DXTRAN Viewpoint 1 One can view DXTRAN as a splitting process much like the forced collision technique wherein each particle is split upon departing a collision or source point into two distinct pieces a theweightthat does notenter the DXTRAN sphere on the next flight either because the particle is not pointed toward the DXTRAN sphere or because the particle
390. iner energy grid with a greater number of points provides a more accurate representation of the cross sections The maximum incident photon energy in MeV for that data table For all incident energies greater than E MCNP assumes the last cross section value given yes indicates that secondary charged particles data are present indicates that such data are not present 10 3 05 APPENDIX G MCNP DATA LIBRARIES PHOTONUCLEAR DATA Table G 5 Continuous Energy Photonuclear Data Libraries Maintained by X 5 Library Eval Length ZAID AWR Name Date Source words NE MeV CP y 1 ok ok 2 ok ok ok ok ok Hydrogen H 2 et 1002 24u 1 9963 lal50u 2001 LANLI T 16 3686 35 30 No Z 6 KKK K KKK K Carbon K K K K K K KK K K K K K KK K K K K K K K K K KK K K 12 6012 240 11 89691 1 1500 1999 LANL T 16 50395 98 150 Yes Z 8 ok 2k ok K Oxygen K K K K K K K K K K 0 16 8016 24u 15 85316 1 1500 1999 LANL T 16 72930 95 150 Yes Z 13 Aluminum K K K K 1 27 13027 24u 26 74975 1 1500 1999 LANL T 16 68599 52 150 Yes Z 14 Silicon K K K K KK 51 28 14028 24u 27 737 la150u 1999 LANL T 16 70693 60 150 Yes Z 20 eek Calcium K K oe K K K K KK K K Ca 40 20040 24u 39 736 la150u 1998 LANL T 16 67051 54 150 Yes 7 26 Iron
391. ing the non DXTRAN particle if it enters the DXTRAN sphere e Usually there should be a rough balance in the summary table of weight created and lost by DXTRAN f DXTRAN cannot be used with reflecting surfaces for the same reasons that point detectors cannot be used with reflecting surfaces See page 2 101 for further explanation 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CRITICALITY CALCULATIONS g Both DXTRAN and point detectors track pseudoparticles to a point Therefore most of the discussion about detectors applies to DXTRAN Refer to the section on detectors page 2 91 for more information 13 Correlated Sampling Correlated sampling estimates the change in a quantity resulting from a small alteration of any type in a problem This technique enables the evaluation of small quantities that would otherwise be masked by the statistical errors of uncorrelated calculations MCNP correlates a pair of runs by providing each new history in the original and altered problems with the same starting pseudorandom number The same sequence of subsequent numbers is used and each history tracks identically until the alteration causes the tracking to diverge The sequencing of random numbers is done by incrementing the random number generator at the beginning of each history by a stride S of random numbers from the beginning of the previous history The default value of S is 152 917 The stride should be a quantity greater th
392. ion x true total cross section x absorption cross section x scattering cross section p the exponential transform parameter used to vary the degree of biasing p lt 1 can be a constant or p X X in which case and u cosine of the angle between the preferred direction and the particle s direction u 1 The preferred direction can be specified on a VECT card At a collision a particle s weight is multiplied by a factor w derived below so that the expected weight colliding at any point is preserved The particle s weight is adjusted such that the weight multiplied by the probability that the next collision is in ds about s remains constant The probability of colliding in ds about s is xe ds where is either 2 or so that preserving the expected collided weight requires N S Xe ds w E e ds t or pE us 2 2 If the particle reaches cell surface time cutoff DXTRAN sphere or tally segment instead of colliding the particle s weight is adjusted so that the weight multiplied by the probability that the particle travels a distance s to the surface remains constant The probability of traveling a distance 5 without collision is 2 148 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VARIANCE REDUCTION Xs so that preserving the expected uncollided weight requires X s 2 e or Ls pXus w
393. ion and other slave routines C History Flow The basic flow of a particle history for a coupled neutron photon electron problem is handled as follows For a given history the random number sequence is set up and the number of the history NPS is incremented The flag IPT is set for the type of particle being run 1 for a neutron 2 for a photon and 3 for an electron Some arrays and variables are initialized to zero The branch of the history NODE is set to 1 Next the appropriate source routine is called Source options are the standard fixed sources the surface source the criticality source or a user provided source All of the parameters describing the particle are set in these source routines including position direction of flight energy weight 10 3 05 2 5 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS INTRODUCTION time and starting cell and possibly surface by sampling the various distributions described on the source input control cards Several checks are made at this time to verify that the particle is in the correct cell or on the correct surface and directed toward the correct cell Next the initial parameters of the first fifty particle histories are printed Then some of the summary information is incremented see Appendix E for an explanation of these arrays Energy time and weight are checked against cutoffs A number of error checks are made Detector contributions are scored and then DXTRAN
394. ion has been made for the ENDF B VI evaluation 40000 50c rmccs gt 40000 56 misc5xs 40000 50d drmccs gt 40000 56 misc5xs 40000 51c endf5p gt 40000 57 misc5xs 40000 51d dre5 gt 40000 574 misc5xs 40000 53c eprixs gt 40000 58c misc5xs The ZAIDs for ENDL based average fission product data files have been changed for the latest library ENDL92 to 49120 42c and 49125 42c Z is now set to 49 to ensure that the appropriate atomic fraction and photon transport library is used You may need to update the atomic weight ratio table in your XSDIR file to include these entries 9 7 The ENDL92FP library is not publicly available The LANL T 16 evaluation for I 127 was accepted for ENDF B VI 2 with modifications These data are processed from the original LANL T 16 evaluation Photon production data for Gd were added to the ENDF B V 0 neutron cross sections by T 16 These data are valid only to MeV Photon production data for 2330 were added by LANL to the original evaluation in 1981 10 3 05 G 39 APPENDIX MCNP DATA LIBRARIES MULTIGROUP DATA 16 There was a processing problem for the URES library that affected the photon production data for 82 183 184 186W 232Th 2380 The URESA library contains the same ACE files as the URES library except that photon production data for the affected isotopes is zeroed The IDs for the affected isotopes have been changed from 49c to 48c Heating numbers in the
395. ional Laboratory report LA 13520 October 1998 McKinney and J Iverson Verification of the Monte Carlo Differential Operator Technique for MCNP Los Alamos National Laboratory Report LA 13098 February 1996 J A Favorite and D Kent Parsons Second Order Cross Terms in Monte Carlo Differential Operator Perturbation Estimates Proceedings of International Conference Mathematical Methods for Nuclear Applications Salt Lake City Utah September 9 13 2001 J A Favorite Alternative Implementation of the Differential Operator Taylor Series Perturbation Method for Monte Carlo Criticality Problems Nucl Sci Eng 142 pp 327 341 2002 F B Brown Random Number Generation with Arbitrary Strides Trans Am Nucl Soc 71 202 1994 B Brown and Y Nagaya The MCNP5 Random Number Generator Trans Am Nucl Soc 87 230 232 2002 10 3 05 2 209 PHYSICS AND MATHEMATICS CHAPTER 2 GEOMETRY DATA d 10 3 05 APPENDIX G MCNP DATA LIBRARIES ENDF B REACTION TYPES APPENDIX G MCNP DATA LIBRARIES Appendix G is divided into eight sections Section I lists some of the more frequently used ENDF B reaction types that can be used with the FMn input card Sections II through VII provide details about the data libraries available for use with MCNP and Section is a list of references Information about any specific data library as well as other useful information can be found o
396. ional Laboratory Groups T 16 or X 5 Denotes the year that the evaluation was completed or accepted In cases where this information is not known the date that the data library was produced is given It is rare that a completely new evaluation is produced Most often only a section of an existing evaluation is updated but a new evaluation date is assigned This can be misleading for the users and we encourage you to read the File 1 information for data tables important to your application to understand the history of a specific evaluation This information is available from the Data Team s web site The notation 1985 means before 1985 Indicates the temperature at which the data were processed The temperature enters into the processing of the evaluation of a data file only through the Doppler broadening of cross sections The user must be aware that without the proper use of the TMP card MCNP will attempt to correct the data libraries to the default 300 K by modifying the elastic and total cross sections only Doppler broadening refers to a change in cross section resulting from thermal motion translation rotation and vibration of nuclei in a target material Doppler broadening is done on all cross sections for incident neutrons nonrelativistic energies on a target at some temperature Temp in which the free atom approximation is valid In general an increase in the temperature of the material containing neutron absorbing
397. ional efficiency MCNP allows many techniques that do not exactly simulate physical transport For instance each MCNP particle might represent a number w of particles emitted from a source This number w is the initial weight of the MCNP particle The w physical particles all would have different random walks but the one MCNP particle representing these w physical particles will only have one random walk Clearly this is not an exact simulation however the true number of physical particles is preserved in MCNP in the sense of statistical averages and therefore in the limit of a large number of MCNP source particles of course including particle production or loss if they occur Each MCNP particle result is multiplied by the weight so that the full results of the w physical particles represented by each MCNP particle are exhibited in the final results tallies This procedure allows users to normalize their calculations to whatever source strength they desire The default normalization is to weight one per MCNP particle second normalization to the number of Monte Carlo histories is made in the results so that the expected means will be independent of the number of source particles actually initiated in the MCNP calculation The utility of particle weight however goes far beyond simply normalizing the source Every Monte Carlo biasing technique alters the probabilities of random walks executed by the particles The purpose of such biasing technique
398. ior of the response as a function of the perturbed parameter The magnitude of the second order estimator is a good measure of the range of applicability If this magnitude exceeds 30 of the first order estimator it is likely that higher order terms are needed for an accurate prediction The METHOD keyword on the PERT card allows one to tally the second order term separate from the first See Chapter 3 page 3 153 10 3 05 2 199 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PERTURBATIONS The MCNP perturbation capability assumes that changes in the relative concentrations or densities of the nuclides in a material are independent and neglects the cross differential terms in the second order perturbation term when changing two or more cross sections at once In some cases there will be a large FALSE second order perturbation term See Chapter 3 page 3 154 for further discussion and examples Reference 166 provides more discussion and a method for calculating the cross terms The MCNP perturbation capability has been shown to be inaccurate for some large but very localized perturbations in criticality problems An alternative implementation that only requires postprocessing standard MCNP tallies has been shown to be much more accurate in some cases See Ref 167 2 200 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS REFERENCES XIII REFERENCES 1 L L Carter and E D Cashwell Particle Transport Simulation with the M
399. iple detectors using the same pseudoparticle are almost free e Direct vs total contribution Unless specifically turned off by the user MCNP automatically prints out both the direct and total detector contribution Recall that pseudoparticles are generated at source and collision events The direct contribution is that portion of the tally from pseudoparticles born at source events The total contribution is the total tally from both source and collision events For Mode N P problems with photon detectors the direct contribution is from pseudophotons born in neutron collisions The direct contributions for detailed photon physics will be smaller than the simple physics direct results because coherent scattering is included in the detailed physics total cross section and omitted in the simple physics treatment f Angular distribution functions for point detectors detector estimates require knowledge of the p u term the value of the probability density function at an angle where u cos This quantity is available to MCNP for the standard source and for all kinds of collisions For user supplied source subroutines MCNP assumes an isotropic distribution zdu dQ _ dudo _ 1 pudu T 22 Therefore the variable PSC 1 2 If the source distribution is not isotropic in a user supplied source subroutine the user must also supply a subroutine SRCDX if there are any detectors or DXTRAN spheres in the problem
400. ires information different from the sets of angular and energy distributions found on neutron interaction tables The angular distribution for fluorescence x rays from the relaxation cascade after a photoelectric event is isotropic The angular distributions for coherent and incoherent scattering come from sampling the well known Thomson and Klein Nishina formulas respectively By default this sampling accounts for the form factor and scattering function data at incident energies below 100 MeV Above 100 MeV or at the user s request the form factor and scattering function data are ignored a reasonable approximation for high energy photons The energy of an incoherently scattered photon is calculated from the sampled scattering angle If available this energy is modified to account for the momentum of the bound electron Very few approximations are made in the various processing codes used to transfer photon data from ENDF into the format of MCNP photon interaction tables Cross sections are reproduced exactly as given except as the logarithm of the value Form factors and scattering functions are reproduced as given however the momentum transfer grid on which they are tabulated may be different from that of the original evaluation see the description of the photoatomic table in Appendix F for the momenta grid used by all photoatomic tables Heating numbers are calculated values not given in evaluated sets but inferred from them Fluorescence
401. is called if used in the problem to create particles on the spheres The particles are saved in the bank for later tracking Bookkeeping is started for the pulse height cell tally energy balance The weight window game is played with any additional particles from splitting put into the bank and any losses to Russian roulette terminated Then the actual particle transport is started For an electron source electrons are run separately For a neutron or photon source the intersection of the particle trajectory with each bounding surface of the cell is calculated The minimum positive distance DLS to the cell boundary indicates the next surface JSU the particle is heading toward The distance to the nearest DXTRAN sphere is calculated as is the distance to time cutoff and energy boundary for multigroup charged particles The cross sections for cell ICL are calculated using a binary table lookup in data tables for neutrons or photons New to MCNPS the total photon cross section may include the photonuclear portion of the cross section if photonuclear physics is in use See page 3 129 for a discussion of turning photonuclear physics on The total cross section is modified by the exponential transformation if necessary The distance to the next collision is determined if a forced collision is required the uncollided part is banked The track length of the particle in the cell is found as the minimum of the distance to collision the distance to the su
402. ith an FU card is used to determine what portion of a detector tally comes from what cells This information is similar to the detector diagnostics print but the FT card can be combined with energy and other binning cards The contribution to the normalized rather than unnormalized tally is printed f Binning by source distribution The SCX and SCD options are used to bin a tally score according to what source distribution caused it g Binning by multigroup particle type The PTT option with an FU card is used to bin multigroup tallies by particle type The MCNP multigroup treatment is available for neutron coupled neutron photon and photon problems However charged particles or any other combinations of particles can be run with the various particles masquerading as neutrons and are printed out in the OUTP file as if they were neutrons With the PIT option the tallies can be segregated into particle types by entering atomic weights in units of MeV on the FU card The FU atomic weights must be specified to within 0 1 of the true atomic weight in MeV units thus FU 511 specifies an electron but 510 is not recognized h Binning by particle charge The ELC option allows binning F1 current tallies by particle charge There are three ELC options 1 Cause negative electrons to make negative scores and positrons to make positive scores Note that by tallying positive and negative numbers the relative error is unbounded and this tally may be dif
403. ition of k comes directly from the time integrated Boltzmann transport equation without external sources Puls 1 P P z iPad ydy J J vo mavardzda Pal J J det 5 dE dVdtdEdO which may be rewritten to look more like the definition of V JdVdtdEdQ p V O E O jJ JJ e JdVdtdEdQ f f c OUO 2n O 3n DdVdtdEdO 1 oo paf f f 3n lt DdVdtdEdO 2 168 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CRITICALITY CALCULATIONS The loss rate is on the left and the production rate is on the right The neutron prompt removal lifetime is the average time from the emission of a prompt neutron in fission to the removal of the neutron by some physical process such as escape capture or fission Also even with the TOTNU card to produce delayed neutrons as well as prompt neutrons KCODE default the neutrons are all born at time zero so the removal lifetimes calculated in MCNP are prompt removal lifetimes even if there are delayed neutrons The definition of the prompt removal lifetime is f f ndVdtdEdQ 0 i id oo d f J J v p o baVataEdO V o E O V o E O where is the population per unit volume per unit energy per unit solid angle In a multiplying system in which the population is increasing or decreasing on an asymptotic period t
404. ity function p w where C is a norming constant equal to 5 and cos where is an angle relative to the biasing direction is typically about 1 3 5 defines the ratio of weight of tracks starting in the biasing direction to tracks starting in the opposite direction to be 1 1097 This ratio is equal to e Table 2 8 may help to give the user a feel for the biasing parameter K r Table 2 8 Exponential Biasing Parameter Cumulative Cumulative K Probability Theta Weight Probability Theta Weight 01 0 0 0 990 2 0 0 0 245 25 60 0 995 23 31 325 50 90 1 000 50 48 482 75 120 1 005 75 70 931 1 00 180 1 010 1 00 180 13 40 1 0 0 0 432 3 5 0 0 143 25 42 552 25 23 190 50 64 762 50 37 285 75 93 1 230 75 53 569 1 00 180 3 195 1 00 180 156 5 From this table for 1 we see that half the tracks start in a cone of 64 opening about the axis and the weight of tracks at 64 is 0 762 times the unbiased weight of source particles K 0 01 is almost equivalent to no biasing and K 3 5 is very strong Cone directional biasing can be invoked by specifying cone cosines on the SI card the true distribution on the SP card and the desired biasing probabilities on the SB card Both histogram 10 3 05 2 153 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VARIANCE REDUCTION and linear interpolation can be used For example consider the following case in which the tru
405. l where n refers to the photon weight window energy group This will cause most photons to be born within the weight window bounds Any photons generated at neutron collision sites are temporarily stored in the bank There are two methods for determining the exiting energies and directions depending on the form in which the processed photon production data are stored in a library The first method has the evaluated photon production data processed into an expanded format In this format energy dependent cross sections energy distributions and angular distributions are explicitly provided for every photon producing neutron interaction In the second method used with data processed from older evaluations the evaluated photon production data have been collapsed so that the only information 2 32 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS about secondary photons is in a matrix of 20 equally probable photon energies for each of 30 incident neutron energy groups The sampling techniques used in each method are now described a Expanded Photon Production Method In the expanded photon production method the reaction n responsible for producing the photon is sampled from n 1 N n 0 955 0 i l i l where amp is a random number on the interval 0 1 N is the number of photon production reactions and o is the photon production cross section for reaction i at the incident neutron energy N
406. l fixed grid see the photon table description in Appendix F The fluorescence data use the traditional scheme defined by Everett and Cashwell but updated and consistent with the new data Also included are the bound electron momenta of Biggs et al i e identical to those data in the 03 tables This is the recommended data set For each element the photoatomic interaction libraries contain an energy grid explicitly including the photoelectric edges and the pair production threshold the incoherent coherent photoelectric and pair production cross sections all stored as the logarithm of the value to facilitate log log interpolation The total cross section is not stored instead it is calculated from the partial cross sections as needed The energy grid for each table is tailored specifically for that element The average material heating due to photon scattering is calculated by the processing code and included as a tabulation on the main energy grid The incoherent scattering function and coherent form factors are tabulated as a function of momentum transfer on a predefined fixed momenta grid Average fluorescence data according to the scheme of Everett and Cashwell are also included The most recent data on the 03p and 04p libraries also include momentum profile data for broadening of the photon energy from Compton scattering from bound electrons The determination of directions and energies of atomically scattered photons requ
407. lculation which generates a better set of windows etc In addition to iterating on the generated weight windows the user must exercise some degree of judgment Specifically in a typical generator calculation some generated windows will look suspicious and will have to be reset In MCNP this task is simplified by an algorithm that automatically scrutinizes cell based importance functions either input by the user or generated by a generator By flagging the generated windows that are more than a factor of 4 different from those in adjacent spatial regions often it is easy to determine which generated weight windows are likely to be statistical flukes that should be revised before the next generator iteration For example suppose the lower weight bounds in adjacent cells were 0 5 0 3 0 9 0 05 0 03 0 02 etc here the user would probably want to change the 0 9 to something like 0 1 to fit the pattern reducing the 18 1 ratio between cells 3 and 4 The weight window generator also will fail when phase space is not sufficiently subdivided and no single set of weight window bounds is representative of the whole region It is necessary to turn off the weight windows by setting a lower bound of zero or to further subdivide the geometry or energy phase space Use of a superimposed importance mesh grid for weight window generation is a good way to subdivide the spatial portion of the phase space without complicating the MCNP cell geometry On th
408. le energy center of mass E incident particle energy laboratory Ho cosine of center of mass scattering angle cosine of laboratory scattering angle and A atomic weight ratio mass of nucleus divided by mass of incident particle For point detectors it is necessary to convert duc Pus P Mem where dios BUE 7 E FORME 1 e 3 N E 2 40 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS d Nonfission Inelastic Scattering and Emission Laws Nonfission inelastic reactions are handled differently from fission inelastic reactions For each nonfission reaction N particles are emitted where N is an integer quantity specified for each reaction in the cross section data library of the collision nuclide The direction of each emitted particle is independently sampled from the appropriate angular distribution table as was described earlier The energy of each emitted particle is independently sampled from one of the following scattering or emission laws Energy and angle are correlated only for ENDF 6 laws 44 and 67 For completeness and convenience all the laws are listed together regardless of whether the law is appropriate for nonfission inelastic scattering for example Law 3 fission spectra for example Law 11 both for example Law 9 or neutron induced photon production
409. lem MODE CBE 24 Ge metry Rio Ne 24 Vafiance apes HT 33 DUUFCE SDOGITIGBIOIH a est uad M hM EM 52 Tally 79 Material Specification 117 Energy and Thermal Treatment Specification 127 Problem Cutoff Cards T 135 User Data c P 138 ANOS TT 139 SUMMARY OP MCNP INPUT FILE 157 nod Fe 157 Storage Limitations MP 160 REFERENCES Me C 161 CHAPTER 4 5 4 1 GEOMETRY SPECIFICATION 1 COORDINATE TRANSFORMATIONS aae 16 TRV and M A 18 ji eX nA Ee c 19 REPEATED STRUCTURE AND LATTICE EXAMPLES 2 20 EXAMPLES 39 Examples Simple lt 39 FM Examples General
410. lemental in that they combine the reactions on several isotopes into a single table For example natural tungsten would need tables with ZA equal 74180 74182 74183 74184 and 74186 This can create difficulties when specifying material definitions This has been true in the past e g no neutron table exists for 74180 0 13 atom percent and it is typically ignored This is even more true now that tables must be selected for both neutron and photonuclear interactions The MPN card has been introduced to alleviate this problem In MODE N problems one continuous energy or discrete reaction neutron interaction table is required for each isotope in the problem some older elemental tables are available for neutron interactions In MODE P problems one photoatomic interaction table is required for each element and one photonuclear table is required for each isotope if photonuclear physics is in use In E problems one electron interaction table is required for each element Dosimetry and thermal data are optional Cross sections from dosimetry tables can be used as response functions with the FM card to determine reaction rates Thermal S o tables should be used if the neutrons are transported at sufficiently low energies that molecular binding effects are important MCNP can read from data tables in two formats Data tables are transmitted between computer installations as ASCII text files using an 80 column card image Binary Coded Decim
411. les J p are used to account for the effects of a bound electron on the energy distribution of the scattered photon These Compton profiles are a collection of orbital and total atom data tabulated as a function of the projected precollision momentum of the electron Values of the Compton profiles for the elements are published in tabular form by Biggs et al as a function of Pe The scattered energy of a Doppler broadened photon can be calculated by selecting an orbital shell sampling the projected momentum from the Compton profile and calculating the scattered photon energy from EE 1 cos 0 mc JE E 2EE cos 0 4375 The Compton profiles are related to the incoherent scattering function Z v by 102 0 Y 5 Zap k where k refers to the particular electron subshell J p 2 is the Compton profile of the K shell for a given element and p aX js the maximum momentum transferred and is calculated using E E E binding b Coherent Thomson Scattering Thomson scattering involves no energy loss and thus is the only photon process that cannot produce electrons for further transport and that cannot use the TTB approximation Only the scattering angle 0 is computed and then the transport of the photon continues The differential cross section is o5 Z u du C Z v T udy where C Z v is a form factor modifying the energy independent Thomson cross section T u mro 1 u T
412. les are killed and some particles survive with increased weight The solution is unbiased because total weight is conserved but computer time is not wasted on insignificant particles Weight window As a function of energy geometrical location or both low weighted particles are eliminated by Russian roulette and high weighted particles are split This technique helps keep the weight dispersion within reasonable bounds throughout the problem An importance generator is available that estimates the optimal limits for a weight window Exponential transformation To transport particles long distances the distance between collisions in a preferred direction is artificially increased and the weight is correspondingly artificially decreased Because large weight fluctuations often result it is highly recommended that the weight window be used with the exponential transform Implicit absorption When a particle collides there is a probability that it is absorbed by the nucleus In analog absorption the particle is killed with that probability In implicit absorption also known as implicit capture or survival biasing the particle is never killed by absorption instead its weight is reduced by the absorption probability at each collision Important particles are permitted to survive by not being lost to absorption On the other hand if particles are no longer considered useful after undergoing a few collisions analog absorption efficiently gets ri
413. library ENDFSMT Data were translated to ENDF B VI format with some modifications by LANL The 100XS data library contains data for 9 nuclides up to 100 MeV Heating numbers on this data library are known to be incorrect overestimating the energy deposition Photon production data were added to the existing ENDF evaluation for B in 1984 A complete new evaluation was performed in 1986 The natural carbon data 6000 50c are repeated here with the ZAID of 6012 50c for the user s convenience Both are based on the natural carbon ENDF B V 0 evaluation The delayed gamma ray at an energy of 1 7791 MeV from the reaction 1 gt 1 gt 2851 has been included in the thermal capture photon production data for these two ZAIDs The data libraries previously known as ARKRC GDT2GP IRNAT MISCXS TM169 and T2DDC are now a part of the data library MISCSXS Photon production data were added to ENDF B V 0 neutron files for argon and krypton by T 16 with the intent to roughly estimate photon heating Data for Br Rb I and Cs were taken from incomplete fission product evaluations i This is ENDF B V 0 for after modification by evaluator to get better agreement with ENDL85 51 The following files for Zr have been replaced by the indicated ZAID eliminating the rare problem of having a secondary neutron energy greater than the incident neutron energy caused by an ENDF B V 0 evaluation problem 1 Note that this correct
414. lision 3 Track Length Estimators The track length estimator of accumulated every time the neutron traverses a distance d in a fissionable material cell TL 1 kay i k where i is summed over all neutron trajectories p isthe atomic density in the cell and d isthe trajectory track length from the last event Because fy is the expected number of fission neutrons produced along trajectory d TL A k efr 18 third estimate of the mean number of fission neutrons produced in a cycle per nominal fission source neutron The track length estimator tends to display the lowest variance for optically thin fuel cells for example plates and fast systems where large cross section variations because of resonances may cause high variances in the other two estimators The track length estimator for the prompt removal lifetime for each cycle is accumulated every time the neutron traverses a distance d in any material in any cell 2 172 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CRITICALITY CALCULATIONS TL _ YXIWid v r W S T where W is the source weight summed over all histories in the cycle and v is the velocity Note that d v is the time span of the track Note further that e 4 J 74 Y Wav 1 and in criticality problems 1 oo W ko J These relationships show how JL is rela
415. llision is a function of the momentum of the bound electron involved in the collision To calculate this effect which is seen as a broadening of the Compton peak it is necessary to know the probability with which a photon interacts with an electron from a particular shell and the momentum profile for the electrons of each shell The probabilities and momentum profile data of Biggs et al are included in the 03 tables All other data in 03 are identical to the 02 data The ability to use the new data for broadening of the Compton scattering energy requires MCNPS or later however these tables are compatible with older versions of the code you simply will not access or use the new data The 04 ACE tables were introduced in 2002 and contain the first completely new data set since 1982 These tables were processed from the ENDF B VL 8 library The ENDF B VI 8 2 20 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CROSS SECTIONS photoatomic and atomic relaxation data in turn based upon the EPDL97 library They include incoherent coherent photoelectric and pair production cross sections for incident energies from 1 keV to 100 GeV and Z equal to 1 to 100 They also include coherent form factors incoherent scattering functions and fluorescence data derived from the ENDF B VI 8 data It should be noted that the form factor and scattering data have been evaluated and stored on the traditiona
416. llow histories for the second generation producing yet another fission source distribution and estimate of Koy These generations also called cycles or batches are repeated until the source spatial distribution has converged Once the fission source distribution has converged to its stationary state tallies for reaction rates and may be accumulated by running additional cycles until the statistical uncertainties have become sufficiently small Analysis of the power iteration procedure for solving kep eigenvalue calculations shows that the convergence of the fission source distribution 8 and the estimated eigenvalue Kg can be modeled as k n 1 gt gt 1 gt Sn Da Si k n k 1 1 where o and ko are the fundamental eigenfunction and eigenvalue of the exact transport solution and k are the eigenfunction and eigenvalue of the first higher mode a and b are constants and is the number of cycles performed in the power iteration procedure Note that k is the expected value of and that kg gt k gt 0 so that is less than 1 The quantity k ko is called the 2 166 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CRITICALITY CALCULATIONS dominance ratio DR and is the key physical parameter that determines the convergence rate of the power iteration procedure The DR is a function of problem geometry and materials As the number of cycles n becomes large the error terms
417. lly against considerable odds reached the tally region and is not absorbed just before a tally is made and 2 150 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VARIANCE REDUCTION 2 the history variance in general decreases when the surviving weight that is 0 or W is not sampled but an expected surviving weight is used instead see weight cutoff page 2 143 Two disadvantages are 1 a fluctuation in particle weight is introduced and 2 the time per history is increased see weight cutoff page 2 143 9 Forced Collisions The forced collision method is a variance reduction scheme that increases sampling of collisions in specified cells Because detector contributions and DXTRAN particles arise only from collisions and at the source it is often useful in certain cells to increase the number of collisions that can produce large detector contributions or large weight DXTRAN particles Sometimes we want to sample collisions in a relatively thin cell a fraction of a mean free path to improve the estimate of quantities like a reaction rate or energy deposition or to cause collisions that are important to some other part of the problem The forced collision method splits particles into collided and uncollided parts The collided part is forced to collide within the current cell The uncollided part exits the current cell without collision and is stored in the bank until later when its track is continued at the cell bou
418. lo solutions MEAN 1 anonmonotonic behavior no up or down trend in the estimated mean as a function of the number histories for the last half of the problem 10 3 05 2 129 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS ESTIMATION OF THE MONTE CARLO PRECISION R 2 an acceptable magnitude of the estimated of the estimated mean lt 0 05 for a point detector tally or 0 10 for a non point detector tally 3 a monotonically decreasing R as a function of the number histories for the last half of the problem 4 a 1 JN decrease in the R as a function of N for the last half of the problem VOV 5 the magnitude of the estimated VOV should be less than 0 10 for all types of tallies 6 amonotonically decreasing VOV as a function of N for the last half of the problem 7 a 1 N decrease in the VOV as a function of N for the last half of the problem FOM 8 astatistically constant value of the FOM as a function of N for the last half of the problem 9 anonmonotonic behavior in the FOM as a function of N for the last half of the problem and f x 10 the SLOPE see page 2 126 of the 25 to 201 largest positive negative with a negative DBCN 1 6 entry history scores x should be greater than 3 0 so that the second moment x foo dx will exist if the SLOPE is extrapolated to infinity The seven N dependent checks for the TFC bin are for the last half of the problem The last half of the problem should be
419. log probability density functions The previous paragraph discusses type 3 Splitting refers to dividing the particle s weight among two or more daughter particles and following the daughter particles independently Usually the weight is simply divided evenly among k identical daughter particles whose characteristics are identical to the parent except for a factor 1 k in weight for example splitting in the weight window In this case the expected weight is clearly conserved because the analog technique has one particle of weight wg at 7 t whereas the splitting results in k particles of weight wo k at 7 V t In both cases the outcome is weight Wo at 7 y 1 10 3 05 2 135 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VARIANCE REDUCTION Other splitting techniques split the parent particle into k typically two differing daughter particles The weight of the j daughter represents the expected number of physical particles that would select outcome from a set of k mutually exclusive outcomes For example the MCNP forced collision technique considers two outcomes 1 the particle reaches a cell boundary before collision or 2 the particle collides before reaching a cell boundary The forced collision technique divides the parent particle representing wg physical particles into two daughter particles representing w physical particles that are uncollided and w physical particles that collide The uncollided particle of wei
420. lues Law 7 ENDF law 7 Simple Maxwell Fission Spectrum E u T Ein out SE in Eu C jE 10 3 05 2 43 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS Law 9 Law 11 2 44 The nuclear temperature is a tabulated function of the incident energy The normalization constant C is given by r am Jerr Fa U 20 to 0 lt E lt E U In MCNP this Uis a constant provided in the library and limits density function is sampled by the rejection scheme In 51153 where amp 5 63 and 6 are random numbers on the unit interval and are rejected if 2A oo Gy Hea l Egy 2 3 out na ENDF law 9 Evaporation spectrum Epu JUE gt Eou where the nuclear temperature is a tabulated function of incident energy The energy U is provided in the library and is assigned so that is limited by OXE E U The normalization constant C is given by AE cr sudeste als cmm In MCNP this density function is sampled by Ej T E in nC where 6 and 5 are random numbers on the unit interval and and are rejected if DE rb ENDF law 11 Energy Dependent Watt Spectrum a E i gt Eom T sinh JE out out The constants a and b are tabulated functions of incident energy and U 15 a constant from the library The normalization constan
421. ly killed by falling below the cutoff As mentioned earlier the weight cutoff game was originally envisioned for use with geometry splitting and implicit capture To illustrate the need for a weight cutoff when using implicit capture consider what can happen without a weight cutoff Suppose a particle is in the interior of a very large medium and there are neither time nor energy cutoffs The particle will go from collision to collision losing a fraction of its weight at each collision Without a weight cutoff a particle s weight would eventually be too small to be representable in the computer at which time an error would occur If there are other loss mechanisms for example escape time cutoff or energy cutoff the particle s weight will not decrease indefinitely but the particle may take an unduly long time to terminate Weight cutoff s dependence on the importance ratio can be easily understood if one remembers that the weight cutoff game was originally designed to solve the low weight problem sometimes produced by implicit capture In a high importance region the weights are low by design so it makes no sense to play the same weight cutoff game in high and low importance regions Comments Many techniques in MCNP cause weight change The weight cutoff was really designed with geometry splitting and implicit capture in mind Care should be taken in the use of other techniques Weight cutoff games are unlike time and energy cutoffs I
422. make a trial calculation using a small number of histories per cycle such as 1000 to examine the convergence behavior of k and the source distribution to determine a proper value for and then make a final calculation using a larger number of histories per cycle e g 5000 or more and sufficient active cycles to attain small uncertainties To assist users in assessing convergence of criticality calculations MCNP provides several statistical checks on as discussed in the next sections In addition MCNP calculates a quantity called the entropy of the source distribution H 4 to assist users in assessing the convergence of the source distribution B Estimation of k Confidence Intervals and Prompt Neutron Lifetimes The criticality eigenvalue kep and various prompt neutron lifetimes along with their standard deviations are automatically estimated in every criticality calculation in addition to any user requested tallies k and the lifetimes are estimated for every active cycle as well as averaged over all active cycles the lifetimes are estimated in three different ways These estimates are 49 using observed statistical correlations to provide the optimum final estimate of keff and its standard deviation It is known that the power iteration method with a fixed source size produces a very small negative bias Ak in k that is proportional to 1 N This bias is negligible for all practical problems
423. mal energy at the time and point of collision with isotropic production of one photon of energy 0 511 MeV headed in one direction and another photon of energy 0 511 MeV headed in the opposite direction The rare single 1 022 MeV annihilation photon is ignored The relatively unimportant triplet production process is also ignored The simple physics treatment for pair production is the same as the detailed physics treatment that is described in detail below c Compton scattering The alternative to pair production is Compton scattering on a free electron with probabilityo o Ope In the event of such a collision the objective is to determine the energy E of the scattered photon and cos0 for the angle of deflection from the line of flight This yields at once the energy WGT E E deposited at the point of collision and the new direction of the scattered photon The energy deposited at the point of collision can then be used to make a Compton recoil electron for further transport or for the TTB approximation The differential cross section for the process is given by the Klein Nishina formula 2 2 K a u du a u 2 5 where r is the classical electron radius 2 817938 x 10 cm and are the incident and final photon energies in units of 0 511 MeV E mc Where m is the mass of the electron and c is the speed of light and 1 1 0 The Compton scattering pro
424. marize the salient features of the evaluation below more details can be found in the evaluators documentation The evaluation uses detailed calculations of the electron nucleus bremsstrahlung cross section for electrons with energies below 2 MeV and above 50 MeV The evaluation below 2 MeV uses the results of Pratt Tseng and collaborators based on numerical phase shift calculations 02 103 104 For 50 MeV and above the analytical theory of Davies Bethe Maximom and Olsen is used and is supplemented by the Elwert Coulomb correction factor and the theory of the high frequency limit or tip region given by Jabbur and Pratt Screening effects are accounted for by the use of Hartree Fock atomic form factors The values between these firmly grounded theoretical limits are found by a cubic spline interpolation as described in Refs 85 and 86 Seltzer reports good agreement between interpolated values and those calculated by Tseng and Pratt for 5 and 10 MeV electrons in aluminum and uranium Electron electron bremsstrahlung is also included in the cross section evaluation based on the theory of Haug with screening corrections derived from Hartree Fock incoherent scattering factors The energy spectra for the bremsstrahlung photons are provided in the evaluation No major changes were made to the tabular 10 3 05 2 77 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS angular distributions which are internally calculate
425. mathematical problems When he saw a seemingly limitless array of women cranking out firing tables with desk calculators at the Ballistic Research Laboratory at Aberdeen he proposed that an electronic computer be built to deal with these calculations The result was ENIAC Electronic Numerical Integrator and Computer the world s first computer built for Aberdeen at the University of Pennsylvania It had 18 000 double triode vacuum tubes in a system with 500 000 solder joints John von Neumann was a consultant to both Aberdeen and Los Alamos When he heard about ENIAC he convinced the authorities at Aberdeen that he could provide a more exhaustive test of the computer than mere firing table computations In 1945 John von Neumann Stan Frankel and Nicholas Metropolis visited the Moore School of Electrical Engineering at the University of Pennsylvania to explore using ENIAC for thermonuclear weapon calculations with Edward Teller at Los Alamos After the successful testing and dropping of the first atomic bombs a few months later work began in earnest to calculate a thermonuclear weapon On March 11 1947 John von Neumann sent a letter to Robert Richtmyer leader of the Theoretical Division at Los Alamos proposing use of the statistical method to solve neutron diffusion and multiplication problems in fission devices His letter was the first formulation of a Monte Carlo computation for an electronic computing machine In 1947 while in Los Al
426. mber of substeps m per energy step will have been preset either from the empirically determined default values or by the user based on geometric considerations At most m substeps will be taken in the current major step with the current value for the energy loss rate The number of substeps may be reduced if the electron s energy falls below the boundary of the current major step or if the electron reaches a geometric boundary In these circumstances or upon the completion of m substeps a new major step is begun and the energy loss rate is resampled With the possible exception of the energy loss and straggling calculations the detailed simulation of the electron history takes place in the sampling of the substeps The Goudsmit Saunderson theory is used to sample from the distribution of angular deflections so that the direction of the electron can change at the end of each substep Based on the current energy loss rate and the substep length the projected energy for the electron at the end of the substep is calculated Finally appropriate probability distributions are sampled for the production of secondary particles These include electron induced fluorescent X rays knock on electrons from electron impact ionization and bremsstrahlung photons 10 3 05 2 69 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS Note that the length of the substep ultimately derives from the total stopping power used in Eq 2 3 but
427. me we run a standard MCNP calculation using a fixed neutron source distribution identical in space and energy to the source distribution obtained from the solution of an eigenvalue problem with kep lt 1 Each generation will have the same space and energy distribution as the source The contribution to an estimate of any quantity from one generation is reduced by a factor of from the contribution in the preceding generation The estimate E of a tally quantity obtained in a criticality eigenvalue calculation is the contribution for one generation produced by a unit source of fission neutrons An estimate for a standard MCNP fixed source calculation E is the sum of contributions for all generations starting from a unit source Note that 1 1 is the true system multiplication often called the subcritical multiplication factor The above result depends on our assumptions about the unit fission source used in the standard MCNP run Usually E will vary considerably from the above result depending on the difference between the fixed source and the eigenmode source generated in the eigenvalue problem E will be a fairly good estimate if the fixed source is a distributed source roughly approximating the eigenmode source Tallies from a criticality calculation are appropriate only for a critical system and the tally results can be scaled to a desired fission neutron source power level or total neutron pulse strength 10 3 05 2 181 CHAPT
428. mma energy for reaction at neutron incident energy 2 88 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS TALLIES energy transferred to electrons is assumed to be deposited locally 3 F7 Neutrons The heating number is Q the fission Q value The Q values in MCNP represent the total prompt energy release per fission and are printed in Print Table 98 The total fission cross section is nf Although photonuclear tables may now include fission cross sections that is some circumstances MCNP can model photofission the F7 tally is still illegal for photons 4 Equivalence of F4 F6 and F7 Tallies The F6 and F7 heating tallies are special cases of the F4 track length estimate of cell flux with energy dependent multipliers The following F4 and FM4 combinations give exactly the same results as the F6 and F7 tallies listed In this example material 9 in cell 1 is U with an atom density p of 0 02 atoms barn cm and a mass density 7 80612 g cm for an atom gram ratio of 0 0025621 Note that using 1 p will give the same result as using p p and is a better choice if perturbations are used See Perturbations on page 2 192 F4 N 1 FM4 0 0025621 9 1 4 gives the same result as F6 N 1 F14 N 1 14 0 0025621 9 6 8 gives the same resultas FI7 N 1 F24 P 1 FM24 0 0025621 9 5 6 gives the same resultas F26 P 1 For the photon results to be identical both electron trans
429. mpt and total nu are given yes indicates that secondary charged particles data are present indicates that such data not present yes indicates that delayed neutron data are present no indicates that such data are not present yes indicates that unresolved resonance data are present indicates that such data are not present Numbers in brackets refer to notes on page G 39 Table G 2 contains no indication of a recommended library for each isotope Because of the wide variety of applications MCNP is used to simulate no one data set is best The default cross section set for each isotope is determined by the XSDIR file being used see page 2 18 Finally you can introduce a cross section library of your own by using the XS input card 10 3 05 G 11 APPENDIX G MCNP DATA LIBRARIES NEUTRON CROSS SECTION LIBRARIES Table G 2 Continuous Energy and Discrete Neutron Data Libraries Maintained by X 5 Library Eval Temp Length Emax ZAID AWR Name Source Date K words NE MeV GPD Z2 Hydrogen PPV k 1 1001 24 0 9991 la150n 6 1998 293 6 10106 686 150 0 yes 1001 42c 0 9992 endl92 LLNL 1992 300 0 1968 121 30 0 yes 1001 50c 0 9992 rmccs B V 0 1977 293 6 2766 244 20 0 yes 1001 50d 0 9992 drmccs B V 0 1977 293 6 3175 263 20 0 yes 1001 53c 0 9992 endf5mt 1 0 1977 587 2 4001 394 20 0 1001 60 0 9992 endf60 B VI 1 1989 293 6
430. mpt neutron lifetime estimates are accumulated 2 if fission is possible the three keff estimates are accumulated and 3 if fission is possible n gt 0 fission sites including the sampled outgoing energy of the fission neutron at each collision are stored for use as source points in the next cycle where Wv oj o 1 k eff random number W particle weight before implicit capture weight reduction or analog capture v average number of neutrons produced by fission at the incident energy of this collision with either prompt v or total v default used microscopic material fission cross section microscopic material total cross section and keff estimated collision from previous cycle For the first cycle use the second KCODE card entry number of fission source points to be used in the next cycle The number of fission sites stored at each collision is rounded up or down to an integer including Zero with a probability proportional to its closeness to that integer If the initial guess of keis too low or too high the number of fission sites written as source points for the next cycle will be respectively too high or too low relative to the desired nominal number N bad initial guess of k causes only this consequence A very poor initial guess for the spatial distribution of fissions can cause the first cycle estimate of k to be extremely low This situation can occur when only a fra
431. ms by which this can occur The nuclear data files currently available focus on the energy range up to 150 MeV incident photon energy The value of 150 MeV was chosen as this energy is just below the threshold for the production of pions and the subsequent need for much more complicated nuclear modeling Below 150 MeV the primary mechanisms for photoabsorption are the excitation of either the giant dipole resonance or a quasi deuteron nucleon pair The giant dipole resonance GDR absorption mechanism can be conceptualized as the electromagnetic wave the photon interacting with the dipole moment of the nucleus as a whole 2 64 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS This results in a collective excitation of the nucleus It is the most likely process that is the largest cross section by which photons interact with the nucleus Expected peak cross sections of 6 10 millibarns are seen for the light isotopes and 600 800 millibarns are not uncommon for the heavy elements Thus photonuclear collisions may account for a theoretical maximum of 5 6 of the photon collisions The GDR occurs with highest probability when the wavelength of the photon is comparable to the size of the nucleus This typically occurs for photon energies in the range of 5 20 MeV and has a resonance width of a few MeV For deformed nuclei a double peak is seen due to the variation of the nuclear radius Outside of this resonance region the cross
432. n x E rj gt E 0 gt T where is the macroscopic reaction cross section at energy is the total cross section at energy E and P E E 0 gt 0 dEd0 is the probability distribution function in phase space of the emerging neutron If the track starts with a collision and ends in a boundary crossing P 7 ZU gt E O0 dEdO0 e If the track starts with a boundary crossing and ends with a collision And finally if the track starts and ends with boundary crossings r e 1 First Order For a first order perturbation the differential operator becomes 2 194 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PERTURBATIONS X Xo e beB heH q Ot EEUU m 0 beB heH whereas m 1 OG _ 1 q x h 2 Ox h k 0 then m Yy Bet Ry gt k 0 where EC beB heH Dd ZEL em 2 hE b k x E beB heH for track segment that starts with a particle undergoing reaction type at energy E and is scattered to energy E and collides after a distance Note that and are unity if h E and b a otherwise they vanish For other types of tracks for which the various expressions for r were given in the previous section
433. n the following Data Team web site http www xdiv lanl gov PROJECTS DATA nuclear nuclear html Page I ENDF B Reaction Types G 1 II 5 Data for Use with the MTm 5 III Neutron Cross Section Libraries G 9 IV Multigroup Data G 40 V Photoatomic Data G 43 VI Photonuclear Data 58 Dosimetry Data G 60 VIII References G 74 Il ENDF B REACTION TYPES The following partial list includes some of the more useful reactions for use with the FMn input card and with the cross section plotter see pages 3 99 and 14 The complete ENDF B list can be found in the ENDF B manual The MT column lists the ENDF B reaction number The FM column lists special MCNP reaction numbers that can be used with the FM card and cross section plotter The nomenclature between MCNP and ENDF B is inconsistent in that MCNP often refers to the number of the reaction type as R whereas ENDF B uses MT but they are the same The problem arises because MCNP has an MT input card used for the S a B thermal treatment However the nomenclature between Monte Carlo transport and Deterministic transport techniques can be radically different See Reference 2 on page G 74 for more information Generally only a subset of reactions is available for a particular nuclide Some reaction data are eliminated by MCNP in cross section processing if they are not required by the problem Examples are photon production in a MODE N problem or certain reaction cross
434. n be obtained by printing out the tallies periodically during a calculation using the PRDMP card The 2 128 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS ESTIMATION OF THE MONTE CARLO PRECISION N dependent behavior of R can then be assessed The complete statistical information available can be obtained by creating a new tally and selecting the desired tally bin with the TFn card 2 Information Available for Forming Statistically Valid Confidence Intervals for TFC Bins Additional information about the statistical behavior of each TFC bin result is available A TFC bin table is produced by MCNP after each tally to provide the user with detailed information about the apparent quality of the TFC bin result The contents of the table are discussed in the following subsections along with recommendations for forming valid confidence intervals using this information a Bin Tally Information The first part of the TFC bin table contains information about the TFC bin result including the mean R scoring efficiency the zero and nonzero history score components of R see page 2 118 and the shifted confidence interval center The two components of R can be used to improve the problem efficiency by either improving the history scoring efficiency or reducing the range of nonzero history scores b TheLargest TFC Bin History Score Occurs on the Next History There are occasions when the user needs to make a conservative estima
435. n be studied by batch size and These normality checks test the assumption that the individual cycle amp values behave in the assumed way Even if the underlying individual cycle k values are not normally distributed the three average values and the combined k estimator will be normally distributed if the conditions required by the Central Limit Theorem are met for the average If required this assumption can be tested by making several independent calculations to verify empirically that the population of the average k values appears to be normally distributed with the same population variance as estimated by MCNP MCNP tests for a monotonic trend of the three combined k estimator over the last ten active cycles This type of behavior is not expected in a well converged solution for k and could indicate a problem with achieving or maintaining the normal spatial mode A WARNING message is printed if such a monotonic trend is observed To assist users in assessing the convergence of the fission source spatial distribution MCNP computes a quantity called the Shannon entropy of the fission source distribution 144145 The Shannon entropy is a well known concept from information theory and provides a single number for each cycle to help characterize convergence of the fission source distribution It has been found that the Shannon entropy converges to a single steady state value as the source distribution approaches stationarity Lin
436. n collisional stopping power i e the energy loss per unit path length to collisions resulting in fractional energy transfers less than an arbitrary maximum value Em in the form amp amp NZC p EX t2 y al 2 8 ds s or B where Vg 2x4 f 8 1 lt In 1 2 9 1 2 1 1 In 4e 1 6 T Here and represent energy transfers as fractions of the electron kinetic energy is the mean ionization potential in the same units as E is v c t is the electron kinetic energy in units of the electron rest mass is the density effect correction related to the polarization of the medium Z is the average atomic number of the medium N is the atom density of the medium in cm 7 and the coefficient C is given by 2 10 2 70 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS where rn e and v are the rest mass charge and speed of the electron respectively The density effect correction 6 is calculated using the prescriptions of Sternheimer Berger and Seltzer when using data from the el03 library and using the method of Sternheimer and Peierls when using data from the el library The ETRAN codes and MCNP do not make use of restricted stopping powers but rather treat all collisional events in an uncorrelated probabilistic way Thus only the total energy loss to collisions is needed and Eqs 2 5 2 6 can be evaluated for the special value 1
437. n into 150 equiprobable bins below E 1 and 150 more equiprobable bins above E 1 Half the time is chosen from the upper set of bins and half the time it is chosen from the lower set Particles starting from the upper bins have a different weight from that of particles starting from the lower bins in order to adjust for the bias and a detailed summary is provided when the PRINT option is used Note that in the above example the probability distribution function is truncated below E 005 and above E 20 MCNP prints out how much of the distribution is lost in this manner and reduces the weight accordingly It is possible for the user to choose a foolish biasing scheme For example SPn 5a SIn 005 2971 1 20 SBn 012988 causes each of the 299 bins to be chosen with equal probability This would be all right except that since there are never more than 300 equiprobable bins this allocates only 1 equiprobable bin per user supplied bin The single equiprobable bin for 1 E 20 is inadequate to describe the distribution function over this range Thus the table no longer approximates the function and the source will be sampled erroneously MCNP issues an error message whenever too much of the source distribution is allocated to a single equiprobable bin alerting users to a poor choice of binning which might inadequately represent the function The coarse bins used for biasing should be chosen so that the probability function is roughly eq
438. n neutron problems one neutron interaction table is required for each isotope or element if using the older elemental tables in the problem The form of the ZAIDs is ZZZAAA nnC for a continuous energy table and ZZZAAA nnD for a discrete reaction table The neutron interaction tables available to MCNP are listed in Table G 2 of Appendix G It should be noted that although all nuclear data tables in Appendix G are available to users at Los Alamos users at other installations will generally have only a subset of the tables available Also note that your institution may make their own tables available to you For most materials there are many cross section sets available represented by different values of nn in the ZAIDs because of multiple sources of evaluated data and different parameters used in processing the data An evaluated nuclear data set is produced by analyzing experimentally measured cross sections and combining those data with the predictions of nuclear model calculations in an attempt to extract the most accurate interaction description Preparing evaluated cross section sets has become a discipline in itself and has developed since the early 1960s In the US researchers at many of the national laboratories as well as several industrial firms are involved in such von The American evaluators joined forces in the mid 1960s to create the national ENDF system There has been some confusion due to the use of the term ENDF to refer to
439. n relevant analytic functions to increase understanding of confidence interval coverage rates for Monte Carlo calculations It was found that the two state splitting problem f x decreases geometrically as the score increases by a constant increment This is equivalent to a negative exponential behavior for a continuous f x The f x for the exponential transform problem decreases geometrically with geometrically increasing x Therefore the splitting problem produces a linearly decreasing f x for the history score on a lin log plot of the score probability versus score The exponential transform problem generates a linearly decreasing score behavior with high score negative exponential roll off on a log log plot of the score probability versus score plot In general the exponential transform problem is the more difficult to sample because of the larger impact of the low probability high scores The analytic shapes were compared with a comparable problem calculated with a modified version of MCNP These shapes of the analytic and empirical f x s were in excellent agreement 127 5 Proposed Uses for the Empirical f x in Each TFC Bin Few papers discuss the underlying or empirical f x for Monte Carlo transport problems 129121 MCNP provides a visual inspection and analysis of the empirical f x for the TFC bin of each tally This analysis helps to determine if there are any unsampled regions holes or spikes in the empirical history score PDF f
440. n time and energy cutoffs the random walk is always terminated when the threshold is crossed Potential bias may result if the particle s importance was not zero weight cutoff weight roulette would be a better name does not bias the game because the weight is increased for those particles that survive Setting the weight cutoff is not typically an easy task and requires thought and experimentation Essentially the user must guess what weight is worth following and start experimenting with weight cutoffs in that vicinity 10 3 05 2 143 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VARIANCE REDUCTION 6 Weight Window The weight window Figure 2 23 is a phase space splitting and Russian roulette technique The phase space may be space energy space time or space For each phase space cell the user supplies a lower weight bound The upper weight bound is a user specified multiple of the lower weight bound These weight bounds define a window of acceptable weights If a particle is below the lower weight bound Russian roulette is played and the particle s weight is either increased to a value within the window or the particle is terminated If a particle is above the upper weight bound it is split so that all the split particles are within the window No action is taken for particles within the window Figure 2 24 is a more detailed picture of the weight window Three important weights define the weight window in a phase spac
441. nalog absorption A 1 k at NL 1 where is summed over each analog absorption event in the k nuclide Note that in analog absorption the weight is the same both before and after the collision Because analog absorption includes fission in criticality calculations the frequency of analog absorption at each collision with nuclide kis 6 aT os The analog absorption estimate is very similar to the collision estimator of k except that only the j absorbing nuclide as sampled in the collision is used rather than averaging over all nuclides For implicit absorption the following is accumulated A 1 9f koe Wi v eff NA T where i is summed over all collisions in which fission is possible and at 0 Or is the weight absorbed in the implicit absorption The difference between the implicit absorption estimator bs and the collision estimator bs is that only the nuclide involved in the collision is used for the absorption estimate rather than an average of all nuclides in the material for the collision estimator The absorption estimator with analog absorption is likely to produce the smallest statistical uncertainty of the three estimators for systems where the ratio v a is nearly constant Such would be the case for a thermal system with a dominant fissile nuclide such that the 1 velocity cross section variation would tend to cancel The
442. nce The kinematics of Compton scattering is assumed to be with free electrons without the use of form factors or Compton profiles The total scattering cross section however 10 3 05 2 57 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS includes the incoherent scattering factor regardless of the use of simple or detailed physics Thus strict comparisons with codes using only the Klein Nishina differential cross section are not valid Highly forward coherent Thomson scattering is ignored Thus the total cross section is regarded as the sum of three components O O0 tO t pe Opp t Os a Photoelectric effect This is treated as a pure absorption by implicit capture with a corresponding reduction in the photon weight WGT and hence does not result in the loss of a particle history except for Russian roulette played on the weight cutoff The noncaptured weight WGT 1 o 0 is then forced to undergo either pair production or Compton scattering The captured weight either is assumed to be locally deposited or becomes a photoelectron for electron transport or for the TTB approximation b production In a collision resulting in pair production probability either an electron positron pair is created for further transport or the TTB treatment and the photon disappears or it is assumed that the kinetic energy WGT E 1 022 MeV of the electron positron pair produced is deposited as ther
443. nce data are derived from the atomic relaxation data available ENDF B VI 8 but use the storage and sampling scheme defined by Everett and Cashwell The momentum profile CDBD data are identical to the data found on MCPLIBO3 The entries in each of the columns of Table 4 are described as follows ZAID The nuclide identification number with the form ZZZAAA nnX where ZZZ is the atomic number AAA is always 000 for elemental photoatomic data nn is the unique table identification number X P for continuous energy neutron tables Library Name of the library that contains the data file for that ZAID 10 3 05 G 43 APPENDIX MCNP DATA LIBRARIES PHOTOATOMIC DATA Library Release Date Length Number of Energies max Cross Section Source Form Factor Source Fluorescence Source CDBD Source G 44 The date the library was officially released This does not necessarily correspond to the source evaluation date these tables contain data from many sources The total length of a particular photoatomic table in words The number of energy points NE on the grid used for the photoatomic cross sections for that data table In general a finer energy grid or greater number of points indicates a more accurate representation of the cross sections The maximum incident photon energy for that data table in GeV multiply by 1000 to get the value in units of MeV For all incident energies greater than MCNP a
444. ndary Its weight is W j where W current particle weight before forced collision d distance to cell surface in the particle s direction and x macroscopic total cross section of the cell material That is the uncollided part is the current particle weight multiplied by the probability of exiting the cell without collision The collided part has weight W W 1 pum Which is the current particle weight multiplied by the probability of colliding in the cell The uncollided part is always produced The collided part may be produced only a fraction f of the time in which case the collided weight is 1 e f This is useful when several forced collision cells are adjacent or when too much time is spent producing and following forced collision particles The collision distance is sampled as follows If P x is the unconditional probability of colliding within a distance x P x P d is the conditional probability of colliding within a distance x given that a collision is known to occur within a distance d Thus the position x of the collision must be sampled on the interval 0 x lt d within the cell according to P x P d where 1 and amp isarandom number Solving for x one obtains xd mpl ee aa t 10 3 05 2 151 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VARIANCE REDUCTION Because a forced collision usually yields a collided particle having a relatively small weight
445. ndfSp dre5 rmccs drmccs endf60 lal50n actib actia endf66d endf66a lal50n actib actia endf66d endf66a 1 150 actib actia endf66d endf66a Source LLNL 0 0 B V 0 B V 0 B VLO B VL8 B VL8 B VLO 0 6 LLNL B V 0 B V 0 B VLO 8 B VL8 6 6 B VL8 B VL8 LANL T X LLNL B V 0 B V 0 B V 0 B V 0 B VLO LANL B VL6 6 6 6 6 8 B VL8 6 6 6 6 6 6 6 APPENDIX MCNP DATA LIBRARIES NEUTRON CROSS SECTION LIBRARIES Table G 2 Cont Continuous Energy and Discrete Neutron Data Libraries Maintained by X 5 Eval Date 1992 1978 1978 1978 1978 1978 2000 2000 1978 1978 1989 1997 1992 1973 1973 1973 2000 2000 1997 1997 2000 2000 1989 1992 1976 1976 1976 1976 1976 1997 1997 1997 1997 1997 1997 1999 1999 1997 1997 1997 1997 1997 1997 1997 10 3 05 Temp Length words 7 12 beeeeetieieee Magnesium bake 300 0 293 6 293 6 293 6 293 6 293 6 77 0 293 6 77 0 293 6 300 0 293 6 300 0 293 6 293 6 293 6 77 0 293 6 77 0 293 6 77 0 293 6 300 0 300 0 293 6 293 6 293 6 293 6 293 6 293 6 77 0 293 6 77 0 293 6 293 6 77 0 293 6 77 0 293 6 293 6 77 0 293 6 77
446. ne may start more tracks at high energies and in strategic directions in a shielding problem while correcting the distribution by altering the weights assigned to these tracks Sizable variance reductions may result from such biasing of the source Source biasing samples from a nonanalog probability density function If negative weight cutoff values are used on the CUT card the weight cutoff is made relative to the lowest value of source particle weight generated by the biasing schemes 1 Biasing by Specifying Explicit Sampling Frequencies The SB input card determines source biasing for a particular variable by specifying the frequency at which source particles will be produced in the variable regime If this fictitious frequency does not correspond to the fraction of actual source particles in a variable bin the corrected weight of the source particles in a particular bin is determined by the ratio of the actual frequency defined on the SP card divided by the fictitious frequency defined on the SB card except for the lin lin interpolation where it is defined to be the ratio of the actual to fictitious frequency evaluated at the exact value of the interpolated variable The total weight of particles started in a given SI bin interval is thus conserved 2 Biasing by Standard Prescription Source biasing can use certain built in prescriptions similar in principle to built in analytic source distributions These biasing options are detailed in
447. new ray trace flux calculation These tallies automatically create a source only contribution and a total for each pixel Standard point detector tally modifications can be made to the image tally for example by using the FM PD and FT cards b Pinhole Image Tally FIP The Flux Image by Pinhole FIP tally uses a pinhole as in a pinhole camera to create a neutron or photon image onto a planar rectangular grid that acts much like photographic film Figure 2 13 is a diagram of the FIP image tally Each source and scatter event contributes to one point detector on the image grid pixel intersected by the particle trajectory through the pinhole 2 98 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS TALLIES FIP Planar Image Grid S axis FS Card Point Detector One Scatter Contribution through Pinhole e Direct gt Sampled B oferente Source Point Pinhole b Reference i Point Detector Point NEM F citat EE ransport iM 1 11 Pinhole Center T axis C Card 7 X2 Y2 Z2 One Source Contribution Particle through Pinhole Source Geometry Scatter Figure 2 13 Diagram of an FIP Flux Image by Pinhole tally for a source internal to the object The particle event point and the virtual pinhole point sampled uniformly in area if a radius is specified are used to define the direction cosines of the contribution to be made from
448. ng into yet another coordinate system where most of its elements are zero The parametric coefficients are then simple functions of the remaining elements Finally the coefficients are transformed from that coordinate system back to the 5 7 system For a plottable torus the curves are either a pair of identical ellipses or a pair of concentric circles The parametric coefficients are readily calculated from the surface coefficients and the elements of are simple functions of the parametric coefficients The next step is to reject all curves that lie entirely outside the window by finding the intersections of each curve with the straight line segments that bound the window taking into account the possibility that an ellipse may lie entirely inside the window The remaining curves are plotted one at a time The intersections of the current curve with all of the other remaining curves and with the boundaries of the window are found by solving the simultaneous equations 1 s 2 0 where 1 is the current curve and i 2 is one of the other curves This process generally requires finding the roots of a quartic False roots and roots outside the window are rejected and the value of the parameter p for each remaining intersection is found The intersections then are arranged in order of increasing values of p Each segment of the curve the portion of the curve between two adjacent intersections is ex
449. ng a complete accounting of the creation and loss of all tracks and their energy the number of tracks entering and reentering a cell plus the track population in the cell the number of collisions in a cell the average weight mean free path and energy of tracks in a cell the activity of each nuclide in a cell that is how particles interacted with each nuclide not the radioactivity and a complete weight balance for each cell MCNP also provides seven standard tally types These include seven standard neutron tallies six standard photon tallies and four standard electron tallies These basic tallies can be modified by the user in many ways All tallies are normalized to be per starting particle except in KCODE criticality problems which are normalized to be per fission neutron generation The MCNP tally plotter provides graphical displays of the results see Appendix B Tally Mnemonic Description F1 N Or F1 P or FI E Surface current F2 N or 2 or F2 E Surface flux F4 N or or Track length estimate of cell flux F5a N F5a P Flux at a point or ring detector F6 N or F6P or F6N P Track length estimate of energy deposition F7 N Track length estimate of fission energy deposition F8 N or F8 P or F8 E Pulse height tally F8 B E 2 80 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS TALLIES The above seven tally categories represent the basic MCNP tally types To have many tallies of a given type
450. ng the optical path between the collision site and the DXTRAN sphere This is done in the same way as point detectors see point detector pseudoparticles on page 2 100 MCNP determines the optical path by tracking a pseudoparticle from the collision site to the DXTRAN sphere This pseudoparticle is deterministically tracked to the DXTRAN sphere simply to determine the optical path No distance to collision is sampled no tallies are made and no records of the pseudoparticle s passage are kept for example tracks entering In contrast once the DXTRAN particle is created at the sphere s surface the particle is no longer a pseudoparticle The particle has real weight executes random walks and contributes to tallies DXTRAN Details To explain how the scheme works consider the neighborhood of interest to be a spherical region surrounding a designated point in space In fact consider two spheres of arbitrary radii about the point 20 Further assume that the particle having direction u v w collides at the point P x y z as shown in Figure 2 25 u v w Figure 2 25 The quantities 0 0 n o Ry and Ro defined in the figure Thus L the distance between the collision point and center of the spheres is L Ja y Z 2 On collision a DXTRAN particle is placed at a point on the outer sphere of radius Ro as described below Provision is made for biasing the contri
451. nges the units into an energy tally and multiplies each tally as indicated in Table 2 3 For an F8 pulse height tally the asterisk changes the tally from deposition of pulses to an energy deposition tally and a plus changes the tally to a charge deposition tally Table 2 3 Tallies Modified with an Asterisk or Plus Tally Score Units F1 WE MeV F2 WE MeV cm WT E 2 FA MeV cm V Weste E 2 F5 Rl eee MeV cm 2 R F6 1 60219 10 2219158 2 jerks g MeV m F7 1 60219 10 2218158 wr o E Qs jerks g MeV m 8 Ep x We put in bin Ey MeV F8 tW put in bin Ep charge In addition to the standard tallies MCNP has one special tally type the superimposed mesh tally This feature allows the user to tally particles on a mesh independent of the problem geometry Currently only track length type 4 mesh tallies have been implemented Other track length quantities such as heating and energy deposition can be calculated with the use of a tally multiplier FM card Mesh tallies are invoked by using the FMESH card As in the F card a unique number is assigned to each mesh tally Since only track length mesh tallies are available the mesh tally number must end with a 4 and it must not be identical to any number that is used to identify an F4 tally The track length is computed over the mesh tally cells and is normalized to be per starting particle except in KCODE criticality calculations Not all features of
452. ngle of the photon relative to the direction of the electron according to the formula _ 26 1 p 25 1 where 5 is a random number This sampling method is of interest in the context of detectors and DXTRAN spheres A set of source contribution probabilities p u consistent with the tabular data is not available Therefore detector and DXTRAN source contributions are made using Eq 2 12 Specifying that the generation of bremsstrahlung photons rely on Eq 2 12 allows the user to force the actual transport to be consistent with the source contributions to detectors and DXTRAN p u dy u 8 K shell Electron Impact Ionization and Auger Transitions Date tables on the el03 library use the same K shell impact ionization calculation based upon ITS1 0 as data tables on the el library except for how the emission of relaxation photons is treated the el03 evaluation model has been modified to be consistent with the photo ionization relaxation model In the el evaluation a K shell impact ionization event generated a photon with the average K shell energy The el03 evaluation generates photons with energies given by Everett and Cashwell Both e103 and el treatments only take into account the highest Z component of a material Thus inclusion of trace high Z impurities could mask K shell impact ionization from other dominant components Auger transitions are handled the same for data tables from the el03 and el libraries If an a
453. no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no yes no no no no no yes yes yes no no yes yes yes no no no no no yes yes yes no no yes yes no no no no no no no no yes yes no no no no yes yes G 27 APPENDIX G MCNP DATA LIBRARIES NEUTRON CROSS SECTION LIBRARIES Continuous Energy and Discrete Neutron Data Libraries Maintained by X 5 ZAID AWR 04 155 64155 50c 64155 50d 64155 55c 64155 60c 64155 65c 64155 66c Gd 156 64156 50c 64156 50d 64156 55c 64156 60c 64156 66c Gd 157 64157 50d 64157 50c 64157 55c 64157 60c 64157 65c 64157 66c Gd 158 64158 50d 64158 50c 64158 55c 64158 60c 64158 66c Gd 160 64160 50d 64160 50c 64160 55c 64160 60c 64160 66c 7 67 Holmium ook Ho 165 67165 35c 67165 35d 67165 42c 67165 55c 67165 55d 67165 60c 67165 66c Z 69 153 5920 153 5920 153 5920 153 5920 153 5920 153 5920 154 5830 154 5830 154 5830 154 5830 154 5830 155 5760 155 5760 155 5760 155 5760 155 5760 155 5760 156 5670 156 5670 156 5670 156 5670 156 5670 158 5530 158 5530 158 5530 158 5530 158 5530 163 5135 163 5135 163 5135 163 5130 163 5130 163 5130 163 5130 Tm 169 69169 55 7 71 Lu 175 71175 65c 71175 66c Lu 176 711
454. no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no yes no yes yes yes yes yes no yes yes yes yes yes no yes yes yes yes no no yes no yes yes yes yes yes no yes yes yes yes no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no 0 CP DN UR no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no APPENDIX G MCNP DATA LIBRARIES NEUTRON CROSS SECTION LIBRARIES Table G 2 Cont Continuous Energy and Discrete Neutron Data Libraries Maintained by X 5 E max NE MeV GPD Library Eval Temp Length ZAID AWR Name Source Date words As 75 33075 35d 174 2780 drmccs B V 0 1974 0 0 8480 263 33075 35c 74 2780 rmccsa 0 1974 0 0 50931 6421 33075 42 74 2780 endl92 LLNL lt 1992 300 0 56915 6840 Z 35 eese eoe k k k k kkk k Bromine k k k k k k k kk kk Br 79 35079 55 78 2404 misc5xs 7 9 LANL T 1982 293 6 10431 1589 81 35081 55c 80 2212 misc5xs 7 9 LANL T 1982 293 6 5342 831 7 36 Kr 78 36078 50c 77 2510 rmccsa B V 0 1978 293 6 9057 939 36078 50d 77 251
455. no no no no no no no no no no no 0 CP DN UR no no no no yes yes no no no no no no no no no yes yes no no no no no no no no no no no no no no no no no no yes yes yes yes ZAID Z 72 Hf nat 72000 42c 72000 50d 72000 50c 72000 60c Hf 174 72174 65c 72174 66c Hf 176 72176 65c 72176 66c Hf 177 72177 65 72177 66 Hf 178 72178 65c 72178 66c Hf 179 72179 65c 72179 66c Hf 180 72180 65c 72180 66c Z 73 181 73181 42 73181 50d 73181 50 73181 51c 73181 51d 73181 60c 73181 64c 73181 66c 182 73182 49 73182 60 73182 64 73182 65 73182 66 7 74 Tungsten 7a kak iis W nat 74000 21 74000 55 74000 55 AWR 176 9567 176 9540 176 9540 176 9540 172 4460 172 4460 174 4300 174 4300 175 4230 175 4230 176 4150 176 4150 177 4090 177 4090 178 4010 178 4010 179 3936 179 4000 179 4000 179 4000 179 4000 179 4000 179 4000 179 4000 180 3870 180 3870 180 3870 180 3870 180 3870 182 2706 182 2770 182 2770 W182 74182 24c 74182 48c 74182 50c 74182 50d 74182 55 74182 55 74182 60 74182 61 74182 62 74182 63 74182 64 74182 65 74182 66 180 3900 180 3900 180 3900 180 3900 180 3900 180 3900 180 3900 180 3900 180 3900 18
456. no no no no no no no no no no no no no no no yes no no no no no no yes yes yes yes no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no APPENDIX G MCNP DATA LIBRARIES NEUTRON CROSS SECTION LIBRARIES Table G 2 Cont Continuous Energy and Discrete Neutron Data Libraries Maintained by X 5 Library Eval Temp Length Emax _ ZAID AWR Nene Source words MeV GPD SE WS 23051 42c 50 5063 192 LLNL 1992 300 0 94082 5988 30 0 yes no no 7 24 RRR SSHRC Chromium ioeo Cr nat 0 CP DN UR 24000 42c 24000 50d 24000 50c Cr 50 24050 24c 24050 60c 24050 61c 24050 62c 24050 64c 24050 66c Cr 52 24052 24c 24052 60c 24052 61c 24052 62c 24052 64c 24052 66 Cr 53 24053 24 24053 60 24053 61c 24053 62c 24053 64c 24053 66c Cr 54 24054 24c 24054 60c 24054 61c 24054 62c 24054 64c 24054 66c 7 25 Manganese 51 5493 51 5490 51 5490 49 5170
457. nostic print tables should be examined to see if any one pseudoparticle trajectory made an unusually large contribution to the tally Detector results should be viewed suspiciously if the relative error is greater than 596 Close attention should be paid to the tally statistical analysis and the ten statistical checks described on page 2 129 b Detectors and reflecting white or periodic surfaces Detectors used with reflecting white or periodic surfaces give wrong answers because pseudoparticles travel only in straight lines Consider Figure 2 15 with a point detector and eight source cells The imaginary cells and point detector are also shown on the other side of the mirror The solid line shows the source contribution from the indicated cell MCNP does not allow for the dashed line contribution on the 10 3 05 2 101 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS TALLIES other side of the reflecting surface The result is that contributions to the detector will always be from the solid path instead of from a mixture of solid and dashed contributions This same situation occurs at every collision Therefore the detector tally will be lower with the same starting weight than the correct answer and should not be used with reflecting white or periodic surfaces The effect is even worse for problems with multiple reflecting white or periodic surfaces Detector Source cells Reflecting plane gt Figure 2 15
458. ns from Livermore and evaluations from the Nuclear Physics 16 Group at Los Alamos Evaluated data are processed into a format appropriate for MCNP by codes such as NJ OY The processed nuclear data libraries retain as much detail from the original evaluations as is feasible to faithfully reproduce the evaluator s intent Nuclear data tables exist for neutron interactions neutron induced photons photon interactions neutron dosimetry or activation and thermal particle scattering S a Most of the photon and electron data are atomic rather than nuclear in nature photonuclear data are also included Each data table available to MCNP is listed on a directory file XSDIR Users may select specific data tables through unique identifiers for each table called ZAIDs These identifiers generally contain the atomic number Z mass number A and library specifier ID Over 836 neutron interaction tables are available for approximately 100 different isotopes and elements Multiple tables for a single isotope are provided primarily because data have been derived from different evaluations but also because of different temperature regimes and different processing tolerances More neutron interaction tables are constantly being added as new and revised evaluations become available Neutron induced photon production data are given as part of the neutron interaction tables when such data are included in the evaluations Photon interaction tables exist
459. nse that they provide secondary particle distributions for all light particles i e photons neutrons protons alphas etc At this time MCNP makes use of the photon and neutron emission distributions The selection of photon interaction data has become more complicated Let us first examine the simple cases Photon or photon electron problems where photonuclear events are to be ignored i e photonuclear physics is explicitly off should specify the material composition on the Mn card by mass or weight fraction of each element i e using the form ZZZ000 to describe each element Partial ZAID specification i e only ZZZ000 with no library evaluation number nn will choose the default table the first table listed in the XSDIR This will be overridden if the evaluation identifier nn is given by the PLIB option e g PLIB 02p will select all photoatomic tables for that material from 02 data set Specifying a full ZAID e g 13000 03p will override any other selection and always result in selecting that specific table The next most simple case is a coupled neutron photon problem that will explicitly ignore photonuclear events In this case one should specify the material composition according to the rules discussed in the previous section on neutron data tables Given an isotopic material component e g 13027 the appropriate elemental photoatomic table will be selected e g 13000 If no evaluation identifier is given the default first table
460. nt density for neutron collisions MCNP neutron physics is nonanalog in the joint density sampling particularly in the way that multiple neutrons exiting a collision are totally uncorrelated and do not even conserve energy except in an average sense over many neutron histories Thus neutron tallies must be done with extreme caution when more than one neutron can exit a collision Another aspect of the pulse height tally that is different from other MCNP tallies is that F8 P F8 E and F8 P E are all equivalent All the energy from both photons and electrons if present will be deposited in the cell no matter which tally is specified When the pulse height tally is used with energy bins care must be taken because of negative scores from nonanalog processes and zero scores caused by particles passing through the pulse height cell without depositing energy In some codes like the Integrated TIGER Series these events cause large contributions to the lowest energy bin pulse height score In other codes no contribution is made MCNP compromises by counting these events in a zero bin and an epsilon bin so that these scores can be segregated out It is recommended that your energy binning for an F8 tally be something like E8 0 Le 5 1 2 3 4 5 Knock on electrons in MCNP are nonanalog in that the energy loss is included in the multiple scattering energy loss rate rather than subtracted out at each knock on event Thus knock ons cause n
461. ntimony 51000 01p mcplib 1982 461 51 0 1 B IV B IV E amp C n a 51000 02p mcplib02 1993 695 90 100 B IV 89 E amp C n a 51000 03p meplib03 2002 2378 90 100 B IV 89 B IV E amp C BM amp M 51000 04p mcplib04 2002 8414 1096 100 B VL8 8 B VI8 BM amp M Z 52 Tellurium 52000 01p meplib 1982 473 53 0 1 B IV B IV E amp C n a 52000 02p mcplib02 1993 707 92 100 B IV 89 E amp C n a 52000 03p meplib03 2002 2390 92 100 B IV 89 B IV E amp C BM amp M 52000 04p mcplib04 2002 8162 1054 100 B VL8 8 B VI8 7 53 KK KKK KKK Iodine 53000 01p meplib 1982 473 53 0 1 B IV B IV E amp C n a 53000 02p mcplib02 1993 707 92 100 B IV 89 E amp C n a 53000 03p mcplib03 2002 2390 92 100 B IV 89 B IV E amp C BM amp M 53000 04p meplib04 2002 8492 1109 100 B VL8 8 B VI8 BM amp M Z 54 Xenon K K K K K K K 54000 01p mcplib 1982 473 53 0 1 B IV B IV E amp C n a 54000 02p mcplib02 1993 707 92 100 B IV 89 E amp C n a 54000 03p mcplib03 2002 2390 92 100 B IV 89 B IV E amp C BM amp M 54000 04p mcplib04 2002 8324 1081 100 B VL8 8 8 BM amp M Z 55 Cesium 55000 01p meplib 1982 497 57 0 1 B IV B IV E amp C n a 55000 02p meplib02 1993 731 96 100 B IV 89 E amp C n a 55000 03p meplib03 2002 2513 96 100 B IV 89 B IV E amp C BM amp M 55000 04p meplib04 2002 8417 1080 100 B VL8 8 B VI8
462. nts the intersection of A and B or A B The only way regions of space can be added is with the union operator An intersection of two spaces always results in a region no larger than either of the two 10 3 05 1 15 CHAPTER 1 MCNP OVERVIEW MCNP GEOMETRY spaces Conversely the union of two spaces always results in a region no smaller than either of the two spaces a b Figure 1 5 A simple example will further illustrate the concept of Figure 1 5 and the union operator to solidify the concept of adding and intersecting regions of space to define a cell See also the second example in Chapter 4 In Figure 1 6 we have two infinite planes that meet to form two cells Cell 1 is easy to define it is everything in the universe to the right of surface 1 that is a positive sense that is also in common with or intersected with everything in the universe below surface 2 that is a negative sense Therefore the surface relation of cell 1 is 1 2 b Figure 1 6 Cell 2 is everything in the universe to the left negative sense of surface 1 plus everything in the universe above positive sense surface 2 or 1 2 illustrated in Figure 1 66 by all the shaded regions of space If cell 2 were specified as 1 2 that would represent the region of space common to 1 and 2 which is only the cross hatched region in the figure and is obviously an improper specification for cell 2 Returning to Figure 1 4 on page 1
463. nued by going back to the previous paragraph and repeating the steps If the distance to collision is less than the distance to surface or if a multigroup charged particle reaches the distance to energy boundary the particle undergoes a collision For neutrons the collision analysis determines which nuclide is involved in the collision samples the target velocity of the collision nuclide for the free gas thermal treatment generates and banks any photons ACEGAM handles analog capture or capture by weight reduction plays the weight cutoff game 2 6 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS GEOMETRY handles S a thermal collisions and elastic or inelastic scattering For criticality problems fission sites are stored for subsequent generations Any additional tracks generated in the collision are put in the bank The energies and directions of particles exiting the collision are determined Multigroup and multigroup adjoint collisions are treated separately The collision process and thermal treatments are described in more detail later in this chapter see page 2 28 The collision analysis for photons is similar to that for neutrons but includes either the simple or the detailed physics treatments See page 3 129 for a discussion of turning photonuclear physics on The simple physics treatment is valid only for photon interactions with free electrons i e it does not account for electron binding effects when sam
464. number of collisions leading to many contributions to this tally The SD card can be used to input a new volume that divides the tally In other words if V is input on the SD card the tally will be divided by instead of There are cases where MCNP cannot calculate the volume of a taller region In these cases the user must input an entry on an SD card corresponding to the taller cell 2 Surface Flux F2 The average particle scalar flux on a surface of Table 2 2 is estimated using a surface crossing estimator that may be thought of as the limiting case of the cell flux or track length estimator when the cell becomes infinitely thin as illustrated in Figure 2 8 gt Tally surface of area A 7 Figure 2 8 Diagram for description of the surface flux tally As the cell thickness 6 approaches zero the cell volume approaches and the track length through the cell approaches 6 lo Thus 2 86 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS TALLIES ds lim 0 lim 5 0 V W 6 un AX _ more formal derivation of the surface flux estimator be found in Ref 116 For particles grazing the surface 1 1 very large and MCNP approximates the surface flux estimator in order to satisfy the requirement of one central limit theorem An unmodified surface flux estimator has an infinite variance and thus conf
465. nuous Energy Photoatomic Data Libraries Maintained by X 5 Library Release Length Emax CS FF Fluor ZAID Name Date Words NE GeV Source Source Source Z 73 Tantalum 73000 01 mcplib 1982 521 61 0 1 B IV B IV E amp C 73000 02 mceplib02 1993 755 100 100 B IV 89 E amp C 73000 03 meplib03 2002 2834 100 100 B IV 89 B IV E amp C 73000 04 mcplib04 2002 9698 1244 100 B VL8 8 8 a 74 KKK KK KKK Tungsten 74000 01 mcplib 1982 521 61 0 1 B IV B IV E amp C 74000 02 meplib02 1993 755 100 100 B IV 89 E amp C 74000 03 meplib03 2002 2834 100 100 B IV 89 B IV E amp C 74000 04p 04 2002 9716 1247 100 B VL8 8 8 7 75 Rhenium 75000 01 mcplib 1982 521 61 0 1 B IV B IV E amp C 75000 02 mcplib02 1993 755 100 100 B IV 89 E amp C 75000 03 mcplib03 2002 2933 100 100 B IV 89 B IV E amp C 75000 04 mcplib04 2002 9797 1244 100 B VL8 8 8 7 76 Osmium 76000 01 mcplib 1982 521 61 0 1 B IV B IV E amp C 76000 02 meplib02 1993 755 100 100 B IV 89 B IV E amp C 76000 03 mcplib03 2002 2933 100 100 B IV 89 B IV E amp C 76000 04 mcplib04 2002 9977 1274 100 B VL8 8 8 Z 77 KKK KK KKK Iridium 77000 01p mcplib 1982 521 61 0 1 B IV B IV E amp C 77000 02 mcplib02 1993 755 100 100 B IV 89 B IV E amp C 77000 03 mcplib03 20
466. o Z The parameter v is the inverse length v sin 0 2 X 1 where x 10 m c h4 2 29 1445cm The maximum value of vis kaJ2 41 21660 at u 1 The essential features of Z v are indicated in Figure 2 5 Figure 2 5 For hydrogen an exact expression for the form factor is used 1 Ley where fis the inverse fine structure constant f 137 0393 and f J2 96 9014 I 1 v 1 The Klein Nishina formula is sampled exactly by Kahn s method below 1 5 MeV and by Koblinger s method above 1 5 MeV as analyzed and recommended by Blomquist and Gelbard The outgoing energy E and angle u are rejected according to the form factors For next event estimators such as detectors and DXTRAN the probability density for scattering toward the detector point must be calculated 2 60 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS 2 1 2 p p 5 Za v K a E SZ at 2 3 1 where nr 2494351 and o Z and Z v are looked up in the data library The new energy of the photon accounts for the effects of a bound electron The electron binding effect on the scattered photon s energy distribution appears as a broadening of the energy spectrum due to the precollision momentum of the electron This effect on the energy distribution of the incoherently scattered photon is called Doppler broadening The Hartree Fock Compton profi
467. o no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no APPENDIX G MCNP DATA LIBRARIES NEUTRON CROSS SECTION LIBRARIES Table G 2 Cont Continuous Energy and Discrete Neutron Data Libraries Maintained by X 5 no no no no no no no no no no no no no no no no no no no no no no no no 0 CP DN UR no no no no no no no no no no no no no no no no no no no no no no no no Library Eval Temp Length _ ZAID AWR Name Source Date words NE MeV GPD CP 7015 42c 14 8713 endl92 LLNL 1992 300 0 22590 352 30 0 yes no no 7015 55 14 8710 rmccsa LANL T 1983 293 6 20920 744 20 0 yes no no 7015 55d 14 8710 drmccs LANL T 1983 293 6 15273 263 20 0 yes no no 7015 60c 14 8710 endf60 B VLO 1993 293 6 24410 653 20 0 yes no no 7015 66c 14 8710 endf66a B VLO 1993 293 6 31755 880 20 0 yes no no 8016 21c 15 8575 100xs3 LANL T X 1989 300 0 45016 1427 100 0 yes no no 8016 24c 15 8531 la150n 6 1996 293 6 164461 1935 150 0 yes no yes 8016 42c 15 8575 endl92 LLNL 1992 300 0 9551 337 30 0 yes no no 8016 50c 15 8580 rmccs B V 0 1972 293 6 37942 1391 20 0 yes no no 8016 50d 15 8580 drmccs B V 0 1972 293 6 20455 263 200 yes no no 8016 53c 15 8580 endf5mt 1 B V 0 1972 587 2 37989 1398 20 0 yes no no 8016 54c 15 8580 endf5mt 1 B V
468. o somewhat more accurate In MCNP elliptical tori symmetric about any axis parallel to a coordinate axis may be specified The volume and surface area of various tallying segments of a torus usually will be calculated automatically 2 Ambiguity Surfaces The description of the geometry of a cell must eliminate any ambiguities as to which region of space is included in the cell That is a particle entering a cell should be able to determine uniquely which cell it is in from the senses of the bounding surfaces This is not possible in a geometry such as shown in Figure 2 2 unless an ambiguity surface is specified Suppose the figure is rotationally symmetric about the y axis A particle entering cell 2 from the inner spherical region might think it was entering cell 1 because a test of the senses of its coordinates would satisfy the description of cell 1 as well as that of cell 2 In such cases an ambiguity surface is introduced such as plane a An ambiguity surface need not 2 10 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS GEOMETRY be a bounding surface of a cell but it may be and frequently is It can also be the bounding surface of some cell other than the one in question However the surface must be listed among those in the problem and must not be a reflecting surface see page 2 12 The description of cells 1 and 2 in Figure 2 2 is augmented by listing for each its sense Figure 2 2 relative to surfa
469. ode factors encompass the physics features included in a calculation as well as the mathematical models used uncertainties in the data such as the transport and reaction cross sections Avogadro s number atomic weights etc the quality of the representation of the differential cross sections in energy and angle and coding errors bugs of the applicable physics must be included in a calculation to produce accurate results Even though the evaluations are not perfect more faithful representation of the evaluator s data should produce more accurate results The descending order of preference for Monte Carlo data for calculations is continuous energy thinned continuous energy discrete reaction and multigroup Coding errors can always be a problem because no large code is bug free MCNP however is a very mature heavily used production code With steadily increasing use over the years the likelihood of a serious coding error continues to diminish The second area problem modeling factors can quite often contribute to a decrease in the accuracy of a calculation Many calculations produce seemingly poor results because the model of the energy and angular distribution of the radiation source is not adequate Two other problem modeling factors affecting accuracy are the geometrical description and the physical characteristics of the materials in the problem The third general area affecting calculational accuracy involves user errors in the
470. of detectors or other tallies It involves deterministically transporting particles on collision to some arbitrary user defined sphere in the neighborhood of a tally and then calculating contributions to the tally from these particles Contributions to the detectors or to the DXTRAN spheres can be controlled as a function of a geometric cell or as a function of the relative magnitude of the contribution to the detector or DXTRAN sphere The DXTRAN method is a way of obtaining large numbers of particles on user specified DXTRAN spheres DXTRAN makes it possible to obtain many particles in a small region of interest that would otherwise be difficult to sample Upon sampling a collision or source density function DXTRAN estimates the correct weight fraction that should scatter toward and arrive without collision at the surface of the sphere The DXTRAN method then puts this correct weight on the sphere The source or collision event is sampled in the usual manner except that the particle is killed if it tries to enter the sphere because all particles entering the sphere have already been accounted for deterministically 14 Correlated sampling The sequence of random numbers in the Monte Carlo process is chosen so that statistical fluctuations in the problem solution will not mask small variations in that solution resulting from slight changes in the problem specification The j history will always start at the same point in the random number sequ
471. of the plotted quantities satisfies the required convergence criteria correct detector result obtained from a 5 million history ring detector tally is 5 72 x 10 n cm 27 0 0169 0 023 slope 4 6 19 The apparently converged 14 000 history point detector result is a factor of four below the correct result If you were to run 200 000 histories you would see the point detector result increasing to 3 68 x 10 s R 0 20 0 30 1 6 FOM 1 8 The magnitudes of R and the VOV are much too large for the point detector result to be accepted The slope of f x is slowly increasing but has only reached a value of 1 6 This slope is still far too shallow compared to the required value of 3 0 The ring detector result of 5 06 x 10 nem Zs R 0 0579 VOV 0 122 slope 2 8 FOM 22 at 192 000 histories is interesting All of these values are close to being acceptable but just miss the requirements The ring detector result is more than two estimated standard deviations below the correct result Column 2 shows the results as a function of N for 5 million histories The ring detector result of 5 72 x 10 n em 5 R 0 0169 VOV 0 023 slope 4 6 FOM 19 now appears very well behaved in all categories This tally passed all 10 statistical checks There appears to be no reason to question the validity of this tally The point detector result is 4 72 x 10 n cm 2 5 R 0 11 VOV 0 28 slope 2 1 FOM 0 4
472. ographs 2 97 FIC 3 82 FIP 3 83 FIR 3 82 Flux Tallies 2 85 FMESH card 3 114 FMn card 3 95 Reactions G 1 FOM also see Figure of Merit 3 108 Forced collisions 2 6 2 136 2 139 2 151 to 2 152 3 42 D 8 Fraction Atomic 3 118 Free Gas Thermal temperature TMP card 3 132 Index 5 MCNP MANUAL INDEX FSn tally segment card 3 102 Thermal treatment 2 28 FSn tally segment card 3 102 FTn card 3 112 FUn TALLYX input card 3 105 Fusion Energy Spectrum D D 3 64 G Gas Material Specification 3 118 Gaussian Distribution Position 3 65 Time 3 65 Gaussian energy broadening 2 106 Gaussian fusion energy spectrum 3 64 General Plane Defined by Three Points 3 17 General Source SDEF card 3 53 Geometry Cone 2 9 Surfaces 2 0 Torus 2 9 Geometry Cards 3 24 to 3 32 AREA 3 25 FILL 3 29 LAT 3 28 Repeated structures cards 3 25 to 3 32 TRCL 3 28 TRn 3 30 to 3 32 Universe U 3 26 VOL 3 24 Geometry Errors 3 8 Geometry splitting 2 6 2 139 2 140 D 8 Giant Dipole Resonance 2 64 H HEX 3 19 3 22 History Cutoff NPS card 3 137 Monte Carlo method 2 1 History Particle Flow 2 5 D 7 Horizontal Input Format 3 4 HSRC 3 77 HTGR Modeling 3 32 Index 6 KSRC card 3 77 IDUM array 3 138 IDUM card 3 138 IMP card 3 34 Implicit Capture 2 34 Importance 3 7 3 26 3 34 Theory of 2 146 Zero 3 8 3 12 3 35 3 44 3 77 3 85 Incoherent Photon Scattering Detailed p
473. olecules and crystalline solids Two processes are allowed 1 inelastic scattering with cross section o and a coupled energy angle representation derived from an ENDF 5 scattering law and 2 elastic scattering with no change in the outgoing neutron energy for solids with cross section and an angular treatment derived from lattice parameters The elastic scattering treatment is chosen with probability Oin This thermal scattering treatment also allows the representation of scattering by multiatomic molecules for example BeO For the inelastic treatment the distribution of secondary energies is represented by a set of equally probable final energies typically 16 or 32 for each member of a grid of initial energies from an upper limit of typically 4 eV down to 10 eV along with a set of angular data for each initial and final energy The selection of a final energy given an initial energy can be characterized by sampling from the distribution N f 1 p E lt 5 lt 1 nD S E pE where and E are adjacent elements on the initial energy grid Nis the number of equally probable final energies and E is the j discrete final energy for incident energy E There are two allowed schemes for the selection of a scattering cosine following selection of a final energy and final energy index j In each case the j set of angular d
474. om Los Alamos Scientific Laboratory October 1966 12 Metropolis and S Ulam The Monte Carlo Method J Amer Stat Assoc 44 335 1949 13 Herman Kahn Modifications of the Monte Carlo Method Proceeding Seminar on Scientific Computation Nov 1949 IBM New York 20 27 1950 14 A S Householder E Forsythe and Germond Ed Monte Carlo Methods NBS Applied Mathematics Series Vol 12 6 1951 15 Lehmer Mathematical Methods in Large Scale Computing Units Ann Comp Lab Harvard Univ 26 141 146 1951 16 Herman Kahn Applications of Monte Carlo AECU 3259 Report Rand Corporation Santa Monica CA 1954 17 E D Cashwell and C J Everett A Practical Manual on the Monte Carlo Method for Random Walk Problems Pergamon Press Inc New York 1959 18 Robert Johnston General Monte Carlo Neutronics Code Los Alamos Scientific Laboratory Report LAMS 2856 March 1963 19 E D Cashwell J R Neergaard M Taylor and D Turner MCN A Neutron Monte Carlo Code Los Alamos Scientific Laboratory Report LA 4751 January 1972 20 E D Cashwell J R Neergaard C J Everett R G Schrandt W M Taylor and D Turner Monte Carlo Photon Codes MCG and MCP Los Alamos National Laboratory Report LA 5157 MS March 1973 10 3 05 2 201 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS REFERENCES 21 22 23 24 25 26 2
475. on 1 N where is the number of source particles per generation Thus it is desirable to make N as large as possible Any value of N gt 500 should be sufficient to reduce the bias to a small level The eigenvalue bias has been shown to be 1 2 2 eff 7 Mary Ok 2 34 Ak where is the true standard deviation for the final 18 the approximate standard deviation computed assuming the individual k values are statistically independent and 2 2 Okr gt O approx 10 3 05 2 183 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CRITICALITY CALCULATIONS The standard deviations are computed at the end of the problem Because the o s decrease as 1 1 I Akg is independent of the number of active cycles Recall that 15 proportional to UN the number of neutrons per keg cycle Eqn 2 31 can be written as the following inequality I key ok 2k 2 35 eff This inequality is useful for determining an upper limit to the number of active cycles that should be used for a calculation without having A amp dominate hep Ifo ker 15 0 0010 which is a reasonable value for criticality calculations and J 1 16 1000 then Ak a lt 0 5 and will not dominate kep confidence interval If k is reasonably well approximated by MCNP s estimated standard deviation this ratio will be much less than 0 5 The total running time for th
476. on by the collision nuclide at the incident energy f atomic fraction for nuclide k nominal source size for cycle and W weight of particle entering collision Because W represents the number of neutrons entering the i collision i 5 W gt is the expected number of neutrons to be produced from all fission processes in the collision Thus C e ue k eff 18 the mean number of fission neutrons produced per cycle The collision estimator tends to be best sometimes only marginally so in very large systems The collision estimate of the prompt removal lifetime for any active cycle is the average time required for a fission source neutron to be removed from the system by either escape capture n On or fission EW W where 7 and are the times from the birth of the neutron until escape or collision W is the weight lost at each escape W Wris the weight lost to and fission at each collision fio ii W W W di ED KOT where o is the microscopic capture n On cross section and is the weight entering the collision 2 170 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CRITICALITY CALCULATIONS 2 Absorption Estimators The absorption estimator for k for any active cycle is made when a neutron interacts with fissionable nuclide The estimator differs for analog and implicit absorption For a
477. on energy spectrum 3 64 Watt fission spectrum 3 77 3 128 3 135 3 136 WC2 3 135 Weight cutoff 3 135 Weight Window Cards 3 43 to 3 47 Energies or Times WWE 3 44 Generation Cards 3 46 to 3 51 Generation Energies or Times WWGED 3 47 Generator WWG card 3 47 Parameter WWP 3 45 White Boundaries 2 13 3 11 3 12 WWE Card 3 44 WWG Card 3 47 WWGE Card 3 47 WWN Card 2 32 3 44 WWP Card 3 45 X X Card 3 15 xM also see Multiply 3 4 XSn Card 3 123 Y Y Card 3 15 Z Z Card 3 15 ZA 3 120 ZAID 2 24 3 118 3 121 and S o p 3 134 and the AWTAB card 3 123 ZA ZB ZC E 44 Zero Importance 3 8 3 12 3 35 3 44 3 77 3 85 ZZZAAA also see ZAID 2 15 Index 11 MCNP MANUAL INDEX Complement Operator 2 8 Symbols Complement Operator 2 8 3 9 3 81 3 95 1 3 12 3 31 3 80 3 86 1 3 81 3 86 3 1 3 1 Index 12 10 3 05 3 11 3 81 3 86
478. on neutrons produced in generation per fission neutron started A generation is the life of a neutron from birth in fission to death by escape parasitic capture or absorption leading to fission In MCNP the computational equivalent of a fission generation is a K cycle that is a cycle is a computed estimate of an actual fission generation Processes such as 2 and are considered internal to a cycle and do not act as termination Because fission neutrons are terminated in each cycle to provide the fission source for the next cycle a single history can be viewed as continuing from cycle to cycle The effect of the delayed neutrons is included by using the total v when the data are available In a Mode N P problem secondary photon production from neutrons is turned off during inactive 10 3 05 2 163 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CRITICALITY CALCULATIONS cycles MCNP uses three different estimators for k We recommend using for the final k result the statistical combination of all three 140 It is extremely important to emphasize that the result from a criticality calculation is a confidence interval for k that is formed using the final estimated the estimated standard deviation properly formed confidence interval from a valid calculation should include the true answer the fraction of time used to define the confidence interval There will always be some probability that the true answ
479. on the unit interval For histogram interpolation the sampled energy is 2 42 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS i 1 E E Lk Pik For linear linear interpolation the sampled energy is 2 PLk 1 Plk Pgh ee Cpe og k 1 k E E pt H Pik 1 k E The secondary energy is then interpolated between the incident energy bins i and i 1 to properly preserve thresholds Let By 1 8 1 E out gs LX E Ej 1 The final step is to adjust the energy from the center of mass system to the laboratory system if the energies were given in the center of mass system Law 4 is an independent distribution i e the emission energy and angle are not correlated The outgoing angle is selected from the angular distribution as described on page 2 36 Data tables built using this methodology are designed to sample the distribution correctly in a statistical sense and will not necessarily sample the exact distribution for any specific collision Law 5 ENDF law 5 General evaporation spectrum The function g x is tabulated versus X and the energy is tabulated versus incident energy Ej The law is then Ea This density function is sampled by WS T Ej where is a tabulated function of the incident energy and c amp is a table of equiprobable x va
480. one none inco inco inco inco APPENDIX G MCNP DATA LIBRARIES NEUTRON CROSS SECTION LIBRARI Table G 1 Cont Thermal S o p Cross Section Libraries ES Library Date of Temp Num of Numof Elastic ZAID Source Name Processing Angles Energies Data Zirconium in Zirconium Hydride 40000 40090 40091 40092 40094 40096 zr h 01t endf5 tmccs 09 08 86 300 8 32 inco zr h 02t endf5 tmccs 09 08 86 400 8 32 inco zr h 04t endf5 tmccs 09 08 86 600 8 32 inco zr h O5t endf5 tmccs 09 08 86 800 8 32 inco 71 06 endf5 tmccs 09 08 86 1200 8 32 inco zr h 60t endf6 3 sab2002 09 14 99 294 16 64 inco zr h 61t endf6 3 sab2002 09 14 99 400 16 64 inco zr h 62t endf6 3 sab2002 09 14 99 600 16 64 inco zr h 63t endf6 3 sab2002 09 14 99 800 16 64 inco zr h 64t endf6 3 sab2002 09 14 99 1000 16 64 inco zr h 65t endf6 3 sab2002 09 14 99 1200 16 64 inco NEUTRON CROSS SECTION LIBRARIES Table G 2 lists all the continuous energy and discrete neutron data libraries that are maintained Not all libraries are publicly available The entries in each of the columns of Table G 2 are described as follows ZAID Atomic Weight Ratio Library Source The nuclide identification number with the form ZZZAAA nnX where ZZZ the atomic number AAA is the mass number 000 for elements nn is the unique table identification number X C for continuous energy neutron tables X D for discrete reaction tables The atomic weight ratio AWR is th
481. onent of a material for example hydrogen in light water Thermal ZAIDs may be entered on the MTn card s as XXXXXX or XXXXXX nnT Multigroup Tables Multigroup cross section libraries are the only libraries allowed in multigroup adjoint problems Neutron multigroup problems cannot be supplemented with S a B thermal libraries the thermal effects must be included in the multigroup neutron library Photon problems cannot be supplemented with electron libraries the electrons must be part of the multigroup photon library The form of ZAID is ZZZAAA nnM for neutrons or other particles masquerading as neutrons or ZZZAAA nnG for photons 2 24 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS Although continuous energy data are more accurate than multigroup data the multigroup option is useful for a number of important applications 1 comparison of deterministic S transport codes to Monte Carlo 2 use of adjoint calculations in problems where the adjoint method is more efficient 3 generation of adjoint importance functions 4 cross section sensitivity studies 5 solution of problems for which continuous cross sections are unavailable and 6 charged particle transport using the Boltzmann Fokker Planck algorithm in which charged particles masquerade as neutrons Multigroup cross sections are very problem dependent Some multigroup libraries are available from the Transport Methods Gro
482. ons the coherent form factors and incoherent scattering function for this data set come from two sources For Z equal to 84 85 87 88 89 91 and 93 these values are based on the compilation of Storm and Israel and include data for incident photon energies from 1 keV to 15 MeV For all other elements from Z equal to 1 through 94 the data are based on ENDF B IV and include data for incident photon energies from keV to 100 MeV Fluorescence data for Z equal to 1 through 94 are taken from work by Everett and Cashwell as derived from multiple sources The 02 ACE tables were introduced in 1993 and are an extension of the Olp to higher incident energies Below 10 MeV the data are identical to the 01 data i e the cross sections form factors scattering function and fluorescence data in this region are identical From 10 MeV to the top of the table either 15 or 100 MeV depending on the table the cross section values are smoothly transitioned from the 01 values to the values from the Livermore Evaluated Photon Data Library EPDL89 Above this transition region the cross section values are derived from the EPDL89 data and are given for incident energies up to 100 GeV The pair production threshold was also corrected for some tables The 03 ACE tables were introduced in 2002 and are an extension of the 02 tables to include additional data The energy of a photon after an incoherent Compton co
483. onte Carlo Method ERDA Critical Review Series TID 26607 1975 2 IvanLux and Laszlo Koblinger Monte Carlo Particle Transport Methods Neutron and Photon Calculations CRC Press Boca Raton 1991 3 C J Everett and E D Cashwell Third Monte Carlo Sampler Los Alamos National Laboratory Report LA 9721 MS March 1983 4 Compte de Buffon Essai d arithmetique morale Supplement a la Naturelle Vol 4 1777 5 A Hall On an Experimental Determination of Pi Messeng Math 2 113 114 1873 6 J M Hammersley and D C Handscomb Monte Carlo Methods John Wiley amp Sons New York 1964 7 Marquis Pierre Simon de Laplace Theorie Analytique des Probabilities Livre 2 pp 356 366 contained in Oeuvres Completes de Laplace de L Academie des Sciences Paris Vol 7 part 2 1786 8 Lord Kelvin Nineteenth Century Clouds Over the Dynamical Theory of Heat and Light Philosophical Magazine series 6 2 1 1901 9 W W Wood Early History of Computer Simulations in Statistical Mechanics and Molecular Dynamics International School of Physics Enrico Fermi Varenna Italy 1985 Molecular Dynamics Simulation of Statistical Mechanical Systems XCVII Corso Soc Italiana di Fisica Bologna 1986 10 Necia Grant Cooper Ed From Cardinals to Chaos Reflections on the Life and Legacy of Stanislaw Ulam Cambridge University Press New York 1989 11 Fermi Invention Rediscovered at LASL The At
484. opes are absorption elastic scattering and fission has a 6 keV threshold inelastic reaction all other stable isotopes have higher inelastic thresholds Metastable nuclides like Am have inelastic reactions all the way down to zero but these inelastic reaction cross sections are neither constant nor 1 v cross sections and these nuclides are generally too massive to be affected by the thermal treatment anyway Furthermore fission is very insensitive to incident neutron energy at low energies The fission secondary energy and angle distributions are nearly flat or constant for incident energies below about 500 keV Therefore it makes no significant difference if E is used only for elastic scatter or for other inelastic collisions as well At thermal energies whether E or E is used only makes a difference for elastic scattering 10 3 05 2 29 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS If the energy of the neutron is greater than 400 kT and the target is not the velocity of the target 15 set to zero Otherwise the target velocity is sampled as follows The free gas kernel is a thermal interaction model that results in a good approximation to the thermal flux spectrum in a variety of applications and can be sampled without tables The effective scattering cross section in the laboratory system for a neutron of kinetic energy is d eff 1 H 2 1 Here v a is relative velocity between
485. os Scientific Laboratory technical memorandum TD 6 8 79 July 1979 Edward C Snow and John D Court Radiography Image Detector Capability in MCNP4B Trans Am Nucl Soc 79 99 1998 MCNPX User s Manual Version 2 4 0 Los Alamos National Laboratory report LA CP 02 408 September 2002 S P Pederson R A Forster and T E Booth Confidence Interval Procedures for Monte Carlo Transport Simulations Nucl Sci Eng 127 54 77 1997 Guy Estes and Ed Cashwell Variance Error Estimator 6 27 78 8 31 78 Dubi the Analysis of the Variance in Monte Carlo Calculations Nucl Sci Eng 72 108 1979 See also I Lux Efficient Estimation of Variances Nucl Sci Eng 92 607 1986 Shane P Pederson Mean Estimation in Highly Skewed Samples Los Alamos National Laboratory Report LA 12114 MS 1991 T E Booth Analytic Comparison of Monte Carlo Geometry Splitting and Exponential Transform Trans Am Nucl Soc 64 303 1991 T E Booth A Caution on Reliability Using Optimal Variance Reduction Parameters Trans Am Nucl Soc 66 278 1991 T E Booth Analytic Monte Carlo Score Distributions for Future Statistical Confidence Interval Studies Nucl Sci Eng 112 159 1992 R A Forster A New Method of Assessing the Statistical Convergence of Monte Carlo Solutions Trans Am Nucl Soc 64 305 1991 R A Forster S P Pederson T E Booth Two
486. ote that there is no correlation between the sampling of the type of photon production reaction and the sampling of the type of neutron reaction described on page 2 35 Just as every neutron reaction for example n 2n has associated energy dependent angular and energy distributions for the secondary neutrons every photon production reaction for example n py has associated energy dependent angular and energy distributions for the secondary photons The photon distributions are sampled in much the same manner as their counterpart neutron distributions All non isotropic secondary photon angular distributions are represented by either 32 equiprobable cosine bins or by a tabulated angular distribution The distributions are given at a number of incident neutron energies All photon scattering cosines are sampled in the laboratory system The sampling procedure is identical to that described for secondary neutrons on page 2 36 Secondary photon energy distributions are also a function of incident neutron energy There are two representations of secondary photon energy distributions allowed in ENDF 6 format tabulated spectra and discrete line photons Correspondingly there are two laws used in MCNP for the determination of secondary photon energies Law 4 provides for representation of a tabulated photon spectra possibly including discrete lines Law 2 is used solely for discrete photons These laws are described in more detail beginning on page
487. other or b the outgoing energy and outgoing angle are correlated In the latter case the outgoing energy may be specified as a function of the sampled outgoing angle or the outgoing angle may be specified as a function of the sampled outgoing energy Details of the possible data representations and sampling schemes are provided in the following sections a Sampling of Angular and Energy Distributions The cosine of the angle between incident and exiting particle directions is sampled from angular distribution tables in the collision nuclide s cross section library The cosines are either in the center of mass or target at rest system depending on the type of reaction Data are provided at a number of incident neutron energies If E is the incident neutron energy if E is the energy of table n and if E is the energy of table n 1 then a value of u is sampled from table n 1 with probability E E E 1 Ep and from table n with probability E 1 EY E En There two options in MCNP for representing and sampling a non isotropic scattering cosine The first method involves the use of 32 equally probable cosine bins The second method is to sample a tabulated distribution as a function of When the method with 32 equiprobable cosine bins is employed a random number on the interval 0 1 is used to select the i cosine bin such that J 32 1 The value of p is then computed as H p 32 6 00 T
488. other words if m is input the SD card the tally will be divided by m instead of m As with the F4 tally there are cases where MCNP cannot calculate the area of a tally surface In such cases the user must input an entry on an SD card corresponding to the surface tally Energy deposition for photons and electrons can be computed with the F8 tally See page 2 89 However this is not a track length estimator 10 3 05 2 87 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS TALLIES The F7 tally includes the gamma ray heating because the fission photons are deposited locally The F6 N tally deposits the photons elsewhere so it does not include gamma ray heating Thus for fissionable materials the F7 N result will be greater than the F6 N result even though F7 N includes only fission and F6 includes all reactions The true heating is found by summing the neutron and photon F6 tallies in a coupled neutron photon calculation In a neutron only problem F6 will give the right heating of light materials only if in the physical experiment all photons escape the geometry F7 will give about the right heating of fissionable materials only if in the physical experiment no photons come from elsewhere all fission photons are immediately captured and nonfission reactions can be ignored By definition the F7 tally cannot be used for photons Examples of the mnemonic used to combine neutron and photon F6 tallies are F6 N P and F516 P N MC
489. otoelectric effect The detailed physics treatment is used below energy EMCPF on the PHYS P card and because the default value of EMCPF is 100 MeV that means it is almost always used by default It is the best treatment for most applications particularly for high Z nuclides or deep penetration problems The detailed physics treatment for next event estimators such as point detectors is inadvisable as explained on page 2 64 unless the NOCOH option is used on the PHYS P card to turn off coherent scattering a Incoherent Compton Scattering To model Compton scattering it is necessary to determine the angle 0 of scattering from the incident line of flight and thus the new direction the new energy of the photon and the recoil kinetic energy of the electron The recoil kinetic energy can be deposited locally can be transported in Mode P E problems or default can be treated with the TTB approximation 10 3 05 2 59 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS Incoherent scattering is assumed to have the differential cross section 2 u du I Z v K a w du where 2 is an appropriate scattering factor modifying the Klein Nishina cross section in Eq 2 2 Qualitatively the effect of Z v is to decrease the Klein Nishina cross section per electron more extremely in the forward direction for low E and for high Z independently For any 2 2 increases from Z 0 0 to Z o
490. ources should be consulted to determine if they are appropriate for your application Although the various conversion factor sets differ from one another it seems to be the consensus of the health physics community that they do not differ significantly from most health physics applications where accuracies of 20 are generally acceptable Some of the differences in the various sets are attributable to different assumptions about source directionality phantom geometry and depth of penetration The neutron quality factors derived primarily from animal experiments are also somewhat different Be aware that conversion factor sets are subject to change based on the actions of various national and international organizations such as the National Council on Radiation Protection and Measurements NCRP the International Commission on Radiological Protection ICRP the International Commission on Radiation Units and Measurements ICRU the American National Standards Institute ANSI and the American Nuclear Society ANS Changes may be based on the reevaluation of existing data and calculations or on the availability of new information Currently a revision of the 1977 ANSI AN S conversion factors is underway and the ICRP and NCRP are considering an increase in the neutron quality factors by a factor of 2 to 2 5 In addition to biological dose factors a reference is given for silicon displacement kerma factors for potential use in radiation effect
491. ovided by the user The 10 3 05 1 5 CHAPTER 1 MCNP OVERVIEW INTRODUCTION TO MCNP FEATURES tallies may also be reduced by line of sight attenuation Tallies may be made for segments of cells and surfaces without having to build the desired segments into the actual problem geometry tallies are functions of time and energy as specified by the user and are normalized to be per starting particle Mesh tallies are functions of energy and are also normalized to be per starting particle In addition to the tally information the output file contains tables of standard summary information to give the user a better idea of how the problem ran This information can give insight into the physics of the problem and the adequacy of the Monte Carlo simulation If errors occur during the running of a problem detailed diagnostic prints for debugging are given Printed with each tally is also its statistical relative error corresponding to one standard deviation Following the tally is a detailed analysis to aid in determining confidence in the results Ten pass no pass checks are made for the user selectable tally fluctuation chart TFC bin of each tally The quality of the confidence interval still cannot be guaranteed because portions of the problem phase space possibly still have not been sampled Tally fluctuation charts described in the following section are also automatically printed to show how a tally mean error variance of the variance and slop
492. owing down from 0 5 MeV to 0 0625 MeV will have about 30 collisions while a photon in the same circumstances will experience fewer than ten An electron accomplishing the same energy loss will undergo about 10 individual interactions This great increase in computational complexity makes a single collision Monte Carlo approach to electron transport unfeasible for most situations of practical interest Considerable theoretical work has been done to develop a variety of analytic and semi analytic multiple scattering theories for the transport of charged particles These theories attempt to use the fundamental cross sections and the statistical nature of the transport process to predict probability distributions for significant quantities such as energy loss and angular deflection The most important of these theories for the algorithms in MCNP are the Goudsmit Saunderson theory for angular deflections the Landau theory of energy loss fluctuations and the Blunck Leisegang enhancements of the Landau theory These theories rely on a variety of approximations that restrict their applicability so that they cannot solve the entire transport problem In particular it is assumed that the energy loss is small compared to the kinetic energy of the electron In order to follow an electron through a significant energy loss it is necessary to break the electron s path into many steps These steps are chosen to be long enough to encompass many collisions so tha
493. parentheses in this last expression are not required because intersections are done before unions Another expression for cell 2 rather than 1 is 1 3 4 2 For the user ambiguity surfaces are specified the same way as any other surface simply list the signed surface number as an entry on the cell card For MCNP if a particular ambiguity surface appears on cell cards with only one sense it is treated as a true ambiguity surface Otherwise it still functions as an ambiguity surface but the TRACK subroutine will try to find intersections with it thereby using a little more computer time 3 Reflecting Surfaces A surface can be designated a reflecting surface by preceding its number on the surface card with an asterisk Any particle hitting a reflecting surface is specularly mirror reflected Reflecting planes are valuable because they can simplify a geometry setup and also tracking in a problem They can however make it difficult or even impossible to get the correct answer The user is cautioned to check the source weight and tallies to ensure that the desired result is achieved Any tally in a problem with reflecting planes should have the same expected result as the tally in the same problem without reflecting planes Detectors or DXTRAN used with reflecting surfaces give WRONG answers see page 2 101 The following example illustrates the above points and should make MCNP users very cautious in the use of reflecting surface
494. ple the 17th level probability from the table for a given collision This position in the probability table must be maintained for the neutron trajectory until the next collision regardless of particle splitting for variance reduction or surface crossings into various other materials whose nuclides may or may not have probability table data Correlation must also be retained in the unresolved energy range when two or more cross section sets for an isotope that utilize probability tables are at different temperatures The impact of the probability table approach has been studied and found to have negligible impact for most fast and thermal systems Small but significant changes in reactivity may be observed for plutonium and 2330 systems depending upon the detailed shape of the spectrum However the probability table method can produce substantial increases in reactivity for systems that include large amounts of 2287 and have high fluxes within the unresolved resonance region Calculations for such systems will produce significantly nonconservative results unless the probability table method is employed 2 56 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS D Photon Interactions Sampling of a collision nuclide analog capture implicit capture and many other aspects of photon interactions such as variance reduction are the same as for neutrons The collision physics are completely different MCNP has two photon in
495. pling emission distributions the detailed treatment is the default and includes form factors and Compton profiles for electron binding effects coherent Thomson scatter and fluorescence from photoelectric capture see page 2 57 New as of MCNPS there may also be photonuclear physics if photonuclear physics is in use Additionally photonuclear biasing is available similar to forced collisions to split the photon updating the weight by the interaction probabilities and force one part to undergo a photoatomic collision and the second part to undergo a photonuclear collision The collision analysis samples for the collision nuclide treats photonuclear collisions treats photoelectric absorption or capture with fluorescence in the detailed physics treatment incoherent Compton scatter with Compton profiles and incoherent scattering factors in the detailed physics treatment to account for electron binding coherent Thomson scatter for the detailed physics treatment only again with form factors and pair production Secondary particles from photonuclear collisions either photons or neutrons are sampled using the same routines as for inelastic neutron collisions see Elastic and Inelastic Scattering on page 2 35 Electrons are generated for incoherent scatter pair production and photoelectric absorption These electrons may be assumed to deposit all their energy instantly if IDES 1 on the PHYS P card or they may produce electrons with t
496. plot option MCPLOT with the TFC command mnemonics Any history scores that are outside the x grid are counted as either above or below to provide this information to the user Negative history scores can occur for some electron charge deposition tallies The MCNP default is that any negative history score will be lumped into one bin below the lowest history score in the built in grid the default is 1 x 10 If DBCN 16 is negative f x will be created from the negative scores and the absolute DBCN 16 value will be used as the score grid multiplier Positive history scores then will be lumped into the lowest bin because of the sign change Figure 2 20 and Figure 2 21 show two simple examples of empirical f x s from MCNP for 10 million histories each Figure 2 20 is from an energy leakage tally directly from a source that is uniform in energy from 0 to 10 MeV The analytic f x is a constant 0 1 between 0 and 10 MeV The empirical f x shows the sampling which is 0 1 with statistical noise at the lower x bins where fewer samples are made in the smaller bins FILE CONSTNTR TALLY 1 TALLY FLUCTUATION CHART BIN TALLIES MCNP 4A x E 11 01 93 13 02 0 1 L TALLY2 1 4 FON 1 10000000 4 F BIN NORMED RUNTPE CONSTNTR gore E DUMP 3 t F SURFACE 1 2 F D FLAG DIR 1 a u USER 1 5 SEGMENT 1 E M MULT 1 C COSINE 1 oF E E ENERGY 1 4 T TIME 1 CONSTNTR 2
497. ponse function Often only dosimetry data 15 available for rare nuclides A full description of the use of dosimetry data can be found in Reference 34 This memorandum also gives a listing of all reaction data that is available for each ZAID There have been no major revisions of the LLNL ACTL data since LLLDOS was produced Users need to remember that dosimetry data libraries are appropriate only when used as a source of R E for FM tally multipliers Dosimetry data libraries cannot be used as a source of data for materials through which actual transport is required Table G 6 lists the available dosimetry data libraries for use with MCNEP the evaluation source and date and the length of the data in words Table G 6 Dosimetry Data Libraries for MCNP Tallies ZAID AWR Library Source Date Length Z2 Hydrogen 1001 30 1 00782 LLNL ACTL 1983 209 1002 30y 2 01410 LLNL ACTL 1983 149 1003 30y 3 01605 LLNL ACTL 1983 27 2 PELE k kkk kkk EIER SER SI EERE REE BE kkk kkk 2003 30y 3 01603 LLNL ACTL 1983 267 3 ae oe ae oe ak Lithium eek ok oko 2k ok 3006 24y 5 96340 531dos ENDF B V 1978 735 3006 26y 5 96340 532dos ENDF B V 1977 713 3006 30y 6 01512 LLNL ACTL 1983 931 3007 26y 6 95570 532dos ENDF B V 1972 733 3007 30y 7 01601 LLNL ACTL 1983 201 Z 4
498. port and the thick target bremsstrahlung approximation PHYS P j 1 must be turned off In the F6 P tally if a photon produces an electron that produces a photon the second photon is not counted again Itis already tallied in the first photon heating In the F4 P tally the second photon track is counted so the F4 tally will slightly overpredict the tally The photon heating tally also can be checked against the F8 energy deposition tally by dividing the F6 tally by a unit mass with the SD card Results will only be statistically identical because the tallies are totally independent and use different estimators The FM card can also be used to make the surface flux tally F2 and point and ring detector tallies F5 calculate heating on a surface or at a point respectively D Pulse Height Tallies The pulse height tally provides the energy distribution of pulses created in a cell that models a physical detector It also can provide the energy deposition in a cell Although the entries on the F8 card are cells this is not a track length cell tally F8 tallies are made at source points and at surface crossings 10 3 05 2 89 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS TALLIES The pulse height tally is analogous to a physical detector The F8 energy bins correspond to the total energy deposited in a detector in the specified channels by each physical particle history All the other MCNP tallies record the energy of a scoring tr
499. position MCNP tallies are normalized to be per starting particle except for a few special cases with criticality sources Currents can be tallied as a function of direction across any set of surfaces surface segments or sum of surfaces in the problem Charge can be tallied for electrons and positrons Fluxes across any set of surfaces surface segments sum of surfaces and in cells cell segments or sum of cells are also available Similarly the fluxes at designated detectors points or rings are standard tallies as well as radiography detector tallies Fluxes can also be tallied on a mesh superimposed on the problem geometry Heating and fission tallies give the energy deposition in specified cells A pulse height tally provides the energy distribution of pulses created in a detector by radiation In addition particles may be flagged when they cross specified surfaces or enter designated cells and the contributions of these flagged particles to the tallies are listed separately Tallies such as the number of fissions the number of absorptions the total helium production or any product of the flux times the approximately 100 standard ENDF reactions plus several nonstandard ones may be calculated with any of the MCNP tallies In fact any quantity of the form Jeunruag can be tallied where is the energy dependent fluence and is any product or summation of the quantities in the cross section libraries or a response function pr
500. problem input or in user supplied subroutines and patches to MCNP The user can also abuse variance reduction techniques such that portions of the physical phase space are not allowed to contribute to the results Checking the input and output carefully can help alleviate these difficulties A last item that is often overlooked is a user s thorough understanding of the relationship of the Monte Carlo tallies to any measured quantities being calculated Factors such as detector efficiencies data reduction and interpretation etc must be completely understood and included in the calculation or the comparison is not meaningful 2 Factors Affecting Problem Precision The precision of a Monte Carlo result is affected by four user controlled choices 1 forward vs adjoint calculation 2 tally type 3 variance reduction techniques and 4 number of histories run The choice of a forward vs adjoint calculation depends mostly on the relative sizes of the source and detector regions Starting particles from a small region is easy to do whereas transporting particles to a small region is generally hard to do Because forward calculations transport particles from source to detector regions forward calculations are preferable when the detector or tally region is large and the source region is small Conversely because adjoint calculations transport particles backward from the detector region to the source region adjoint calculations are preferable
501. q 2 4 Reaction 233U n f 1 070 235 1 1 088 2380 n f 1 116 10 3 05 2 51 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS Table 2 1 Continued Recommended Gaussian Widths from Eq 2 4 Reaction 239Pu n f 1 140 241 pu n f 1 150 2385py SF 1 135 20py SF 1 151 2 py SF 1 161 2 Cm SF 1 091 244Cm SF 1 103 46Cm SF 1 098 48Cm SF 1 108 250Cf SF 1 220 252Cf SF 1 245 254 SF 1 215 254Em SF 1 246 ISF Spontaneous fission Assuming that the widths of the multiplicity distributions are independent of the initial excitation energy of the fissioning system l the relationship between different factorial moments is easily calculated as a function of The corresponding calculated relationships between the first three factorial moments are in good agreement with experimental neutron induced fission data up to an incoming neutron energy of 10 MeV This implies that an energy independent width can be used with confidence up to an incoming neutron energy of at least 10 MeV The Gaussian widths in Table 2 1 are used for fission multiplicity sampling in MCNP when the fifth entry on the PHYS N card is 1 Induced fission multiplicities for isotopes not listed in Table 2 1 use a Gaussian width that is linearly dependent on the mass number of the fissioning system The direction of each emitted neutron is sampled independently from the appropriate angular distribution table by the procedure describe
502. r Production in the field of free Electrons Z Naturforsch 30a 1975 1099 10 3 05 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS REFERENCES C M ller Zur Theorie des Durchgang schneller Elektronen durch Materie Ann Physik 14 1932 568 D P Sloan New Multigroup Monte Carlo Scattering Algorithm Suitable for Neutral and Charged Particle Boltzmann and Fokker Planck Calculations Ph D dissertation Sandia National Laboratories report SAND83 7094 May 1983 J Adams and M Hart Multigroup Boltzmann Fokker Planck Electron Transport Capability in MCNP Trans Am Nucl Soc 73 334 1995 G I Bell and S Glasstone Nuclear Reactor Theory Krieger Publishing Company Malabar Florida Chap 1 org 1970 reprint 1985 E E Lewis and W F Miller Jr Computational Methods of Neutron Transport American Nuclear Society Inc La Grange Park Illinois Chap 1 1993 Dubi Monte Carlo Calculations for Nuclear Reactors in CRC Handbook of Nuclear Reactors Calculations Yigel Ronen Ed CRC Press Inc Boca Raton Florida Vol II Chap II 1986 J E Stewart A General Point on a Ring Detector Transactions of the American Nuclear Society 28 643 1978 R A Forster Ring Detector and Angle Biasing Los Alam
503. r and C Little Impact of MCNP Unresolved Resonance Probability Table Treatment on Uranium and Plutonium Benchmarks Sixth International Conference on Nuclear Criticality Safety ICNC 99 September 20 24 1999 Versailles France pp 522 531 10 3 05 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS REFERENCES H Kahn Applications of Monte Carlo AEC 3259 The Rand Corporation April 1956 L Koblinger Direct Sampling from the Klein Nishina Distribution for Photon Energies Above 1 4 MeV Nucl Sci Eng 56 218 1975 R N Blomquist and E M Gelbard An Assessment of Existing Klein Nishina Monte Carlo Sampling Methods Nucl Sci Eng 83 380 1983 Grodstein X Ray Attenuation Coefficients from 10 keV to 100 MeV National Bureau of Standards Circular No 583 1957 S Goudsmit and J L Saunderson Multiple Scattering of Electrons Phys Rev 57 1940 24 L Landau On the Energy Loss of Fast Particles by Ionization J Phys USSR 8 1944 201 O Blunck and S Leisegang Zum Energieverlust schneller Elektronen in dii nnen Schichten Z Physik 128 1950 500 M J Berger Carlo Calculation of the Penetration and Diffusion of Fast Charged Particles in Methods in Computational Physics Vol 1 edited by B Alder S Fernbach and
504. r coupled neutron photon problems specifying a particular isotope on a material card will invoke the neutron set for that isotope and the corresponding photon set for that element For example an entry of 1003 on a material card will cause MCNP to use ZAID 1003 50m for neutron data and 1000 01g for photon data Table G 3 MGXSNP A Coupled Neutron Photon Multigroup Data Library Neutron Photon ZAID AWR Length ZAID AWR Length 1001 50m 0 999172 3249 1000 01g 0 999317 583 1002 55m 1 996810 3542 1003 50m 2 990154 1927 2003 50m 2 990134 1843 2000 01g 3 968217 583 2004 50m 3 968238 1629 3006 50m 5 963479 3566 3000 01g 6 881312 583 3007 55m 6 955768 3555 4007 35m 6 949815 1598 4000 01g 8 934763 557 4009 50m 8 934807 3014 5010 50m 9 926970 3557 5000 01g 10 717168 583 5011 56m 10 914679 2795 6000 50m 1 11 896972 2933 6000 01g 11 907955 583 6012 50m 1 11 896972 2933 G 40 10 3 05 ZAID 7014 50m 7015 55m 8016 50m 9019 50m 11023 50m 12000 50m 13027 50m 14000 50m 15031 50m 16032 50m 17000 50m 18000 35m 19000 50m 20000 50m 22000 50m 23000 50m 24000 50m 25055 50m 26000 55m 27059 50m 28000 50m 29000 50m 31000 50m 33075 35m 36078 50m 36080 50m 36082 50m 36083 50m 36084 50m 36086 50m 40000 50m 41093 50m 42000 50m 45103 50m 45117 90m 46119 90m 47000 55m 47107 50m 47109 50m 48000 50m 50120 35m 50998 99m 50999 99m 54000 35m 56138 50m 63000 35m 63151 55m 63153 55m 64000 35m Table Cont APPEN
505. r parameters such as starting cell s or surface s Information about the geometrical extent of the source can also be given In addition source variables may depend on other source variables for example energy as a function of angle thus extending the built in source capabilities of the code The user can bias all input distributions In addition to input probability distributions for source variables certain built in functions are available These include various analytic functions for fission and fusion energy spectra such as Watt Maxwellian and Gaussian spectra Gaussian for time and isotropic cosine and monodirectional for direction Biasing may also be accomplished by special built in functions A surface source allows particles crossing a surface in one problem to be used as the source for a subsequent problem The decoupling of a calculation into several parts allows detailed design or analysis of certain geometrical regions without having to rerun the entire problem from the beginning each time The surface source has a fission volume source option that starts particles from fission sites where they were written in a previous run MCNP provides the user three methods to define an initial criticality source to estimate kepp the ratio of neutrons produced in successive generations in fissile systems C and Output The user can instruct MCNP to make various tallies related to particle current particle flux and energy de
506. r surfaces generated by surfaces of revolution about any axis even a skew axis If a tally is segmented the segment volumes or areas are computed For nonrotationally symmetric or nonpolyhedral cells a stochastic volume and surface area method that uses ray tracing is available See page 2 186 A Symmetric Volumes and Areas The procedure for computing volumes and surface areas of rotationally symmetric bodies follows 1 Determine the common axis of symmetry of the cell If there is none and if the cell is not a polyhedron MCNP cannot compute the volume except stochastically and the area of each bounding surface cannot be computed on the side of the asymmetric cell 2 Convert the bounding surfaces to q form ar br ds e 0 where s is the axis of rotational symmetry in the 7 5 coordinate system All MCNP surfaces except tori are quadratic surfaces and therefore can be put into q form 3 Determine all intersections of the bounding surfaces with each other in the 7 5 coordinate system This procedure generally requires the solution of a quartic equation For spheres ellipses and tori extra intersection points are added so that these surfaces are not infinite The list of intersections are put in order of increasing s coordinate If no intersection is found the surface is infinite its volume and area on one side cannot be computed 4 Integrate over each bounding surface segment between intersection
507. rael MCNP S o p Detector Scheme Los Alamos National Laboratory report LA 11952 October 1990 G I Bell and S Glasstone Nuclear Reactor Theory Van Nostrand Reinhold Company New York 1970 J M Otter C Lewis and L B Levitt UBR A Code to Calculate Unresolved Resonance Cross Section Probability Tables AI AEC 13024 July 1972 E Prael Application of the Probability Table Method to Monte Carlo Temperature Difference Calculations Transactions of the American Nuclear Society Vol 17 p 261 November 1973 R N Blomquist R M Lell and E M Gelbard VIM A Continuous Energy Monte Carlo Code at ANL A Review of the Theory and Application of Monte Carlo Methods April 21 23 1980 Oak Ridge Tennessee ORNL RSIC 44 L Carter C Little J S Hendricks and E MacFarlane New Probability Table Treatment in MCNP for Unresolved Resonances 7998 ANS Radiation Protection and Shielding Division Topical Conference April 19 23 1998 Nashville Vol II pp 341 347 A Bohr and B R Mottelson Nuclear Structure 2nd Ed World Scientific Singapore 1998 J S Levinger Neutron Production by Complete Absorption of High Energy Photons Nucleonics Vol 6 No 5 pp 64 67 1950 J S Levinger The High Energy Nuclear Photoeffect Physical Review Vol 84 No 1 pp 43 51 1951 M B Chadwick P Oblozinsky P E Hodgson and Reffo Pauli Blocking in the Quas
508. raries An F4 tally multiplied by 67H converts it to an F6 tally or an F5 detector tally multiplied by the same quantity calculates heating at a point see page 2 91 The FM card can modify any flux or current tally of the form Q E dE into f R E E dE where R E is any combination of sums and products of energy dependent quantities known to MCNP o E p x dE where x is the thickness of the attenuator p is its atom density and o is its total cross section Double o E p x The FM card can also model attenuation Here the tally is converted to f parentheses allow the calculation of R E dE More complex expressions of o E p x are allowed so that many attenuators may be stacked This is useful for calculating attenuation in line of sight pipes and through thin foils and detector coatings particularly when done in conjunction with point and ring detector tallies Beware however that attenuation assumes 10 3 05 2 105 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS TALLIES that the attenuated portion of the tally is lost from the system by capture or escape and cannot be scattered back in Two special FM card options are available The first option sets R E 1 E to score tracks or collisions The second option sets R E l velocity to score population or prompt removal lifetime 4 Special Treatments A number of special tally treatments are available using the FT tall
509. re given in Ref 116 Somewhat heuristic derivations follow Note that the surface current is a total but the cell and surface fluxes are averages A Surface Current Tally The tally is a simple count of the number of particles represented by the Monte Carlo weight crossing a surface in specified bins The number of particles at time fina volume element 4 with directions within dQ and energies within dE is Q E t d rdQdE Let the volume element 4 contain the surface element dA with surface normal and along Q for a distance vdt as depicted in Figure 2 7 Then the differential volume element is d T vdtlQ n dA All the particles within this volume element with directions within dQ and energies within dE will cross surface dA in time dt Thus the number of particles crossing surface dA in time dt is lo nivn E t aOdEdtdA The number of particles crossing surface in energy bin time bin j and angle bin kis thus faf ar dQ dA IQ al va 2 E t D 95 Jg The range of integration over energy time and angle cosine is controlled by E T and C cards If the range of integration is over all angles no C card then the F1 tally is a count of the number of particles with any trajectory crossing the surface in each energy and time bin and thus has no direction associated with it 4 Ae m dr vatlQ ildA 4 7 4
510. rface JSU one mean free path in the case of a mesh based weight window the distance to a DXTRAN sphere the distance to time cutoff or the distance to energy boundary Track length cell tallies are then incremented Some summary information is incremented The particle s parameters time position and energy are then updated If the particle s distance to a DXTRAN sphere of the same type as the current particle is equal to the minimum track length the particle is terminated because particles reaching the DXTRAN sphere are already accounted for by the DXTRAN particles from each collision If the particle exceeds the time cutoff the track is terminated If the particle was detected leaving a DXTRAN sphere the DXTRAN flag is set to zero and the weight cutoff game is played The particle is either terminated to weight cutoff or survives with an increased weight Weight adjustments then are made for the exponential transformation If the minimum track length is equal to the distance to surface crossing the particle is transported to surface JSU any surface tallies are processed and the particle is processed for entering the next cell Reflecting surfaces periodic boundaries geometry splitting Russian roulette from importance sampling and loss to escape are treated For splitting one bank entry of NPA particle tracks is made for an NPA 1 for 1 split The bank entries or retrievals are made on a last in first out basis The history is conti
511. rmal 1 14 Thermal 1 14 Thermal 1 14 Thermal 1 14 Thermal 1 14 Thermal 1 14 Thermal 1 14 Thermal 1 14 Thermal 1 14 10 3 05 APPENDIX H FISSION SPECTRA CONSTANTS AND FLUX TO DOSE FACTORS FLUX TO DOSE CONVERSION FACTORS B Constants for the Watt Fission Spectrum sinh bE 1 Neutron Induced Fission Incident Neutron Energy MeV a MeV b MeV l n 232 Thermal 1 0888 1 6871 1 1 1096 1 6316 14 1 1700 1 4610 2330 Thermal 0 977 2 546 1 0 977 2 546 14 1 0036 2 6377 2350 Thermal 0 988 2 249 1 0 988 2 249 14 1 028 2 084 Thermal 0 88111 3 4005 1 0 89506 3 2953 14 0 96534 2 8330 239 Thermal 0 966 2 842 1 0 966 2 842 14 1 055 2 383 2 Spontaneous Fission a MeV b MeV l 240py 0 799 4 903 22 py 0 833668 4 431658 0 891 4 046 om 0 906 3 848 252Cf 1 025 2 926 FLUX TO DOSE CONVERSION FACTORS This section presents several flux to dose rate conversion factor sets for use on the DE and DF tally cards to convert from calculated particle flux to human biological dose equivalent rate These sets of conversion factors are not the only ones in existence nor are they recommended by this 10 3 05 H 3 APPENDIX H FISSION SPECTRA CONSTANTS AND FLUX TO DOSE FACTORS FLUX TO DOSE CONVERSION FACTORS publication Rather they are presented for convenience should you decide that one is appropriate for your use The original publication cited or other s
512. roximation so long as the average energy loss in a single collision is much greater than the average width of a resonance that is if the narrow resonance approximation is valid Then the detail in the resonance structure following a collision is statistically independent of the magnitude of the cross sections prior to the collision 10 3 05 2 55 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS The utilization of probability tables is not a new idea in Monte Carlo applications A code to calculate such tables for Monte Carlo fast reactor applications was utilized in the early 1970s Temperature difference Monte Carlo calculations and a summary of the VIM Monte Carlo code that uses probability tables are pertinent early examples Versions of MCNP up through and including 4B did not take full advantage of the unresolved resonance data provided by evaluators Instead smoothly varying average cross sections were used in the unresolved range As a result any neutron self shielding effects in this energy range were unaccounted for Better utilizations of unresolved data have been known and demonstrated for some time and the probability table treatment has been incorporated into MCNP Version 4C and its successors The column UR in Table G2 of Appendix G lists whether unresolved resonance probability table data is available for each nuclide library Sampling cross sections from probability tables is straightforward At each of
513. rtion without the nn of the ZAID on the Mn card The default nnX can be changed for all isotopes of a material by using the NLIB keyword entry on the Mm card Given the NLIB option MCNP will choose only tables with the given nn identifier However if a specific table is desired MCNP will always use the table requested by a fully specified ZAID i e ZZZAAA nnX Careful users will want to think about what neutron interaction tables to choose There is unfortunately no strict formula for choosing the tables The following guidelines and observations are the best that can be offered 1 Users should in general use the most recent data available The nuclear data evaluation community works hard to continually update these libraries with the most faithful representations of the cross sections and emission distributions 2 Consider checking the sensitivity of the results to various sets of nuclear data Try for example a calculation with ENDF B VI 6 cross sections and then another with ENDL Cross sections If the results of a problem are extremely sensitive to the choice of nuclear data it is advisable to find out why 3 Consider differences in evaluators philosophies The Physical Data Group at Livermore is justly proud of its extensive cross section efforts their evaluations manifest a philosophy of reproducing the data with the fewest number of points Livermore evaluations are available mainly in the 40 series We at Los Alamo
514. rvive anyway so it might be appropriate to produce only 1 p 01 and have these not be killed 10 3 05 2 161 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VARIANCE REDUCTION 2 162 immediately by the DXTRAN weight cutoff Or the p s can often be set such that all DXTRAN particles from all cells are created on the DXTRAN sphere with roughly the same weight Choosing the p s is often difficult and the method works well typically when the material exponential attenuation is the major source of the weight fluctuation Often the weight fluctuation arises because the probability of scattering toward the DXTRAN sphere varies greatly depending on what nuclide is hit and what the collision orientation is with respect to the DXTRAN sphere For example consider a highly forward peaked scattering probability density If the DXTRAN sphere were close to the particle s precollision direction will be large if the DXTRAN sphere were at 105 to the precollision direction will be small The DD game can be used to reduce the weight fluctuation on the DXTRAN sphere caused by these geometry effects as well as the material exponential attenuation effects The DD game selectively roulettes the DXTRAN pseudoparticles during creation depending on the DXTRAN particles weight compared to some reference weight This is the same game that is played on detector contributions and is described on page 2 102 The reference weight c
515. ry Release 1 Los Alamos National Laboratory internal memorandum XTM RCL 95 259 and report LA UR 96 24 1995 available URL http www xdiv lanl gov PROJECTS DATA nuclear doc text100xs html S C Frankle R C Reedy and P Young ACTI A MCNP Continuous Energy Neutron Data Library for Prompt Gamma Ray Spectroscopy Los Alamos National Laboratory report LA UR 02 7783 Dec 2002 available URL http www xdiv lanl gov PROJECTS DATA nuclear doc acti html C Little Argon and Krypton Cross section Files Los Alamos National Laboratory internal memorandum June 30 1982 10 3 05 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 APPENDIX G MCNP DATA LIBRARIES REFERENCES C Little Cross Sections in ACE Format for Various IP Target Materials Los Alamos National Laboratory internal memorandum August 19 1982 C Little Y 89 cross sections for MCNP Los Alamos National Laboratory internal memorandum X 6 RCL 85 419 1985 R C Little Modified ENDF B V 0 Y 89 cross sections for MCNP Los Alamos National Laboratory internal memorandum X 6 RCL 85 443 1985 R E Seamon Revised ENDF B V Zirconium Cross Sections Los Alamos National Laboratory internal memorandum X 6 RES 92 324 1992 available URL http www xdiv lanl gov PROJECTS DATA nuclear doc zr40 B5eval html S Frankle ENDL Fission Products
516. ry Unfortunately these two goals usually conflict Decreasing S normally requires more time because better information is required Increasing normally increases 5 because there is less time per history to obtain information However the situation is not hopeless It is often possible either to decrease 5 substantially without decreasing N too much or to increase substantially without increasing 5 too much so that R decreases Many variance reduction techniques in MCNP attempt to decrease R by either producing or destroying particles Some techniques do both In general techniques that produce tracks work by decreasing S we hope much faster than N decreases and techniques that destroy tracks work by increasing N we hope much faster than S increases 2 136 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VARIANCE REDUCTION 4 Strategy Successful use of MCNP variance reduction techniques is often difficult tending to be more art than science The introduction of the weight window generator has improved things but the user is still fundamentally responsible for the choice and proper use of variance reducing techniques Each variance reduction technique has its own advantages problems and peculiarities However there are some general principles to keep in mind while developing a variance reduction strategy Not surprisingly the general principles all have to do with understanding both the physical problem and the var
517. ry Tape 531 ENDF B V Activation Tape 532 and 1 evaluated neutron activation cross section library from the Lawrence Livermore National Laboratory Various codes have been used to process evaluated dosimetry data into the format of MCNP dosimetry tables Data on dosimetry tables are simply energy cross section pairs for one or more reactions The energy grids for all reactions are independent of each other Interpolation between adjacent energy points can be specified as histogram linear linear linear log log linear or log log With the 10 3 05 2 23 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CROSS SECTIONS exception of the tolerance involved in any reconstruction of pointwise cross sections from resonance parameters evaluated dosimetry cross sections can be reproduced on the MCNP data tables with no approximation ZAIDs for dosimetry tables must be entered on material cards that are referenced by FM cards under no circumstances may a material card specifying dosimetry data tables be referenced by a cell card The complete ZAID ZZZAAA nnY must be given there are no defaults for dosimetry tables E Neutron Thermal 5 Tables Thermal S a B tables are not required but they are absolutely essential to get correct answers problems involving neutron thermalization Thermal tables have ZAIDs of the form XXXXXX nnT where XXXXXX is a mnemonic character string The data on these tables encompass thos
518. s r ds for volumes f r h 2 ds surface areas A bounding surface segment lies between two intersections that bound the cell of interest A numerical integration is required for the area of a torroidal surface all other integrals are directly solved by integration formulas The sense of a bounding surface to a cell determines the sign of V The area of each surface is determined cell by cell twice once for each side of the surface An area will be calculated unless bounded on both sides by asymmetric or infinite cells B Polyhedron Volumes and Areas A polyhedron is a body bounded only by planes that can have an arbitrary orientation The procedure for calculating the volumes and surface areas of polyhedra is as follows 2 186 10 3 05 C CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VOLUMES AND AREAS For each facet side planar surface determine the intersections 7 5 of the other bounding planes in the r s coordinate system The 7 5 coordinate system 15 redefined for each facet to be an arbitrary coordinate system in the plane of the facet Determine the area of the facet 1 52 Gi 17 50 Gri tr gt and the coordinates of its centroid r 5 2 2 1 6a II 2 2 So 1 6a y ri 1 risit 5 5 5 The sums are over all bounding edges of the facet where and i 7 are the ends of the bounding edge such that in going from i to i 1 the facet is on the ri
519. s Fl x at a Detector ga 91 Additional Tally FeatUtes Rr 104 ESTIMATION OF THE MONTE CARLO PRECISION 108 Monte Carlo Means Variances and Standard Deviations 109 Pr ec isi n and ACCUTACY 110 The Central Limit Theorem and Monte Carlo Confidence Intervals 112 Estimated Relative Errors in epe dd ated Setup etudes ERE 113 Fig re of Merit c 116 Separation of Relative Error into Two Components eene 118 Vafianceof the Variance 120 Empirical History Score Probability Density Function f x 122 Forming Statistically Valid Confidence Intervals 127 A Statistically Pathological Output Example eee ene 131 VARIANCE REDUCTION Med dM UN DIA UON 134 Considerati NS RON 134 Variance Reduction Techniques 139 CRITICALITY CALCULATIONS In OR IER tar rni miu 163 Criticality Program MP P 164 Estimation of Confidence Intervals and Prompt Neutron Lifetimes 167 R
520. s MN 4 1 1 and A mass of collision nuclide in units of the mass of neutron atomic weight ratio c Inelastic Reactions The treatment of inelastic scattering depends upon the particular inelastic reaction chosen Inelastic reactions are defined as n y reactions such as n n 2n n f in which y includes at least one neutron For many inelastic reactions such as n 2n more than one neutron can be emitted for each incident neutron The weight of each exiting particle is always the same as the weight of the incident particle minus any implicit capture The energy of exiting particles is governed by various scattering laws that are sampled independently from the cross section files for each exiting particle Which law is used is prescribed by the particular cross section evaluation used In fact more than one law can be specified and the particular one used at a particular time is decided with a random number In an n 2n reaction for example the first particle emitted may have an energy sampled from one or more laws but the second particle emitted may have an energy sampled from one or more different laws depending upon specifications in the nuclear data library Because emerging energy and scattering angle is sampled independently for each particle there is no correlation between the emerging particles Hence energy is not conserved in an individual reaction because for example a 14 MeV particle co
521. s P 1 n u tQ np 2 No 11 lt 1 lt 1 a Ps o s ds vP ntn noe nosna where u ww P u scattering probability density function for scattering through the angle cos u in the lab system for the event sampled at x y z number of particles emitted from the event and 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VARIANCE REDUCTION Ps r s ds the attenuation along the line between P x y z and P the point on the a sphere where the particle is placed In arriving at the weight factor note that the density function for sampling is given by Q Q 1 np n ng n nsl 1 Q 1 np n nogl 105157 Thus the weight of the DXTRAN particle is the weight of the incoming particle at modified by the ratio of the probability density function for actually scattering from P and arriving at P without collision to the density function actually sampled in choosing P Therefore particles in the outer cone have weights 5 times higher than the weights of similar particles in the inner cone The attenuation is calculated at the energy obtained by scattering through the angle p The energy is uniquely determined from p in elastic scattering and also in level scattering whereas for other nonelastic events the energy is sampled from the corresponding probability density function for energy and may not depend on p Auxiliary Games for DXTRAN The major disadvant
522. s Reflecting surfaces should never be used in any situation without a lot of thought Consider a cube of carbon 10 cm on a side sitting on top of a 5 MeV neutron source distributed uniformly in volume The source cell is a 1 cm thick void completely covering the bottom of the carbon cube and no more The average neutron flux across any one of the sides but not top or bottom is calculated to be 0 150 0 5 per cm per starting neutron from an MCNP F2 tally and the flux at a point at the center of the same side is 1 55e 03 n cm 51 from an MCNP 5 tally The cube can be modeled by half a cube and a reflecting surface All dimensions remain the same except the distance from the tally surface to the opposite surface which becomes the reflecting surface is 5 cm The source cell is cut in half also Without any source normalization the flux across the surface is now 0 302 0 5 96 which is twice the flux in the nonreflecting geometry The detector flux is 2 58E 03 1 96 which is less than twice the point detector flux in the nonreflecting problem The problem is that for the surface tally to be correct the starting weight of the source particles has to be normalized it should be half the weight of the nonreflected source particles The detector results will always be wrong and lower for the reason discussed on page 2 101 In this particular example the normalization factor for the starting weight of source particles should be 0 5
523. s in the cell must remain on only one side of any particular surface Thus there can be no concave corners in a cell specified only by intersections Figure 1 4 a cell formed by the intersection of five surfaces ignore surface 6 for the time being illustrates the problem of concave corners by allowing a particle or point to be on two sides of a surface in one cell Surfaces 3 and 4 form a concave corner in the cell such that points p and p are on the same side of surface 4 that is have the same sense with respect to 4 but point is on the other side of surface 4 opposite sense Points p and have the same sense with respect to surface 3 but p has the opposite sense One way to remedy this dilemma and there are others is to add surface 6 between the 3 4 corner and surface 1 to divide the original cell into two cells 1 14 10 3 05 CHAPTER 1 MCNP OVERVIEW MCNP GEOMETRY Figure 1 4 With surface 6 added to Figure 1 4 the cell to the right of surface 6 is number 1 cells indicated by circled numbers to the left number 2 and the outside cell number 3 The cell cards in two dimensions all cells void are 101 2 36 2 0 1 6 4 5 Cell 1 is a void and is formed by the intersection of the region above positive sense surface 1 with the region to the left negative sense of surface 2 intersected with the region below negative sense surface 3 and finally intersected with the region to the right positive sense o
524. s infinity The variance of the population of x values is a measure of the spread in these values and is given by 2 2 2 2 o flax E x EQ The square root of the variance is o which is called the standard deviation of the population of scores As with E x o is seldom known but can be estimated by Monte Carlo as S given by for large N N m gt 1 75 2 151 2 2 RE 7 2 1 5 x X 2 192 and 1 2 19b x y2 X 2 196 10 3 05 2 109 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS ESTIMATION OF THE MONTE CARLO PRECISION The quantity S is the estimated standard deviation of the population of x based on the values of x that were actually sampled The estimated variance of x is given by N 2 20 l ZIA These formulas do not depend on any restriction on the distribution of x or x such as normality beyond requiring that E x and c exist and are finite The estimated standard deviation of the mean X is given 5 It is important to note that S is proportional to 1 which is the inherent drawback to the Monte Carlo method To halve 5 four times the original number of histories must be calculated calculation that can be computationally expensive The quantity 5 can also be reduced for a specified N by making S smaller reducing the inherent spread of the tally results This can be accomplished by using variance reduction techniqu
525. s thus it appears from a transport viewpoint that no scattering took place For a point detector to sample this scattering the point must lie on the original track u 1 which is seldom the case Thus photon point detector variances generally will be much greater with detailed photon physics than with simple physics unless coherent scattering is turned off with NOCOH 1 on the PHYS P card as explained on page 2 64 c Photoelectric effect The photoelectric effect consists of the absorption of the incident photon of energy with the consequent emission of several fluorescent photons and the ejection or excitation of an orbital electron of binding energy e lt giving the electron a kinetic energy of E e Zero one or two fluorescent photons are emitted These three cases are now described 2 62 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS 1 Zero photons greater than 1 keV are emitted In this event the cascade of electrons that fills up the orbital vacancy left by the photoelectric ejection produces electrons and low energy photons Auger effect These particles can be followed in Mode P E problems or be treated with the TTB approximation or be assumed to deposit energy locally Because no photons are emitted by fluorescence some may be produced by electron transport or the TTB model the photon track is terminated This photoelectric capture of the photon is scored like analog captur
526. s are particularly proud of the evaluation work being carried out in the Nuclear Physics Group T 16 generally these evaluations are the most complex because they are the most thorough Recent evaluations from Los Alamos are available in the 66c series 4 Be aware of the neutron energy spectrum in your problem For high energy problems the thinned and discrete reaction data are probably not bad approximations Conversely it is essential to use the most detailed continuous energy set available for problems influenced strongly by transport through the resonance region 5 Check the temperature at which various data tables have been processed Do not use a set that is Doppler broadened to 3 000 K for a room temperature calculation 6 Foracoupled neutron photon problem be careful that the tables you choose have photon production data available If possible use the more recent sets that have been processed into expanded photon production format 7 Users should be aware of the differences between the 50 series of data tables and the 51C series Both are derived from ENDF B V The 50 series is the most faithful reproduction of the evaluated data The 51C series also called the thinned series has been processed with a less rigid tolerance than the 50C series As with discrete reaction data tables although by no means to the same extent users should be careful when using the thinned
527. s assessment of electronic semiconductor devices The use of these factors is subject to the same caveats stated above for biological dose rates A Biological Dose Equivalent Rate Factors In the following discussions dose rate will be used interchangeably with biological dose equivalent rate In all cases the conversion factors will contain the quality factors used to convert the absorbed dose in rads to rem The neutron quality factors implicit in the conversion factors are also tabulated for information For consistency all conversion factors are given in units of rem h per unit flux particles cm s rather than in the units given by the original publication The interpolation mode chosen should correspond to that recommended by the reference For example the ANSI ANS publication recommends log log interpolation significant differences at interpolated energies can result if a different interpolation scheme is used l Neutrons The NCRP 38 and ICRP 21 neutron flux to dose rate conversion factors and quality factors are listed in Table H 1 Note that the 1977 ANSI ANS factors referred to earlier were taken from NCRP 38 and therefore are not listed separately 2 Photons The 1977 ANSI ANS and the ICRP 21 photon flux to dose rate conversion factors are given in Table H 2 No tabulated photon conversion factors have been provided by the NCRP as far as can be determined Note that the 1977 ANSI ANS and the ICRP 21 conversion factor sets d
528. s entering cell 23 turn out to be much more important than a user thought Maybe 10 of the answer should come from tracks entering cell 23 The user could run 100 000 particles and get 9096 of the true tally with an estimated error of 190 with absolutely no indication that anything is amiss However suppose the biasing had been set such that on average for every 2 138 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VARIANCE REDUCTION 10 000 particles one track entered cell 23 about 10 tracks total The tally probably will be severely affected by at least one high weight particle and will hover closer to the true tally with a larger and perhaps erratic error estimate The essential point is this following ten tracks into cell 23 does not cost much computer time and it helps ensure that the estimated error cannot be low when the tally is seriously in error Always make sure that all regions of the problem are sampled enough to be certain that they are unimportant B Variance Reduction Techniques There are four classes of variance reduction techniques that range from the trivial to the esoteric Truncation Methods are the simplest of variance reduction methods They speed up calculations by truncating parts of phase space that do not contribute significantly to the solution The simplest example is geometry truncation in which unimportant parts of the geometry are simply not modeled Specific truncation methods available in
529. s in Eigenvalue Calculations Progress in Nuclear Energy 24 p 237 1990 G D Spriggs R D Busch K J Adams D K Parsons L Petrie and J S Hendricks the Definition of Neutron Lifetimes in Multiplying and Nonmultiplying Systems Los Alamos National Laboratory Report LA 13260 MS March 1997 M Halperin Almost Linearly Optimum Combination of Unbiased Estimates Amer Stat Ass J 56 36 43 1961 R C Gast and N R Candelore The Recap 12 Monte Carlo Eigenfunction Strategy and Uncertainties WAPD TM 1127 L 1974 S S Shapiro and M B Wilk An Analysis of Variance Test for Normality Biometrika 52 p 591 1965 B D Agostino Omnibus Test of Normality for Moderate and Large Size Samples Biometrika 58 p 341 1971 L Carter T L Miles and S E Binney Quantifying the Reliability of Uncertainty Predictions in Monte Carlo Fast Reactor Physics Calculations Nucl Sci Eng 113 p 324 1993 10 3 05 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS REFERENCES K M Case F de Hoffmann and G Placzek Introduction to the Theory of Neutron Diffusion Volume I Los Alamos Scientific Laboratory report June 1953 J S Hendricks Calculation of Cell Volumes and Surface Areas in MCNP Los Alamos National Laboratory report LA 81
530. s is to increase the number of particles that sample some part of the problem of special interest 1 without increasing sometimes actually decreasing the sampling of less interesting parts of the problem and 2 without erroneously affecting the expected mean physical result tally This procedure properly applied increases precision in the desired result compared to an unbiased calculation taking the same computing time For example if an event is made 2 times as likely to occur as it would occur without biasing the tally ought to be multiplied by 1 2 so that the expected average tally is unaffected This tally multiplication can be accomplished by multiplying the particle weight by 1 2 because the tally contribution by a particle is always multiplied by the particle weight in MCNP Note that weights need not be integers In short particle weight is a number carried along with each MCNP particle representing that particle s relative contribution to the final tallies Its magnitude is determined to ensure that whenever MCNP deviates from an exact simulation of the physics the expected physical result nonetheless is preserved in the sense of statistical averages and therefore in the limit of large MCNP particle numbers Its utility is in the manipulation of the number of particles sampling just a part of the problem to achieve the same results and precision obviating a full unbiased calculation which has a longer computing time 2 P
531. s section provides an energy loss distribution determined by the energy E of the electron the path length s to be traversed and the properties of the material Let us symbolize a sampling of this distribution as an application of a straggling operator L E s A that provides a sampled value of the energy loss In versions of MCNP earlier than 5 release 1 40 all parameters needed for sampling straggling were precomputed and associated with the standard energy boundaries E and the corresponding ranges 5 In effect the code was restricted to calculations based on discrete arguments of the operator L E us A As a result the proper assignment of an electron transport step to an energy group n required a rather subtle logic Eventually two algorithms for apportioning straggled energy loss to electron substeps were made available With release 1 40 a third algorithm is provided as discussed below a MCNP Energy Indexing Algorithm The first energy indexing algorithm also called the bin centered treatment developed for MCNP is arguably the less successful of the two existing algorithms but for historical reasons 2 74 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS remains the default option It was an attempt to keep the electron substeps aligned as closely as possible with the energy groups that were used for their straggling samples A simplified description of the MCNP algorithm is as follows An ele
532. s systems the collision and track length estimators are likely to be strongly positively correlated There may be a negative bias 46 in the estimated standard deviation of k gfor systems where the locations of fission sites in one generation are correlated with the locations of fission sites in successive generations The statistical methods used in MCNP for estimating standard deviations in ke calculations do not account for the effects of intergenerational correlation leading to underprediction of standard deviations These systems are typically large with small neutron leakage The magnitude of this effect can be estimated by batching the cycle k values in batch sizes much greater than one cycle 8 which MCNP provides automatically For problems where there is a reason to suspect the results a more accurate calculation of this effect can be done by making several independent calculations of the same problem using different random number sequences and observing the variance of the population of independent k values The larger the number of independent calculations that can be made the better the distribution of values can be assessed 7 Creating and Interpreting k Confidence Intervals The result of a Monte Carlo criticality calculation or any other type of Monte Carlo calculation is a confidence interval For criticality this means that the result is not just but k plus and minus some number of estimated standard deviations
533. s within the guidelines the empirical f x appears to be otherwise completely sampled and the largest history score appears to be a once in a lifetime occurrence a good confidence interval can still be formed If a conservative large answer is required the printed result that assumes the largest history score occurs on the very next history can be used Comparing several empirical f x s for the above problem with 200 million histories that have been normalized so that the mean of each f x is unity you see that the point detector at 390 cm clearly is quite Cauchy like see Eq 2 25 for many decades The point detector at 4000 cm is a much easier tally by a factor of 10 000 as exhibited by the much more compact empirical f x The large score tail decreases in a manner similar to the negative exponential f x The surface flux estimator is the most compact f x of all The blip on the high score tail is caused by the average cosine approximation of 0 05 between cosines of 0 and 0 1 see page 2 87 This tally is 30 000 times more efficient than the point detector tally VII VARIANCE REDUCTION A General Considerations 1 Variance Reduction and Accuracy Variance reducing techniques in Monte Carlo calculations reduce the computer time required to obtain results of sufficient precision Note that precision is only one requirement for a good Monte Carlo calculation Even a zero variance calculation cannot accurately predict natural
534. scent photon born as discussed above is assumed to be emitted isotropically and can be transported provided that E gt 1 keV The binding energies and are very nearly the x ray absorption edges because the x ray absorption cross section takes an abrupt jump as it becomes energetically possible to eject or excite the electron of energy first E e then e then e etc The jump can be as much as a factor of 20 for example K carbon A photoelectric event is terminal for elements Z 12 because the possible fluorescence energy is below 1 keV The event is only a single fluorescence of energy above keV for 31 gt Z2 12 but double fluorescence each above 1 keV is possible for Z gt 31 For Z 2 31 primary lines and are possible and in addition for Z 37 the KB line is possible In all photoelectric cases where the photon track is terminated because either no fluorescent photons are emitted or the ones emitted are below the energy cutoff the termination is considered to be caused by analog capture in the output file summary table and not energy cutoff d Pair Production This process is considered only in the field of a nucleus The threshold is 1 m M 1 022 MeV where M is the nuclear mass and m is the mass of the electron There are three cases 10 3 05 2 63 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS 1 In the case of electron transport Mode
535. se height energy deposition surface estimators Tracks undergoing collisions are used to calculate multiplication and criticality collision estimators Within a given cell of fixed composition the method of sampling a collision along the track is determined using the following theory The probability of a first collision for a particle between and dl along its line of flight is given by ed where X is the macroscopic total cross section of the medium and is interpreted as the probability per unit fength of a collision Setting the random number on 0 1 to be 5 l e a it follows that 5 But because 1 is distributed in the same manner as and hence may be replaced by we obtain the well known expression for the distance to collision 1 cyh C Neutron Interactions When a particle representing any number of neutrons depending upon the particle weight collides with a nucleus the following sequence occurs 1 the collision nuclide is identified 10 3 05 2 27 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS 2 either the S a treatment is used or the velocity of the target nucleus is sampled for low energy neutrons photons are optionally generated for later transport 4 neutron capture that is neutron disappearance by any process is modeled 5 unless the S a treatment is used either elastic scatt
536. sion Directory Mp 16 INSTALLING AND BUILDING 5 ON WINDOWS PCs 21 Installing MCNP5 Windows PCs 12er 22 Building MCNP on Windows PCs 2 26 PARALLEL CONFIGURATION INFORMATION 30 TESTING PERFORMED DATE iat ono eue dese 32 MODIFYING MCNP WITH PATCHES 34 MENP VERIFICATION m pers o oid qu du ua aE dE RE UID 38 CONVERTING CROSS SECTION FILES WITH 39 REFERENCES 42 APPENDIX D MODIFYING MONP 1 PREPROCESSORS iecit quta pu und ern tern E coda AR REPAIR 1 PROGRAMMING LANGUAGE 1 SYMBOLIC NAMES ada Up MER eia aina a ie S xix aM S RE 2 SYSTEM DEPENDENCE deett chiens 2 COMMON BLOCKS erdt ege ie PED e s n D esl Sup Acn de I Mae 3 DYNAMICALLY ALLOCATED STORAGE 2 tanus bh tetur tnrba to secta daria 4 THE RUNTPE EILE iv 4 wc eU E 5 SUBROUTINE USAGE IN MCNPS VE a XR DARE arua 6 MEONP Structure c
537. sorption With energy splitting the low energy photon track population can be built up rather than rapidly depleted as would occur naturally with the high photoelectric absorption cross section Particles can be split as they move up or down in energy at up to five different energy levels Russian roulette In many cases the number of tracks increases with decreasing energy especially neutrons near the thermal energy range These tracks can have many collisions requiring appreciable computer time They may be important to the problem and cannot be completely eliminated with an energy cutoff but their number can be reduced by playing a Russian roulette game to reduce their number and computer time If a track s energy drops through a prescribed energy level the roulette game is played based on the input value of the survival probability If the game is won the track s history is continued but its weight is increased by the reciprocal of the survival probability to conserve weight b Time Splitting Roulette Time splitting roulette is similar to the energy splitting and roulette game just discussed except a particle s time can only increase in contrast with a particle s energy that may increase or decrease Time splitting roulette is independent of spatial cell If the problem has a space time dependence the space time dependent weight window is normally a better choice 1 2 142 Splitting In some cases particles are more important
538. specific sampling frequencies corresponding to SP card entries or by standard analytic biasing functions A third biasing category can be used in conjunction with standard analytic source probability functions for example a Watt fission spectrum A negative entry on an SP card that is SPn iab causes MCNP to sample source distribution n from probability function i with input variables a b Sampling schemes are typically unbiasable For example for SPn 5 a the evaporation spectrum f E C E exp E a is sampled according to the sampling prescription E log 6 62 where and 61 are random numbers Biasing this sampling scheme is usually very difficult or impossible Fortunately there is an approximate method available in MCNP for biasing any arbitrary probability function 5 The code approximates the function as a table then uses the usual SB card biasing scheme to bias this approximate table function The user inputs a coarse bin structure to govern the bias and the code adds up to 300 additional equiprobable bins to assure accuracy For example suppose we wish to sample the function f E E exp E a 2 154 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VARIANCE REDUCTION and suppose that we want half the source to be in the range 005 lt E lt 1 and the other half to be in the range 1 lt E lt 20 Then the input 15 SPn 5a SIn 005 1 20 SBnC 0 5 MCNP breaks up the functio
539. ss multigroup libraries Process electron libraries including calculation of range tables straggling tables scattering angle distributions and bremsstrahlung MCRUN sets up multitasking and multiprocessing runs histories and returns to print write RUNTPE dumps or process another criticality cycle Under MCRUN MCNP runs neutron photon or electron histories Start a source particle Find the distance to the next boundary cross the surface and enter the next cell Find the total neutron cross section and process neutron collisions producing photons as appropriate Find the total photon cross section and process photon collisions producing electrons as appropriate e Use the optional thick target bremsstrahlung approximation if no electron transport Follow electron tracks Process optional multigroup collisions Process detector tallies or DXTRAN Process surface cell and pulse height tallies Periodically write output file restart dumps update to next criticality cycle rendezvous for multitasking and updating detector and DXTRAN Russian roulette criteria etc e Go to the next criticality cycle Print output file summary tables Print tallies Generate weight windows Plot tallies cross sections and other data MCPLOT GKS graphics simulation routines PVM and MPI distributed processor multiprocessing routines Random number generator and control Mathematics character manipulat
540. ss sections where x is anything except neutrons Thus o is the sum of 6 Ond etc For all particles killed by analog absorption the entire particle energy and weight are deposited in the collision cell b Implicit Absorption For implicit absorption also called survival biasing the neutron weight W is reduced to W as follows o W If the new weight is below the problem weight cutoff specified on the CUT card Russian roulette is played resulting overall in fewer particles with larger weight For implicit absorption a fraction of the incident particle weight and energy is deposited in the collision cell corresponding to that portion of the particle that was absorbed Implicit absorption is the default method of neutron absorption in MCNP c Implicit Absorption Along a Flight Path Implicit absorption also can be done continuously along the flight path of a particle trajectory as is the common practice in astrophysics In this case the distance to scatter rather than the distance to collision is sampled The distance to scatter is 2 34 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS 1 x In 1 The particle weight at the scattering point is reduced to account for the expected absorption along the flight path reduced weight after expected absorption along flight path weight at the start of the flight path absorption cross sec
541. ssumes the last cross section value given max This entry indicates the source from which the cross section data are derived There are four sources for the cross section data 1 S amp I indicates data from the Storm and Israel 1970 compilation 2 B IV indicates data from ENDF B IV 3 B IV 89 indicates data from ENDF B IV merged with data from EPDL89 and 4 B VL8 indicates data from ENDF B VI release 8 This entry indicates the source from which the form factor data are derived There are three sources for the form factor data 1 Unknown indicates that data date back to unknown origins 2 B IV indicates data from ENDF B IV and 3 B VI 8 indicates data from ENDF B VI release 8 This entry indicates the source from which the fluorescence data are derived There are two sources for the fluorescence data 1 E amp C indicates data from Everett and Cashwell s original work and 2 B VL 8 indicates data in the Everett and Cashwell format derived from ENDF B VI release 8 This entry indicates the source from which the momentum profile CDBD data for Doppler broadening of the Compton scattered energy are derived Currently the only source for the CDBD data is Biggs Mendelsohn and Mann s 1975 compilation 10 3 05 1000 01p 1000 02p 1000 03p 1000 04p Z 2 2000 01p 2000 02p 2000 03p 2000 04p Z 3 3000 01p 3000 02p 3000 03p 3000 04p 2 4 4000 01 4000 02 4000 03 4000 04 2 5
542. st released in 1977 is the successor to their work and has been under continuous development for the past 25 years Neither the code nor the manual is static The code is changed as needs arise and the manual is changed to reflect the latest version of the code This particular manual refers to Version 5 MCNPS and this manual are the product of the combined effort of many people in the Diagnostics Applications Group X 5 in the Applied Physics Division X Division at the Los Alamos National Laboratory X 5 Monte Carlo Team Thomas E Booth H Grady Hughes Anthony Zukaitis Forrest B Brown Russell D Mosteller Marsha Boggs CCN 12 Jeffrey S Bull Richard E Prael Roger Martz CCN 7 R Arthur Forster Avneet Sood John T Goorley Jeremy E Sweezy X 5 Data Team Joann M Campbell Robert C Little Morgan C White Stephanie C Frankle Technical Editors Sheila M Girard The code and manual can be obtained from the Radiation Safety Information Computational Center RSICC P O Box 2008 Oak Ridge TN 37831 6362 Jeremy E Sweezy MCNP Team Leader lt jsweezy lanl gov gt 10 3 05 iii 10 3 05 MCNP A General Monte Carlo N Particle Transport Code Version 5 X 5 Monte Carlo Team Diagnostics Applications Group Los Alamos National Laboratory ABSTRACT MCNP is a general purpose Monte Carlo N Particle code that can be used for neutron photon electron or coupled neutron photon electron transport including the capability
543. standing the output are discussed in the following sections A Weight At the most fundamental level weight is a tally multiplier That is the tally contribution for a weight w is the unit weight tally contribution multiplied by w Weight is an adjustment for deviating from a direct physical simulation of the transport process Note that if a Monte Carlo code always sampled from the same distributions as nature does then the Monte Carlo code would have the same mean and variance as seen in nature Quite often the natural variance is unacceptably high and the Monte Carlo code modifies the sampling using some form of variance reduction see Section VII on page 2 134 The variance reduction methods use weighting schemes to produce the same mean as the natural transport process but with lower calculational variance than the natural variance of the transport process With the exception of the pulse height tally F8 all tallies in MCNP are made by individual particles In this case weight is assigned to the individual particles as a particle weight The 10 3 05 2 25 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS manual discusses the particle weight cases first and afterward discusses the weight associated with the F8 tally 1 Particle Weight If MCNP were used only to simulate exactly physical transport then each MCNP particle would represent one physical particle and would have unit weight However for computat
544. starting weight in each cycle is a constant N These M particles are written to the SRCTP file at certain cycle intervals The SRCTP file can be used as the initial source in a subsequent criticality calculation with a similar though not identical geometry Also k quantities are accumulated as is described below 4 Convergence The first Z cycles in a criticality calculation are inactive cycles where the spatial source changes from the initial definition to the correct distribution for the problem No keff accumulation summary table activity table or tally information is accrued for inactive cycles Photon production perturbations and DXTRAN are turned off during inactive cycles Z is the third entry on the KCODE card for the number of cycles to be skipped before tally accumulation After the first J cycles the fission source spatial distribution is assumed to have achieved equilibrium active cycles begin and and tallies are accumulated Cycles are run until either a time limit is reached or the total cycles on the KCODE card have been completed Criticality calculations with MCNP are based on an iterative procedure called power iteration 19 After assuming an initial guess for the fission source spatial distribution i e first generation histories are followed to produce a source for the next fission neutron generation and to estimate a new value for kep The new fission source distribution is then used to fo
545. state by the emission of one or more gamma rays The gamma ray energies follow the well known patterns for relaxation The only reactions 10 3 05 2 65 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS that do not produce gamma rays are direct reactions where the photon is absorbed and all available energy is transferred to a single emission particle leaving the nucleus in the ground state Reactions at higher energies above the pion production threshold require more complete descriptions of the underlying nuclear physics The delta resonance and other absorption mechanisms become significant and the amount of energy involved in the reaction presents the opportunity for the production of more fundamental particles While beyond the scope of this current work descriptions of the relevant physics may be found in the paper by Fasso et 1 68 New photonuclear data tables used to extend the traditional photon collision routines Because of the sparsity of photonuclear data the user is allowed to toggle photonuclear physics on or off with the fourth entry on the PHYS p card and the code defaults to off Once turned on the total photon cross section photoatomic plus photonuclear the photonuclear cross section is absent from this calculation when photonuclear physics is off is used to determine the distance to the next photon collision For simple physics this implies the sum of the photoelectric pair production incoher
546. statistical checks of the tallies see page 2 129 should all be passed If the statistical checks are not passed the error estimates should be considered erratic and unreliable no matter how small the relative error estimate 15 Erratic error estimates occur typically because a high weight particle tallies from an important region of phase space that has not been well sampled A high weight particle in a given region of phase space is a particle whose weight is some nontrivial fraction of all the weight that has tallied from that region because of all previous histories A good example is a particle that collides very close to a point or ring detector If not much particle weight has previously collided that close to the detector the relative error estimate will exhibit a jump for that history Another example is coherent photon scattering towards a point detector see page 2 64 To avoid high weight particles in important regions the user should try to ensure that these regions are well sampled by many particles and try to minimize the weight fluctuation among these particles Thus the user should try to use biasing techniques that preferentially push particles into important regions without introducing large weight fluctuations in these regions The weight window can often be very useful in minimizing weight fluctuations caused by other variance reduction techniques If despite a user s efforts an erratic error estimate occurs the user should
547. sults Keep in mind the footnote to Table 1 1 For example if an important but highly unlikely particle path in phase space has not been sampled in a problem the Monte Carlo results will not have the correct expected values and the confidence interval statements may not be correct The user can guard against this situation by setting up the problem so as not to exclude any regions of phase space and by trying to sample all regions of the problem adequately Despite one s best effort an important path may not be sampled often enough causing confidence interval statements to be incorrect To try to inform the user about this behavior MCNP calculates a figure of merit FOM for one tally bin of each tally as a function of the number of histories and prints the results in the tally fluctuation charts at the end of the output The FOM is defined as 1 R T where Tis the computer time in minutes The more efficient a Monte Carlo calculation is the larger the FOM will be because less computer time is required to reach a given value of R The FOM should be approximately constant as N increases because is proportional to N and T is proportional to N Always examine the tally fluctuation charts to be sure that the tally appears well behaved as evidenced by a fairly constant FOM A sharp decrease in the FOM indicates that a seldom sampled particle path has significantly affected the tally result and relative error estimate In this case
548. sure that the normal spatial mode for fission sources was achieved 3 all cells with fissionable material were sampled 4 the average combined kp appears to be varying randomly about the average value for the active cycles 5 average combined k 4 by cycles skipped does not exhibit a trend during the latter stages of the calculation 6 the confidence intervals for the batched with at least 30 batch values combined keff do not differ significantly from the final result 7 the impact of having the largest of each of the three k estimators occurring on the next cycle is not too great on the final confidence interval and 8 the combined figure of merit should be stable The combined k figure of merit should be reasonably stable but not as stable as a tally figure of merit because the number of histories for 2 184 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VOLUMES AND AREAS each cycle is not exactly the same and the combined k relative error may experience some changes because of changes in the estimated covariance matrix for the three individual estimators Plots using the z option can be made of the three individual and average k estimators by cycle as well as the three estimator combined k Use these plots to better understand the results If there is concern about a calculation the k 4 by cycles skipped table presents the results that would be obtained in the final result box for differing numbers o
549. t material regions but may be affected by problems of sampling and variance reduction techniques 10 3 05 1 13 CHAPTER 1 MCNP OVERVIEW MCNP GEOMETRY such as splitting and Russian roulette the need to specify an unambiguous geometry and the tally requirements The tally segmentation feature may eliminate most of the tally requirements Be cautious about making any one cell very complicated With the union operator and disjointed regions a very large geometry can be set up with just one cell The problem is that for each track flight between collisions in a cell the intersection of the track with each bounding surface of the cell is calculated a calculation that can be costly if a cell has many surfaces As an example consider Figure 1 3a It is just a lot of parallel cylinders and is easy to set up However the cell containing all the little cylinders is bounded by twelve surfaces counting a top and bottom A much more efficient geometry is seen in Figure 1 3b where the large cell has been broken up into a number of smaller cells a b Figure 1 3 l Cells Defined by Intersections of Regions of Space The intersection operator in MCNP is implicit it is simply the blank space between two surface numbers on the cell card If a cell is specified using only intersections all points in the cell must have the same sense with respect to a given bounding surface This means that for each bounding surface of a cell all point
550. t 3 for 1 and 25 of the time split 2 for 1 The weight assigned to each particle is W 1 which is the expected weight to minimize dispersion of weights On the other hand if a particle of weight W passes from a cell of importance 7 to one of lower importance so that I I lt 1 Russian roulette is played and the particle is killed with probability 1 I7I or followed further with probability weight W I T Geometry splitting with Russian roulette is very reliable It can be shown that the weights of all particle tracks are the same in a cell no matter which geometrical path the tracks have taken to get to the cell assuming that no other biasing techniques e g implicit capture are used The variance of any tally is reduced when the possible contributors all have the same weight The assigned cell importances can have any value they are not limited to integers However adjacent cells with greatly different importances place a greater burden on reliable sampling Once a sample track population has deteriorated and lost some of its information large splitting ratios like 20 to 1 can build the population back up but nothing can regain the lost information It is generally better to keep the ratio of adjacent importances small for example a factor of a few and have cells with optical thicknesses in the penetration direction less than about two mean free paths MCNP prints a warning message if adjacent importances or w
551. t C is given by c P aab E Fn M EB erf San a B aexp _ sinh b E 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS where the constant limits the range of outgoing energy so that 0 lt E s U This density function is sampled as follows Let 2 ge 19 1 1 Then ag In 51 18 rejected if 1 2 1 In gt bE where and 6 are random numbers on the unit interval Law 22 UK law 2 Tabular linear functions of incident energy out Tables of P and are given at a number of incident energies If E S E ij then the i P and T tables are used ip Ci Cy En Tg gt where is chosen according to k k 1 Py j 1 where amp is a random number on the unit interval 0 1 Law 24 UK law 6 Equiprobable energy multipliers The law is The library provides a table of K equiprobable energy multipliers T for a grid of incident neutron energies For incident energy such that lt lt 1 the random numbers amp on the unit interval are used to find T k 6 K 1 T T 5T 1 and then out Law 44 Tabular Distribution ENDF Law 1 Lang 2 Kalbach 87 correlated energy angle scattering Law 44 is an extension of Law 4 For each incident energy there is a pointer to a table of secondary en
552. t Codes SAND91 1634 1992 M A Gardner J Howerton Evaluated Neutron Activation Cross Section Library Evaluation Techniques and Reaction Index Lawrence Livermore National Laboratory report UCRL 50400 Vol 18 October 1978 J U Koppel and D Houston Reference Manual for ENDF Thermal Neutron Scattering Data General Atomics report GA 8744 Revised ENDF 269 July 1978 J C Wagner E L Redmond II S P Palmtag and J S Hendricks MCNP Multigroup Adjoint Capabilities Los Alamos National Laboratory report LA 12704 December 1993 J E Morel L J Lorence Jr R P Kensek J A Halbleib and D P Sloan A Hybrid Multigroup Continuous Energy Monte Carlo Method for Solving the Boltzmann Fokker Planck Equation Nucl Sci Eng 124 p 369 389 1996 Thomas E Booth Monte Carlo Variance Reduction Approaches for Non Boltzmann Tallies Los Alamos National Laboratory report LA 12433 December 1992 Thomas E Booth Pulse Height Tally Variance Reduction in MCNP Los Alamos National Laboratory report LA 13955 2002 J Lorence Jr J E Morel D Valdez Physics Guide to CEPXS A Multigroup Coupled Electron Photon Cross Section Generating Code Version 1 0 SAND89 1685 1989 and User s Guide to CEPXS ONED ANT A One Dimensional Coupled Electron Photon Discrete Ordinates Code Package Version 1 0 SAND89 1661 1989 and L J Lorence Jr W E Nelson
553. t DXTRAN producing the same tally contributions and so forth However if the non DXTRAN particle s next flight attempts to enter the sphere the particle must be killed or there would be on average twice as much weight crossing the DXTRAN sphere as there should be because the weight crossing the sphere has already been accounted for by the DXTRAN particle The DXTRAN Particle Although the DXTRAN particle does not confuse people nearly as much as the non DXTRAN particle the DXTRAN particle is nonetheless subtle The most natural approach for scattering particles toward the DXTRAN sphere would be to sample the scattering angle Q proportional to the analog density This approach is not used because it is too much work to sample proportional to the analog density and because it is sometimes useful to bias the sampling To sample in an unbiased fashion when it is known that points to the DXTRAN sphere one samples the conditional density Peon Q P Q ND the set S Q points toward the sphere and multiplies the weight by f P Q d Q the probability of scattering into the cone S Q see Figure 2 25 However it is too much work to calculate the above integral for each collision Instead an arbitrary density function P Q is sampled and the weight is multiplied by Po _ P Q 10 3 05 2 157 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VARIANCE REDUCTION 2 158 The total weight
554. t LA 12740 M October 1994 E MacFarlane W Muir and M Boicourt NJOY Nuclear Data Processing System Volume I User s Manual Los Alamos National Laboratory report LA 9303 M Vol I ENDF 324 May 1982 E MacFarlane W Muir and M Boicourt NJOY Nuclear Data Processing System Volume II The NJOY RECONR BROADR HEATR and THERMR Modules Los Alamos National Laboratory report LA 9303 M Vol II ENDF 324 May 1982 R A Forster R C Little J F Briesmeister and J S Hendricks MCNP Capabilities For Nuclear Well Logging Calculations IEEE Transactions on Nuclear Science 37 3 1378 June 1990 A Geist et al 3 User s Guide and Reference Manual ORNL TM 12187 Oak Ridge National Laboratory 1993 McKinney Practical Guide to Using MCNP with PVM Trans Am Nucl Soc 71 397 1994 McKinney MCNP4B Multiprocessing Enhancements Using PVM Los Alamos National Laboratory memorandum X 6 GWM 95 212 1995 10 3 05 1 19 1 20 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS INTRODUCTION CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS IL INTRODUCTION Chapter 2 discusses the mathematics and physics of MCNP including geometry cross section libraries sources variance reduction schemes Monte Carlo simulation of neutron and photon transport and tallies This discussion is not meant to be exhaustive many details of
555. t multiple scattering theories are valid but short enough that the mean energy loss in any one step is small so that the approximations necessary for the multiple scattering theories are satisfied The energy loss and angular deflection of the electron during each of the steps can then be sampled from probability distributions based on the appropriate multiple scattering theories This accumulation of the effects of many individual collisions into single steps that are sampled probabilistically constitutes the condensed history Monte Carlo method 10 3 05 2 67 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS The most influential reference for the condensed history method is the 1963 paper by Martin J Berger Based on the techniques described in that work Berger and Stephen M Seltzer developed the ETRAN series of electron photon transport codes These codes have been maintained and enhanced for many years at the National Bureau of Standards now the National Institute of Standards and Technology The ETRAN codes are also the basis for the Integrated TIGER Series a system of general purpose application oriented electron photon transport codes developed and maintained by John A Halbleib and his collaborators at Sandia National Laboratories in Albuquerque New Mexico The electron physics in MCNP is essentially that of the Integrated TIGER Series Version 3 0 The ITS radiative and collisional stopping power and bremsstra
556. ta tables is used in MCNP is described in Section IV beginning on page 2 25 There are two broad objectives in preparing nuclear data tables for MCNP First the data available to MCNP should reproduce the original evaluated data as much as is practical Second new data should be brought into the MCNP package in a timely fashion thereby giving users access to the most recent evaluations Nine classes of data tables exist for MCNP They are 1 continuous energy neutron interaction data 2 discrete reaction neutron interaction data 3 continuous energy photoatomic interaction 2 14 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CROSS SECTIONS data 4 continuous energy photonuclear interaction data 5 neutron dosimetry cross sections 6 neutron S a B thermal data 7 multigroup neutron coupled neutron photon and charged particles masquerading as neutrons 8 multigroup photon and 9 electron interaction data It is understood that photoatomic and electron data are atomic in nature i e one elemental table is acceptable for any isotope of the element For example any isotope of tungsten may use a table with a ZA of 74000 Likewise it is understood that neutron and photonuclear tables are nuclear or isotopic in nature i e each isotope requires its own table For tables describing these reactions it is necessary to have a table for every isotope in a material Note that some older neutron evaluations are e
557. tallies with small relative errors because coherent scattering is highly peaked in the forward direction Consequently coherent scattering becomes undersampled because the photon must be traveling directly at the detector point and undergo a coherent scattering event When the photon is traveling nearly in the direction of the point detector or the chosen point a ring detector or DXTRAN sphere the PSC term p t of the point detector see page 2 91 becomes very large causing a huge score for the event and severely affecting the tally Remember that is not a probability that can be no larger than unity it is a probability density function the derivative of the probability and can approach infinity for highly forward peaked scattering Thus the undersampled coherent scattering event is characterized by many low scores to the detector when the photon trajectory is away from the detector small and very few very large scores huge when the trajectory is nearly aimed at the detector Such undersampled events cause a sudden increase in both the tally and the variance a sudden drop in the figure of merit and a failure to pass the statistical checks for the tally as described on page 2 129 3 Photonuclear Physics Treatment New in MCNPS photonuclear physics may be included when handling a photon collision A photonuclear interaction begins with the absorption of a photon by a nucleus There are several mechanis
558. tally F4 to tabulate volumes and the surface flux tally F2 to tabulate areas The cell flux tally is inversely proportional to cell volume Thus in cells whose volumes are known the unit flux will result in a tally of unity and in cells whose volume is uncalculated the unit flux will result in a tally of volumes Similarly the surface flux 10 3 05 2 187 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PLOTTER tally is inversely proportional to area so that the unit flux will result in a tally of unity wherever the area is known and a tally of area wherever it is unknown X PLOTTER The MCNP plotter draws cross sectional views of the problem geometry according to commands entered by the user See Appendix B for the command vocabulary and examples of use The pictures can be drawn on the screen of a terminal or to a postscript file as directed by the user The pictures are drawn in a square viewport on the graphics device The mapping between the viewport and the portion of the problem space to be plotted called the window is user defined A plane in problem space the plot plane is defined by specifying an origin ro and two perpendicular basis vectors and b The size of the window in the plot plane is defined by specifying two extents The picture appears in the viewport with the origin at the center the first basis vector pointing to the right and the second basis vector pointing up The width of the picture is twice the first ex
559. te Carlo calculation itself and not to the accuracy of the result compared to the true physical value A statement regarding accuracy requires a detailed analysis of the uncertainties in the physical data modeling sampling techniques and approximations etc used in a calculation The guidelines for interpreting the quality of the confidence interval for various values of R are listed in Table 1 1 1 6 10 3 05 CHAPTER 1 MCNP OVERVIEW INTRODUCTION TO MCNP FEATURES Table 1 1 Guidelines for Interpreting the Relative Error R Range of R Quality of the Tally 0 5 to 1 0 Not meaningful 0 2 to 0 5 Factor of a few 0 1 to 0 2 Questionable 0 10 Generally reliable 0 05 Generally reliable for point detectors R 5 z X and represents the estimated relative error at the 16 level These interpretations of R assume that all portions of the problem phase space are being sampled well by the Monte Carlo process For all tallies except next event estimators hereafter referred to as point detector tallies the quantity R should be less than 0 10 to produce generally reliable confidence intervals Point detector results tend to have larger third and fourth moments of the individual tally distributions so a smaller value of R 0 05 is required to produce generally reliable confidence intervals The estimated uncertainty in the Monte Carlo result must be presented with the tally so that all are aware of the estimated precision of the re
560. te of a tally result Conservative is defined so that the results will not be less than the expected result One reasonable way to make such an estimate is to assume that the largest observed history score would occur again on the very next history N 1 MCNP calculates new estimated values for the mean R VOV FOM and shifted confidence interval center for the TFC bin result for this assumption The results of this proposed occurrence are summarized in the TFC bin information table The user can assess the impact of this hypothetical happening and act accordingly c Description of the 10 Statistical Checks for the TFC Bin MCNP prints the results of ten statistical checks of the tally in the TFC bin at each print In a Status of Statistical Checks table the results of these ten checks are summarized at the end of the output for all TFC bin tallies The quantities involved in these checks are the estimated mean R VOV FOM and the large history score behavior of f x Passing all of the checks should provide additional assurance that any confidence intervals formed for a TFC bin result will cover the expected result the correct fraction of the time At a minimum the results of these checks provide the user with more information about the statistical behavior of the result in the TFC bin of each tally The following 10 statistical checks are made on the TFCs printed at the end of the output for desirable statistical properties of Monte Car
561. ted to the definition of on page 2 169 oo jJ JJ e JdVdtdEdQ f o dVdtdEdQ f 4 Other Lifetime Estimators In addition to the collision absorption and track length estimators of the prompt removal lifetime t MCNP provides the escape capture n On and fission prompt lifespans and lifetimes for all KCODE problems having a sufficient number of settle cycles Further the average time of printed in the problem summary table is related to the lifespans and track length estimates of many lifetimes can be computed using the 1 tally multiplier option on the FM card for track length tallies In KCODE problems MCNP calculates the lifespan of escape capture fission lp and removal _ j LEM EW EW WT to These sums are taken over all the active histories in the calculation If KC8 0 on the KCODE card then the sums are over both active and inactive cycle histories but KC8 1 the default is assumed for the remainder of this discussion The capture and fission contributions are accumulated at each collision with a nuclide so these are absorption estimates Thus 10 3 05 2 173 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CRITICALITY CALCULATIONS A I RT The difference is that is the average of the for each cycle and is the
562. tent and the height is twice the second extent If the extents are unequal the picture is distorted The central task of the plotter is to plot curves representing the intersections of the surfaces of the geometry with the plot plane within the window All plotted curves are conics defined here to include straight lines The intersection of a plane with any MCNP surface that is not a torus is always a conic A torus is plotted only if the plot plane contains the torus axis or is perpendicular to it in which case the intersection curves are conics The first step in plotting the curves is to find equations for them starting from the equations for the surfaces of the problem Equations are needed in two forms for each curve a quadratic equation and a pair of parametric equations The quadratic equations are needed to solve for the intersections of the curves The parametric equations are needed for defining the points on the portions of the curves that are actually plotted The equation of a conic is As 2Hst B 265 2Ft C 0 where s and 1 are coordinates in the plot plane They are related to problem coordinates x y z by gt gt _ gt gt r fot s t tb or in matrix form 100 1 1 X a b E y Yo 4 by t d 20 b 5 In matrix form the conic equation is 2 188 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PLOTTER 1 1 s t
563. ter an important cell where the particles can be split 2 Geometry splitting Russian roulette will preserve weight variations The technique is dumb in that it never looks at the particle weight before deciding appropriate action An example is geometry splitting Russian roulette used with source biasing 3 Geometry splitting Russian roulette are turned on or off together 10 3 05 2 141 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VARIANCE REDUCTION 4 Particles are killed immediately upon entering a zero importance cell acting as a geometry cutoff 4 Energy Splitting Roulette and Time Splitting Roulette a Energy Splitting Roulette Energy splitting and roulette typically are used together but the user can specify only one if desired Energy splitting roulette is independent of spatial cell If the problem has a space energy dependence the space energy dependent weight window is normally a better choice l Splitting In some cases particles are more important in some energy ranges than in others For example it may be difficult to calculate the number of 7 U fissions because the thermal neutrons are also being captured and not enough thermal neutrons are available for a reliable sample In this case once a neutron falls below a certain energy level it can be split into several neutrons with an appropriate weight adjustment A second example involves the effect of fluorescent emission after photoelectric ab
564. teraction models simple and detailed The simple physics treatment ignores coherent Thomson scattering and fluorescent photons from photoelectric absorption It is intended for high energy photon problems or problems where electrons are free and is also important for next event estimators such as point detectors where scattering can be nearly straight ahead with coherent scatter The simple physics treatment uses implicit capture unless overridden with the CUT P card in which case it uses analog capture The detailed physics treatment includes coherent Thomson scattering and accounts for fluorescent photons after photoelectric absorption Form factors and Compton profiles are used to account for electron binding effects Analog capture is always used The detailed physics treatment is used below energy EMCPF on the PHYS P card and because the default value of EMCPF is 100 MeV that means it is almost always used by default It is the best treatment for most applications particularly for high Z nuclides or deep penetration problems The generation of electrons from photons is handled three ways These three ways are the same for both the simple and detailed photon physics treatments 1 If electron transport is turned on Mode P E then all photon collisions except coherent scatter can create electrons that are banked for later transport 2 If electron transport is turned off no E on the Mode card then a thick target bremsstrahlung model
565. th a mixture of both materials and introduce PERT cards to remove each See Appendix B of Ref 165 3 The track length estimate of kin KCODE criticality calculations assumes the fundamental eigenfunction fission distribution is unchanged in the perturbed configuration 4 DXTRAN point detector tallies and pulse height tallies are not currently compatible with the PERT card 5 While there is no limit to the number of perturbations they should be kept to a minimum as each perturbation can degrade performance by 10 20 6 Use caution in selecting the multiplicative constant and reaction number on FM cards used with F4 tallies in perturbation problems 7 The METHOD keyword can indicate if a perturbation is so large that higher than second order terms are needed to prevent inaccurate tallies 8 Ifa perturbation changes the relative concentrations of nuclides MAT keyword it is assumed that the perturbation contribution from each nuclide is independent that is second order differential cross terms are neglected C Accuracy Analyzing the first and second order perturbation results presented in Ref 166 leads to the following rules of thumb The first order perturbation estimator typically provides sufficient accuracy for response or tally changes that are less than 596 The default first plus second order estimator offers acceptable accuracy for response changes that are less than 20 30 This upper bound depends on the behav
566. the Status of Statistical Checks table Messages are provided to the user giving the results of these checks b Asymmetric Confidence Intervals A correlation exists between the estimated mean and the estimated uncertainty in the mean If the estimated mean is below the expected value the estimated uncertainty in the mean 5 will most likely be below its expected value This correlation 10 3 05 2 127 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS ESTIMATION OF THE MONTE CARLO PRECISION is also true for higher moment quantities such as the VOV The worst situation for forming valid confidence intervals is when the estimated mean is much smaller than the expected value resulting in smaller than predicted coverage rates To correct for this correlation and improve coverage rates one can estimate a statistic shift in the midpoint of the confidence interval to a higher value The estimated mean is unchanged The shifted confidence interval midpoint is the estimated mean plus a term proportional to the third central moment The term arises from an Edgeworth expansion to attempt to correct the confidence interval for non normality effects in the estimate of the mean The adjustment term is given by SHIFT X x x QS N Substituting for the estimated mean and expanding produces 3 2 42422 2 2 SHIFT Xx 32x 2x N 2 2x N 2 NXx Zxj The SHIFT should decrease as 1 N This term is added to the estimated mean
567. the example cards above from Figure 1 4 may be written in the form 1 a b c d e 2 e a b c d Note that parentheses are required for the first cell but not for the second although the second could have been written as e a b c d e a b c d e a b c d etc Several more examples using the union operator are given in Chapter 4 Study them to get a better understanding of this powerful operator that can greatly simplify geometry setups B Surface Type Specification The first and second degree surfaces plus the fourth degree elliptical and degenerate tori of analytical geometry are all available in MCNP The surfaces are designated by mnemonics such as C Z for a cylinder parallel to the z axis A cylinder at an arbitrary orientation is designated by the general quadratic GQ mnemonic paraboloid parallel to a coordinate axis is designated by the special quadratic SQ mnemonic The 29 mnemonics representing various types of surfaces are listed in Table 3 1 on page 3 13 C Surface Parameter Specification There are two ways to specify surface parameters in MCNP 1 by supplying the appropriate coefficients needed to satisfy the surface equation and 2 by specifying known geometrical points on a surface that is rotationally symmetric about a coordinate axis l Coefficients for the Surface Equations The first way to define a surface is to use one of the surface type mnemonics from Table 3 1 on page 3 13 and to calculate
568. the appropriate coefficients needed to satisfy the surface equation 10 3 05 1 17 CHAPTER 1 MCNP OVERVIEW MCNP GEOMETRY For example a sphere of radius 3 62 cm with the center located at the point 4 1 3 is specified by S 4 1 3 362 An ellipsoid whose axes are not parallel to the coordinate axes is defined by the GQ mnemonic plus up to 10 coefficients of the general quadratic equation Calculating the coefficients can be and frequently is nontrivial but the task is greatly simplified by defining an auxiliary coordinate system whose axes coincide with the axes of the ellipsoid The ellipsoid is easily defined in terms of the auxiliary coordinate system and the relationship between the auxiliary coordinate system and the main coordinate system is specified a TRn card described on page 3 30 The use of the SQ and GQ surfaces is determined by the orientation of the axes One should always use the simplest possible surface in describing geometries for example using a GQ surface instead of an S to specify a sphere will require more computational effort for MCNP 2 Points that Define a Surface The second way to define a surface is to supply known points on the surface This method is convenient if you are setting up a geometry from something like a blueprint where you know the coordinates of intersections of surfaces or points on the surfaces When three or more surfaces intersect at a point this second method also produces a mor
569. the confidence intervals may not be correct for the fraction of the time that statistical theory would indicate Examine the problem to determine what path is causing the large scores and try to redefine the problem to sample that path much more frequently After each tally an analysis is done and additional useful information is printed about the TFC tally bin result The nonzero scoring efficiency the zero and nonzero score components of the relative error the number and magnitude of negative history scores if any and the effect on the result if 10 3 05 1 7 CHAPTER 1 MCNP OVERVIEW INTRODUCTION TO MCNP FEATURES the largest observed history score in the TFC were to occur again on the very next history are given A table just before the TFCs summarizes the results of these checks for all tallies in the problem Ten statistical checks are made and summarized in Table 160 after each tally with a pass yes no criterion The empirical history score probability density function PDF for the TFC bin of each tally is calculated and displayed in printed plots The TFCs at the end of the problem include the variance of the variance an estimate of the error of the relative error and the slope the estimated exponent of the PDF large score behavior as a function of the number of particles started All this information provides the user with statistical information to aid in forming valid confidence intervals for Monte Carlo results There is no
570. the particular techniques and of the Monte Carlo method itself will be found elsewhere Carter and Cashwell s book Particle Transport Simulation with the Monte Carlo Method a good general reference on radiation transport by Monte Carlo is based upon what is in MCNP A more recent reference is Lux and Koblinger s book Monte Carlo Particle Transport Methods Neutron and Photon Calculations Methods of sampling from standard probability densities are discussed in the Monte Carlo samplers by Everett and Cashwell MCNP was originally developed by the Monte Carlo Group currently the Diagnostic Applications Group Group X 5 in the Applied Physics Division X Division at the Los Alamos National Laboratory Group X 5 improves MCNP releasing a new version every two to three years maintains it at Los Alamos and at other laboratories where we have collaborators or sponsors and provides limited free consulting and support for MCNP users MCNP is distributed to other users through the Radiation Safety Information Computational Center RSICC at Oak Ridge Tennessee and the OECD NEA data bank in Paris France There are about 250 MCNP users at Los Alamos and 3000 users at 200 installations worldwide MCNP is comprised of about 425 subroutines written in Fortran 90 and C MCNP has been made as system independent as possible to enhance its portability and has been written to comply with the ANSI Fortran 90 standard With one source code MCNP is supported
571. the same result as Eq 2 19b Both R an and R g are printed for the tally fluctuation chart bin of each tally so that the dominant component of R can be identified as an aid to making the calculation more efficient These equations can be used to better understand the effects of scoring inefficiency that is those histories that do not contribute to a tally Table 2 7 shows the expected values of R eff aS function of q and the number of histories N This table is appropriate for identical nonzero scores and represents the theoretical minimum relative error possible for a specified q and N It is no surprise that small values of q require a compensatingly large number of particles to produce precise results Table 2 7 Expected Values of a Function of q and N q N 0 001 0 01 0 1 0 5 10 0 999 0 315 0 095 0 032 10 0 316 0 099 0 030 0 010 10 0 100 0 031 0 009 0 003 10 0 032 0 010 0 003 0 001 A practical example of scoring inefficiency is the case of infrequent high energy particles in a down scattering only problem If only a small fraction of all source particles has an energy in the highest energy tally bin the dominant component of the relative error will probably be the scoring efficiency because only the high energy source particles have a nonzero probability of contributing to the highest energy bin For problems of this kind it is often useful to run a separate problem starting only high energy particles from the source and
572. the sections below for the appropriate source variables The SB card input is analogous to that of an SP card for an analytic source distribution that is the first entry is a negative prescription number for the type of biasing required followed by one or more optional user specified parameters which are discussed in the following sections 2 152 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VARIANCE REDUCTION a Direction Biasing The source direction can be biased about a reference axis by sampling from a continuous exponential function or by using cones of fixed size and starting a fixed fraction of particles within each cone The user can bias particles in any arbitrary direction or combination of directions The sampling of the azimuthal angle about the reference axis is not biased In general continuous biasing is preferable to fixed cone biasing because cone biasing can cause problems from the discontinuities of source track weight at the cone boundaries However if the cone parameters cone size and fraction of particles starting in the cone are optimized through a parameter study and the paths that tracks take to contribute to tallies are understood fixed cone biasing sometimes can outperform continuous biasing Unfortunately it is usually time consuming both human and computer and difficult to arrive at the necessary optimization Source directional biasing can be sampled from an exponential probability dens
573. the source or scatter location through the pinhole to one image grid element pixel Once this direction is established a ray trace point detector flux contribution is made to the intersected pixel including attenuation by any material along that path No source or scattering events on the image grid side of the pinhole will contribute to the image The pinhole and associated grid will image both direct source contributions and the direct plus any scattered contributions Standard tally modifications can be made to the image tally for example by using the FM PD and FT cards The magnitude of the flux contribution through the pinhole to a pixel is calculated as follows The flux at a pinhole point P is p Q where is the direction that intersects the pinhole at point P Define to be the cosine of the angle between the detector trajectory and the reference direction which is perpendicular to the plane of the pinhole The particle weight per unit pinhole area or the particle current per unit pinhole area is The weight in a small area dA in the pinhole is dA The total particle weight integrated over the pinhole area Ap is W f pnu dA Ap The FIP tally selects one particle trajectory to carry this weight This trajectory should be sampled in dA from dA 10 3 05 2 99 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS TALLIES Instead the pinhole point P
574. though the same effect can be achieved with an infinite lattice the periodic boundary is easier to use simplifies comparison with other codes having periodic boundaries and can save considerable computation time There is approximately a 55 run time penalty associated with repeated structures and lattices that can be avoided with periodic boundaries However collisions and other aspects of the Monte Carlo random walk usually dominate running time so the savings realized by using periodic boundaries are usually much smaller A simple periodic boundary problem is illustrated in Figure 2 4 Figure 2 4 It consists of a square reactor lattice infinite in the z direction and 10 cm on a side in the x and y directions with an off center 1 cm radius cylindrical fuel pin The MCNP surface cards are 10 3 05 2 13 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CROSS SECTIONS 2 px 5 2 l px 5 3 4 py 5 4 3 py 5 5 c z 2 4 1 The negative entries before the surface mnemonics specify periodic boundaries Card one says that surface is periodic with surface 2 and is a px plane Card two says that surface 2 is periodic with surface and is a px plane Card three says that surface 3 is periodic with surface 4 and is a py plane Card four says that surface 4 is periodic with surface 3 and is a py plane Card five says that surface 5 is an infinite cylinder parallel to the z axis A particle leaving the lattice out the left side sur
575. ticles started at t 0 one has an estimate of 0 7 and the tallies To from a number of time distributed sources 042 be calculated at time as b b Tom vat OOTO by sampling t from Q f and recording each particle s tally shifted by 2 or after the calculation by integrating 047 multiplied by the histogram estimate of 7 0 n 7 The latter method is used in MCNP to simulate a source as a square pulse starting at time a and ending at time b where a and b are supplied by the TMC option d Binning by the number of collisions Tallies can be binned by the number of collisions that caused them with the INC option and an FU card A current tally for example can be subdivided into the portions of the total current coming from particles that have undergone zero one two three collisions before crossing the surface In a point detector tally the user can determine what portion of the score came from particles having their Ist 2nd 3rd collision Collision binning is particularly useful with the exponential transform because the transform reduces variance by reducing the number of collisions If particles undergoing many collisions are the major contributor to a tally then the exponential transform is ill advised When the exponential transform is used the portion of the tally coming from particles having undergone many collisions should be small e Binning by detector cell The ICD option w
576. tigations of Schaart et al and references therein b ITS Energy Indexing Algorithm Developed for the ITS codes earlier than the MCNP algorithm this method also called the nearest group boundary treatment was added to the MCNP code in order to explore some of the energy dependent artifacts of the condensed history approach and in order to offer more consistency with the TIGER Series codes This algorithm differs from the default treatment in two ways First the electron is initially assigned to a group n such that E 4 E 2 EZ E E 4 2 In other words the electron is assigned to the group whose upper limit is closest to the electron s energy Second although the electron will be reassigned when it enters a new geometric cell it will not be reassigned merely for falling out of the current energy group These differences serve to reduce the number of times that unwanted imposition of linear interpolation on partial steps occurs and to allow more equal numbers of excursions above and below the energy group from which the Landau sampling was made As Ref 94 shows these advantages make the ITS algorithm a more accurate representation of the energy loss process as indicated in comparisons with reference calculations and experiments Nevertheless although the reliance on linear interpolation and the systematic errors are reduced neither is completely eliminated It is straightforward to create example calculations that
577. ting the default output blocks in terms of time vs energy they could be printed in blocks of segment vs cosine The tally bin that is monitored for the tally fluctuation chart printed at the problem end and used in the statistical analysis of the tally can be selected TF card Detector tally diagnostic prints are controlled with the DD card Finally the PRINT card controls what optional tables are displayed in the output file VI ESTIMATION OF THE MONTE CARLO PRECISION Monte Carlo results represent an average of the contributions from many histories sampled during the course of the problem An important quantity equal in stature to the Monte Carlo answer or tally itself 1s the statistical error or uncertainty associated with the result The importance of this error and its behavior versus the number of histories cannot be overemphasized because the user not only gains insight into the quality of the result but also can determine if a tally appears statistically well behaved If a tally is not well behaved the estimated error associated with the result generally will not reflect the true confidence interval of the result and thus the answer could be completely erroneous MCNP contains several quantities that aid the user in assessing the quality of the confidence interval The purpose of this section is to educate MCNP users about the proper interpretation of the MCNP estimated mean relative error variance of the variance and history s
578. tion scattering cross section total cross section distance to scatter and random number where W Oa 8 Or l 5 Implicit absorption along a flight path is a special form of the exponential transformation coupled with implicit absorption at collisions See the description of the exponential transform on page 2 148 The path length is stretched in the direction of the particle u 1 and the stretching parameter is p Using these values the exponential transform and implicit absorption at collisions yield the identical equations as does implicit absorption along a flight path Implicit absorption along a flight path is invoked in MCNP as a special option of the exponential transform variance reduction method It is most useful in highly absorbing media that is 2 2 approaches 1 When almost every collision results in absorption it is very inefficient to sample distance to collision However implicit absorption along a flight path is discouraged In highly absorbing media there is usually a superior set of exponential transform parameters In relatively nonabsorbing media it is better to sample the distance to collision than the distance to scatter 5 Elastic and Inelastic Scattering If the conditions for the 5 B treatment are not met the particle undergoes either an elastic or inelastic collision The selection of an elastic collision is made with the probability el el Oin
579. tion is found I Forming Statistically Valid Confidence Intervals The ultimate goal of a Monte Carlo calculation is to produce a valid confidence interval for each tally bin Section VI has described different statistical quantities and the recommended criteria to form a valid confidence interval Detailed descriptions of the information available in the output for all tally bins and the TFC bins are now discussed l Information Available for Forming Statistically Valid Confidence The R is calculated for every user specified tally bin in the problem The VOV and the shifted confidence interval center discussed below can be obtained for all bins with a nonzero entry for the 15th entry on the DBCN card at problem initiation a R Magnitude Comparisons With MCNP Guidelines The quality of MCNP Monte Carlo tallies historically has been associated with two statistical checks that have been the responsibility of the user 1 for all tally bins the estimated relative error magnitude rules of thumb that are shown in Figure 2 5 that is R 0 1 for nonpoint detector tallies and R 0 05 for point detector tallies and 2 a statistically constant FOM in the user selectable TFn card TFC bin so that the estimated is decreasing by 1 N as required by the CLT In an attempt to make the user more aware of the seriousness of checking these criteria MCNP provides checks of the R magnitude for all tally bins A summary of the checks is printed in
580. tion operators as illustrated in the cell cards that describe the simple cube in the preceding paragraphs B Repeated Structure Geometry The repeated structure geometry feature is explained in detail starting on page 3 25 The capabilities are only introduced here Examples are shown in Chapter 4 The cards associated with the repeated structure feature are U universe FILL TRCL URAN and LAT lattice and cell cards with LIKE m BUT The repeated structure feature makes it possible to describe only once the cells and surfaces of any structure that appears more than once in a geometry This unit then can be replicated at other locations by using the LIKE m BUT construct on a cell card The user specifies that a cell is filled with something called a universe The U card identifies the universe if any to which a cell belongs The FILL card specifies with which universe a cell is to be filled A universe is either a lattice or an arbitrary collection of cells The two types of lattice shapes hexagonal prisms and hexahedra need not be rectangular nor regular but they must fill space exactly Several concepts and cards combine in order to use this capability C Surfaces 1 Explanation of Cone and Torus Two surfaces the cone and torus require more explanation The quadratic equation for a cone describes a cone of two sheets just like a hyperboloid of two sheets one sheet is a cone of positive slope and the other has a nega
581. tions Later infrequent large 10 3 05 2 115 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS ESTIMATION OF THE MONTE CARLO PRECISION contributions may cause fluctuations in 5 and to a lesser extent in x and therefore in MCNP calculates FOM for one bin of each numbered tally to aid the user in determining the statistical behavior as a function of N and the efficiency of the tally MCNP TALLY BLOCKS Running History 1 Xi Scores Xx z Sums performed o each history xs 1 Particle batch size is one HYPOTHETICAL TALLY GRID from the present historv Figure 2 18 E MCNP Figure of Merit The estimated relative error squared R should be proportional to 1 N as shown by Eq 2 19b The computer time T used in an MCNP problem should be directly proportional to N therefore R T should be approximately a constant within any one Monte Carlo run It is convenient to define a figure of merit FOM of a tally to be L 2 24a RT MCNP prints the FOM for one bin of each numbered tally as a function of N where the unit of computer time T is minutes The table is printed in particle increments of 1000 up to 20 000 histories Between 20 000 and 40 000 histories the increment is doubled to 2000 This trend 2 116 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS ESTIMATION OF THE MONTE CARLO PRECISION continues producing a table of up to 20 entries The default increment c
582. tive probability distribution that is sampled to obtain index i representing scattering from the i Bragg edge The scattering cosine is then obtained from the relationship 1 2 Using next event estimators such as point detectors with 5 scattering cannot be done exactly because of the discrete scattering angles MCNP uses an approximate scheme that in the next event estimation calculation replaces discrete lines with histograms of width ou lt 1 See also page 2 104 7 Probability Tables for the Unresolved Resonance Range Within the unresolved resonance range e g in ENDF B VI 2 25 25 keV for 235 10 149 03 keV for 2380 and 2 5 30 keV for 23 continuous energy neutron cross sections appear to be smooth functions of energy This behavior occurs not because of the absence of resonances but rather because the resonances are so close together that they are unresolved Furthermore the smoothly varying cross sections do not account for resonance self shielding effects which may be significant for systems whose spectra peak in or near the unresolved resonance range Fortunately the resonance self shielding effects can be represented accurately in terms of probabilities based on a stratified sampling technique This technique produces tables of probabilities for the cross sections in the unresolved resonance range Sampling the cross section in a random walk from these probability tables is a valid physics app
583. tive slope A cell whose description contains a two sheeted cone may require an ambiguity surface to distinguish between the two sheets MCNP provides the option to select either of the two sheets this option frequently simplifies geometry setups and eliminates any ambiguity The 1 orthe 1 entry on the cone surface card causes the one sheet cone treatment to be used If the sign of the entry is positive the specified sheet is the one that extends 10 3 05 2 9 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS GEOMETRY to infinity in the positive direction of the coordinate axis to which the cone axis is parallel The converse is true for a negative entry This feature is available only for cones whose axes are parallel to the coordinate axes of the problem The treatment of fourth degree surfaces in Monte Carlo calculations has always been difficult because of the resulting fourth order polynomial quartic equations These equations must be solved to find the intersection of a particle s line of flight with a toroidal surface In MCNP these equations must also be solved to find the intersection of surfaces in order to compute the volumes and surface areas of geometric regions of a given problem In either case the quartic equation x Bx Dx 4 E 0 is difficult to solve on a computer because of roundoff errors For many years the MCNP toroidal treatment required 30 decimal digits CDC double precision accuracy to solve q
584. to calculate eigenvalues for critical systems The code treats an arbitrary three dimensional configuration of materials in geometric cells bounded by first and second degree surfaces and fourth degree elliptical tori Pointwise cross section data are used For neutrons all reactions given in a particular cross section evaluation such as ENDF B VI are accounted for Thermal neutrons are described by both the free gas and S o D models For photons the code accounts for incoherent and coherent scattering the possibility of fluorescent emission after photoelectric absorption and absorption in electron positron pair production Electron positron transport processes account for angular deflection through multiple Coulomb scattering collisional energy loss with optional straggling and the production of secondary particles including K x rays knock on and Auger electrons bremsstrahlung and annihilation gamma rays from positron annihilation at rest Electron transport does not include the effects of external or self induced electromagnetic fields Photonuclear physics is available for a limited number of isotopes Important standard features that make MCNP very versatile and easy to use include a powerful general source criticality source and surface source both geometry and output tally plotters a rich collection of variance reduction techniques a flexible tally structure and an extensive collection of cross section data 10 3 05 M v
585. to form a confidence interval based on the Central Limit Theorem in which the true answer is expected to lie a certain fraction of the time The number of standard deviations used for example from a Student s t Table determines the fraction of the time that the confidence interval will include the true answer for a selected confidence level For example a valid 99 confidence interval should include the true result 99 of the time There is always some probability in this example 190 that the true result will lie outside of the confidence interval To reduce this probability to an acceptable level either the confidence interval must be increased according to the desired Student s t percentile or more histories need to be run to get a smaller estimated standard deviation MCNP uses three different estimators for key The advantages of each estimator vary with the problem no one estimator will be the best for all problems estimators and their estimated standard deviations are valid under the assumption that they are unbiased and consistent therefore representative of the true parameters of the population This statement has been validated empirically for all MCNP estimators for small dominance ratios The batched keg results table should be used to estimate if the calculated batch size of one standard deviation appears to be adequate 10 3 05 2 177 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS CRITICALITY CALCULATIONS
586. to produce the midpoint of the now asymmetric confidence interval about the mean This value of the confidence interval midpoint can be used to form the confidence interval about the estimated mean to improve coverage rates of the true but unknown mean E x The estimated mean plus the SHIFT is printed automatically for the TFC bin for all tallies A nonzero entry for the 15th DBCN card entry produces the shifted value for all tally bins This correction approaches zero as N approaches infinity which is the condition required for the CLT to be valid Kalos uses slightly modified form of this correction to determine if the requirements of the CLT are substantially satisfied His relation is SN which is equivalent to SHIFT 5 2 The user is responsible for applying this check c Forming Valid Confidence Intervals for Non TFC Bins The amount of statistical information available for non TFC bins is limited to the mean and The VOV and the center of the asymmetric confidence can be obtained for all tally bins with a nonzero 15th entry on the DBCN card in the initial problem The magnitude criteria for R and the VOV if available should be met before forming a confidence interval If the shifted confidence interval center is available it should be used to form asymmetric confidence intervals about the estimated mean History dependent information about R and the VOV if available for non TFC bins ca
587. to use them carry high risk The use of weight windows tends to be more powerful than the use of importances but typically requires more input data and more insight into the problem The exponential transform for thick shields is not recommended for the inexperienced user rather use many cells with increasing importances or decreasing weight windows through the shield Forced collisions are used to increase the frequency of random walk collisions within optically thin cells but should be used only by an experienced user The point detector estimator should be used with caution as should DXTRAN For many problems variance reduction is not just a way to speed up the problem but is absolutely necessary to get any answer at all Deep penetration problems and pipe detector problems for example will run too slowly by factors of trillions without adequate variance reduction Consequently users have to become skilled in using the variance reduction techniques MCNP Most of the following techniques cannot be used with the pulse height tally The following summarizes briefly the main MCNP variance reduction techniques Detailed discussion is in Chapter 2 page 2 134 1 Energy cutoff Particles whose energy is out of the range of interest are terminated so that computation time is not spent following them 2 Time cutoff Like the energy cutoff but based on time Geometry splitting with Russian roulette Particles transported from a region of hi
588. tom has undergone an ionizing transition and can undergo a relaxation if it does not emit a photon it will 2 78 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS emit an Auger electron The difference between el and el03 is the energy with which an Auger electron is emitted given by E gp E 2 forelor 103 respectively The el value is that of the highest energy Auger electron while the el03 value is the energy of the most probable Auger electron It should be noted that both models are somewhat crude 9 Knock On Electrons The M ller cross section for scattering of an electron by an electron is do Cjl 1 T y 2t 1 1 22 ee 2 16 de d E t 1 t 1 1 where E and C have the same meanings as in Eqs 2 5 2 7 When calculating stopping powers one is interested in all possible energy transfers However for the sampling of transportable secondary particles one wants the probability of energy transfers greater than some representing an energy cutoff below which secondary particles will not be followed This probability can be written 1 2 do J 424 The reason for the upper limit of 1 2 is the same as in the discussion of Eq 2 8 Explicit integration of Eq 2 13 leads to C 1 1 1 2r l e 1 8 2 1 wee Fle I amp 1 2 qub Then the normalized probability distribution for the generation of secon
589. torial geometry scheme MCNP gives the user the added flexibility of defining geometrical regions from all the first and second degree surfaces of analytical geometry and elliptical tori and then of combining them with boolean operators The code does extensive internal 1 12 10 3 05 CHAPTER 1 MCNP OVERVIEW MCNP GEOMETRY checking to find input errors In addition the geometry plotting capability in MCNP helps the user check for geometry errors MCNP treats geometric cells in a Cartesian coordinate system The surface equations recognized by MCNP are listed in Table 3 1 on page 3 13 The particular Cartesian coordinate system used is arbitrary and user defined but the right handed system shown in Figure 1 2 is usually chosen X Figure 1 2 Using the bounding surfaces specified on cell cards MCNP tracks particles through the geometry calculates the intersection of a track s trajectory with each bounding surface and finds the minimum positive distance to an intersection If the distance to the next collision is greater than this minimum distance and there are no DXTRAN spheres along the track the particle leaves the current cell At the appropriate surface intersection MCNP finds the correct cell that the particle will enter by checking the sense of the intersection point for each surface listed for the cell When a complete match is found MCNP has found the correct cell on the other side and the transport continues A Cells When
590. tot tot tot yes no yes yes no yes yes no yes yes no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no yes yes yes no no yes yes yes no no no no no no no no no no no no no no no no no no no no no no no no no no no no yes no no no no no no yes yes no no no yes yes no no no no no yes yes APPENDIX G MCNP DATA LIBRARIES NEUTRON CROSS SECTION LIBRARIES Table G 2 Cont Continuous Energy and Discrete Neutron Data Libraries Maintained by X 5 Library Eval Temp Length Emax ZAID AWR Name Source Date K words NE MeV GPD 0 CP DN UR 7 92 Uranium 92232 49c 230 0400 uresa 0 1977 300 0 21813 2820 20 0 both no no yes 92232 60c 230 0400 endf60 0 1977 293 6 13839 1759 20 0 no both no no no 92232 61c 230 0400 0 1977 293 6 18734 1759 20 0 both no yes no 92232 65c 230 0400 endf66e B VLO 1977 3000 1 29048 2318 200 no both no yes yes 92232 66c 230 0400 endf66c B VI O 1977 293 6 32792 2786 20 0 no both no yes yes 92232 68c 230 0438 t16 2003 LANL T16 2003 3000 0 183542 5757 30 0 yes both no yes 92232 69c 230 0438 t16 2003 LANL T16 2003 293 6 197150 7269 30 0 yes both no no yes 9223
591. tte energy splitting roulette time splitting roulette weight cutoff and weight windows Modified Sampling Methods alter the statistical sampling of a problem to increase the number of tallies per particle For any Monte Carlo event it is possible to sample from any arbitrary distribution rather than the physical probability as long as the particle weights are then adjusted to compensate Thus with modified sampling methods sampling is done from distributions that send particles in desired directions or into other desired regions of phase space such as time or energy or change the location or type of collisions Modified sampling methods in MCNP include the exponential transform implicit capture forced collisions source biasing and neutron induced photon production biasing Partially Deterministic Methods are the most complicated class of variance reduction methods They circumvent the normal random walk process by using deterministic like techniques such as next event estimators or by controlling the random number sequence In MCNP these methods include point detectors DXTRAN and correlated sampling Variance reduction techniques used correctly can greatly help the user produce a more efficient calculation Used poorly they can result in a wrong answer with good statistics and few clues that anything is amiss Some variance reduction methods have general application and are not easily misused Others are more specialized and attempts
592. tte game is played according to neutron cell importances for the collision and source cell For a photon produced in cell i where the minimum weight set on the PWT card is wr let J be the neutron importance in cell and let 7 be the neutron importance in the source min cell If W W 1 or more photons will be produced The number of photons created 15 where Np W 5 w 1 1 N lt 10 Each photon is stored in the bank with weight W N If W lt I I Russian roulette is played and the photon survives with probability W I wri and is given the weight wer If weight windows are not used and if the weight of the starting neutrons is not unity setting all the we on the PWT card to negative values will make the photon minimum weight relative to the neutron source weight This will make the number of photons being created roughly proportional to the biased collision rate of neutrons It is recommended for most applications that negative numbers be used and be chosen to produce from one to four photons per source neutron The default values for we on the PWT card are 1 which should be adequate for most problems using cell importances If energy independent weight windows are used the entries on the PWT card should be the same as on the WWNI P card If energy dependent photon weight windows are used the entries on the PWT card should be the minimum WWNn P entry for each cel
593. ttering Detailed physics treatment 2 61 Coherent scattering turning off 2 62 2 64 Coincident detectors 2 103 Collision Nuclide Cross section 2 28 Comment cards 3 4 Source SCn 3 66 Tally 3 91 Complement Operator 2 8 Compton Scattering Detailed physics treatment 2 59 Simple physics treatment 2 58 Computer Time Cutoff 3 138 Cone 2 9 Cone biasing 2 153 Confidence Intervals 2 112 Continue Run 3 2 to 3 3 3 143 Continuous biasing 2 153 Index 3 MCNP MANUAL INDEX Continuous Energy data 2 16 Continuous Energy data 2 16 Coordinate pairs 3 15 Coordinate Transformation TRn card 3 30 to 3 32 Correlated sampling 2 163 Cosine bins 2 18 3 86 3 93 multiplier 3 101 Cn card 3 93 Criticality 2 163 3 137 3 140 3 154 Criticality Source KCODE card 3 76 Cross Sections 2 14 Collision Nuclide 2 28 Default 2 19 Evaluations 3 117 File XSn Card 3 123 Library Identifier 3 118 Neutron 3 118 CTME card 3 138 Cumulative Tally 5 61 Current Tally 2 84 3 105 CUT card 3 135 Cutoffs Cell by cell energy ELPT 3 136 Computer time 3 138 Electron 3 136 Energy 3 135 Energy Physics PHYS card 3 127 to 3 132 History 3 137 Neutron 3 135 Photon 3 136 SWTM 3 136 Time 2 69 2 140 3 135 Weight 3 135 D Data arrays 3 23 3 26 Data Cards also see Cards 3 23 DBCN card 3 142 DDn Card 3 108 DE DF cards H 3 3 99 Debug Information Card 3 142 Debug Prints 3 141 Debugging 3 10
594. ually distributed among them ll Point Detector Tally The point detector is a tally and does not bias random walk sampling Recall from Section VI however that the tally choice affects the efficiency of a Monte Carlo calculation Thus a little will be said here in addition to the discussion in the tally section Although flux is a point quantity flux at a point cannot be estimated by either a track length tally F4 or a surface flux tally F2 because the probability of a track entering the volume or crossing the surface of a point is zero For very small volumes a point detector tally can provide a good estimate of the flux where it would be almost impossible to get either a track length or surface crossing estimate because of the low probability of crossing into the small volume It is interesting that a DXTRAN sphere of vanishingly small size with a surface crossing tally across the diameter normal to the particle s trajectory is equivalent to a point detector Thus many of the comments on DXTRAN are appropriate and the DXC cards essentially are identical to the PD cards 10 3 05 2 155 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VARIANCE REDUCTION For a complete discussion of point detectors see page 2 91 12 DXTRAN DXTRAN typically is used when a small region is being inadequately sampled because particles have a very small probability of scattering toward that region To ameliorate this situation the user can spec
595. uartic equations Even then there were roundoff errors that had to be corrected by Newton Raphson iterations Schemes using a single precision quartic formula solver followed by a Newton Raphson iteration were inadequate because if the initial guess of roots supplied to the Newton Raphson iteration is too inaccurate the iteration will often diverge when the roots are close together The single precision quartic algorithm in MCNP basically follows the quartic solution of Cashwell and Everett When roots of the quartic equation are well separated a modified Newton Raphson iteration quickly achieves convergence But the key to this method is that if the roots are double roots or very close together they are simply thrown out because a double root corresponds to a particle s trajectory being tangent to a toroidal surface and it is a very good approximation to assume that the particle then has no contact with the toroidal surface In extraordinarily rare cases where this is not a good assumption the particle would become lost Additional refinements to the quartic solver include a carefully selected finite size of zero the use of a cubic rather than a quartic equation solver whenever a particle is transported from the surface of a torus and a gross quartic coefficient check to ascertain the existence of any real positive roots As a result the single precision quartic solver is substantially faster than double precision schemes portable and als
596. udies using the individual k estimator with the smallest estimated standard deviation is not recommended Its use can lead to confidence intervals that do not include the true result the correct fraction of the time 4 The studies have shown that the standard deviation of the three combined k eff estimator provides the correct coverage rates assuming that the estimated standard deviations in the individual estimators are accurate This accuracy can be verified by checking the batched results table When significant anti correlations occur among the estimators the resultant much smaller estimated standard deviation of the three combined average has been verified by analyzing a number of independent criticality calculations 8 Analysis to Assess the Validity of a Criticality Calculation The two most important requirements for producing a valid criticality calculation for a specified geometry are sampling all of the fissionable material well and ensuring that the fundamental spatial mode was achieved before and maintained during the active k cycles MCNP has checks to assess the fulfillment of both of these conditions MCNP verifies that at least one fission source point was generated in each cell containing fissionable material A WARNING message is printed on the k results summary page that includes a list of cells that did not have any particles entering and or no collisions and or no fission source points For repeated structure g
597. uld conceivably produce two 12 MeV particles in a single reaction But the net effect of many particle histories is unbiased because on the average the correct amount of energy is emitted Results are biased only when quantities that depend upon the correlation between the emerging particles are being estimated Users should note that MCNP follows a very particular convention The exiting particle energy and direction are always given in the target at rest laboratory coordinate system For the kinematical calculations in MCNP to be performed correctly the angular distributions for elastic discrete 10 3 05 2 39 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS inelastic level scattering and some ENDF 6 inelastic reactions must be given in the center of mass system and the angular distributions for all other reactions must be given in the target at rest system MCNP does not stop if this convention is not adhered to but the results will be erroneous In the checking of the cross section libraries prepared for MCNP at Los Alamos however careful attention has been paid to ensure that these conventions are followed The exiting particle energy and direction in the target at rest laboratory coordinate system are related to the center of mass energy and direction as follows 2 1 T 1 1 Hiab Bem Xr xus gt where E exiting particle energy laboratory E m exiting partic
598. ulse Height Tally F8 Weight Unlike other tallies in MCNP the pulse height tally depends on a collection of particles instead of just individual particles Because of this a weight is assigned to each collection of tallying particles It is this collective weight that multiplies the F8 tally not the particle weight 2 26 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS PHYSICS When variance reduction is used a collective weight is assigned to every collection of particles If variance reduction techniques have made a collection s random walk q times as likely as without variance reduction then the collective weight is multiplied by 1 q so that the expected F8 tally of the collection is preserved The interested reader should consult Refs 45 and 46 for more details B Particle Tracks When a particle starts out from a source a particle track is created If that track is split 2 for 1 at a splitting surface or collision a second track is created and there are now two tracks from the original source particle each with half the single track weight If one of the tracks has an n 2n reaction one more track is started for a total of three A track refers to each component of a source particle during its history Track length tallies use the length of a track in a given cell to determine a quantity of interest such as fluence flux or energy deposition Tracks crossing surfaces are used to calculate fluence flux or pul
599. ultiplied by the negative exponential of the optical path between the collision site and the sphere Thus the DXTRAN weight multiplication is X Pg Un where is the number of mean free paths from the exit site to the chosen point on the DXTRAN sphere Inside the DXTRAN Sphere So far only collisions outside the DXTRAN sphere have been discussed At collisions inside the DXTRAN sphere the DXTRAN game is not played because first the particle is already in the desired region and second it is impossible to define the angular cone of Figure 2 25 If there are several DXTRAN spheres and the collision occurs in sphere i DXTRAN will be played for all spheres except sphere i Terminology Real particle and Pseudoparticle Sometimes the DXTRAN particle is called a pseudoparticle and the non DXTRAN particle is called the original or real particle The terms real particle and pseudoparticle are potentially misleading Both 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VARIANCE REDUCTION particles are equally real both execute random walks both carry nonzero weight and both contribute to tallies The only sense in which the DXTRAN particle should be considered pseudo or not real is during creation A DXTRAN particle is created on the DXTRAN sphere but creation involves determining what weight the DXTRAN particle should have upon creation Part of this weight determination requires calculati
600. unning in parallel on a cluster of scientific workstations new photon libraries 10 3 05 2 3 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS INTRODUCTION ENDF 6 capabilities color X Windows graphics dynamic memory allocation expanded criticality output periodic boundaries plotting of particle tracks via SABRINA improved tallies in repeated structures and many smaller improvements MCNP4B released in 1997 featured differential operator perturbations enhanced photon physics equivalent to ITS3 0 PVM load balance and fault tolerance cross section plotting postscript file plotting 64 bit workstation upgrades PC X windows inclusion of LAHET HMCNP lattice universe mapping enhanced neutron lifetimes coincident surface lattice capability and many smaller features and improvements MCNPAC released in 2000 featured an unresolved resonance treatment macrobodies superimposed importance mesh perturbation enhancements electron physics enhancements plotter upgrades cumulative tallies parallel enhancements and other small features and improvements MCNPS released in 2003 is rewritten in ANSI standard Fortran 90 It includes the addition of photonuclear collision physics superimposed mesh tallies time splitting and plotter upgrades MCNPS also includes parallel computing enhancements with the addition of support for OpenMP and MPI Large production codes such as MCNP have revolutionized science not only in the wa
601. unresolved region are known to be incorrect IV MULTIGROUP DATA Currently only one coupled neutron photon multigroup library is supported by the Data Team MGXSNP MGXSNP is comprised of 30 group neutron and 12 group photon data primarily based on ENDF B V for 95 nuclides The MCNP compatible multigroup data library was produced from the original Sn multigroup libraries MENDF5 and MENDFSG using the code CRSRD in April 1987 202 The original neutron data library MENDFS was produced using the TD Division Weight Function also called CLAW by the processing code NJOY 2 2 7 This weight function is a combination of a Maxwellian thermal 1 E fission fusion peak at 14 0 MeV The data library contains no upscatter groups or self shielding and is most applicable for fast systems All cross sections are for room temperature 300 K PO through P4 scattering matrices from the original library were processed by CRSRD into angular distributions for MCNP using the Carter Forest equiprobable bin treatment When available both total and prompt nubar data are provided The edit reactions available for each ZAID are fully described in Reference 19 Table G 3 describes the MGXSNP data library The ZAIDs used for this library correspond to the source evaluation in the same manner as the ZAID for the continuous energy and discrete data as an example the same source evaluation for natural iron was used to produce 26000 55c 26000 55d and 26000 55m Fo
602. unting statistics Table 2 4 Estimated Relative Error R vs Number of Identical Tallies n for Large N n 1 4 16 25 100 400 R 1 0 0 5 0 25 020 010 0 05 Through use of Eq 2 20 a table of values versus the number of tallies or counts can be generated as shown in Table 2 4 A relative error of 0 5 is the equivalent of four counts which is hardly adequate for a statistically significant answer Sixteen counts is an improvement reducing to 0 25 but still is not a large number of tallies The same is true for n equals 25 When is 100 R is 0 10 so the results should be much improved With 400 tallies an R of 0 05 should be quite good indeed Based on this qualitative analysis and the experience of Monte Carlo practitioners Table 2 5 presents the recommended interpretation of the estimated 16 confidence interval x 1 for various values of R associated with an MCNP tally These guidelines were determined empirically based on years of experience using MCNP on a wide variety of problems Just before the tally fluctuation charts a Status of Statistical Checks table prints how many tally bins of each tally have values of R exceeding these recommended guidelines 2 114 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS ESTIMATION OF THE MONTE CARLO PRECISION Table 2 5 Guidelines for Interpreting the Relative Error R Range of R Quality of the Tally 0 5 to 1 Garbage 0 2 to 0 5 Factor of a few 0 1 to
603. up at Los Alamos but must be used with caution Users are encouraged to generate or get their own multigroup libraries and then use the supplementary code CRSRD to convert them to MCNP format Reference 43 describes the conversion procedure This report also describes how to use both the multigroup and adjoint methods in MCNP and presents several benchmark calculations demonstrating the validity and effectiveness of the multigroup adjoint method To generate cross section tables for electron photon transport problems that will use the multigroup Boltzmann Fokker Planck algorithm the CEPXS code developed by Sandia National Laboratory and available from RSICC can be used The CEPXS manuals describe the algorithms and physics database upon which the code is based the physics package is essentially the same as ITS version 2 1 The keyword MONTE CARLO is needed in the CEPXS input file to generate a cross section library suitable for input into CRSRD this undocumented feature of the CEPXS code should be approached with caution IV PHYSICS The physics of neutron photon and electron interactions is the very essence of MCNP This section may be considered a software requirements document in that it describes the equations MCNP is intended to solve All the sampling schemes essential to the random walk are presented or referenced But first particle weight and particle tracks two concepts that are important for setting up the input and for under
604. was studying the moderation of neutrons in Rome Though Fermi did not publish anything he amazed his colleagues with his predictions of experimental results After indulging himself he would reveal that his guesses were really derived from the statistical sampling techniques that he performed in his head when he couldn t fall asleep During World War II at Los Alamos Fermi joined many other eminent scientists to develop the first atomic bomb It was here that Stan Ulam became impressed with electromechanical computers used for implosion studies Ulam realized that statistical sampling techniques were considered impractical because they were long and tedious but with the development of computers they could become practical Ulam discussed his ideas with others like John von Neumann and Nicholas Metropolis Statistical sampling techniques reminded everyone of games of chance where randomness would statistically become resolved in predictable probabilities It was Nicholas Metropolis who noted that Stan had an uncle who would borrow money from relatives because he just had to go to Monte Carlo and thus named the mathematical method Monte Carlo 1 Meanwhile a team of wartime scientists headed by John Mauchly was working to develop the first electronic computer at the University of Pennsylvania in Philadelphia Mauchly realized that if Geiger counters in physics laboratories could count then they could also do arithmetic and solve
605. ways used the linear congruential scheme of Lehmer though the mechanics of implementation have been modified for portability to different computer platforms A random sequence of integers is generated by I GL4C 2 801 where is the random number multiplier J is the initial random seed is an additive constant and M bit integers and M bit floating point mantissas are assumed The random number is then I The 5 random number generator 9 implements the above algorithm in portable Fortran 90 using either 48 bit integers the default or 63 bit integers The starting random number for history is Io G8 p 1 1 mod 2M where 5 1s the random number stride that 15 the number of random numbers allocated to each single history This initial random number expression is evaluated very efficiently using a fast skip ahead algorithm 168 Successive random numbers for history k are then 1 9 2 GL mod2M The default values of Ip S and C which can be changed with the RAND card are 519 19 073 486 328 125 M 48 0 152 917 1 The values of G M and C may be changed by selecting another set of parameters using the RAND card The 3 other sets of parameters use 63 bit integers and a nonzero additive constant C The period P of the MCNP algorithm using the default parameters is 2 47 04 x 10 2 9 2 10 for the extended ran
606. width Extensive statistical analysis of tally convergence is applied to the tally fluctuation bin of each tally see page 3 107 Ten statistical checks are made including the variance of the variance and the Pareto slope of the history score probability density function These checks are described in detail in Section VI beginning on page 2 108 The tally quantities actually scored in MCNP before the final normalization per starting particle are presented in Table 2 2 The table also gives the physical quantity that corresponds to each tally and it defines much of the notation used in the remainder of this section Table 2 2 Tally Quantities Scored Tally Score Physical Quantit Units Fl W J aE dr aA aO O E r particles W 1 1 gt A 2 L aE at dA ao Q E t rticles F2 Os 414 ara 4 y r E t particles cm E _1 2 F4 we dQ w t Q E t particles cm F5 W p Qp e bp Y T p Q E t particles cm 2 R F6 E H E fag fas av ao S E H E w f Q E t MeV g F7 WTjoyE Q He 4E ar av ao Q E f MeV g F8 We putinbin Ep pulses pulses 10 3 05 2 81 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS TALLIES 2 82 particle weight collective weight from a history for pulse height tally see subsection D page 2 89 particle position vector cm direction vector energy MeV and time sh Ish 10 s
607. xt event estimators or by controlling the random number sequence In MCNP these methods include point detectors DXTRAN and correlated sampling The available MCNP variance reduction techniques are described below 1 Energy Cutoff The energy cutoff in MCNP is either a single user supplied problem wide energy level or a cell dependent energy level Particles are terminated when their energy falls below the energy cutoff The energy cutoff terminates tracks and thus decreases the time per history The energy cutoff should be used only when it is known that low energy particles are either of zero or almost zero importance An energy cutoff is like a Russian roulette game with zero survival probability A number of pitfalls exist 10 3 05 2 139 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS VARIANCE REDUCTION 1 Remember that low energy particles can often produce high energy particles for example fission or low energy neutrons inducing high energy photons Thus even if a detector is not sensitive to low energy particles the low energy particles may be important to the tally 2 CUT card energy cutoff is the same throughout the entire problem Often low energy particles have zero importance in some regions and high importance in others and so a cell dependent energy cutoff is also available with the ELPT card 3 answer will be biased low if the energy cutoff is killing particles that might otherwise hav
608. y AWR 95 90810 96 90810 97 91030 99 91420 Table 6 Cont Dosimetry Data Libraries for MCNP Tallies Library APPENDIX MCNP DATA LIBRARIES Source LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL Z EE E k k kk kk k k Molybdenum KKK K K K K KK K K K K K K K K K K KK K K K K KK K K K K KK K K 42090 30y 42091 30y 42092 26y 42092 30y 42093 30y 42093 31y 42094 30y 42095 30y 42096 30y 42097 30y 42098 26y 42098 30y 42099 30y 42100 26y 42100 30y 42101 30y 89 91390 90 91180 91 21000 91 90680 92 90680 92 90680 93 90510 94 90580 95 90470 96 90600 97 06440 97 90540 98 90770 99 04920 99 90750 100 91000 53240 53240 532405 LLNL ACTL LLNL ACTL ENDF B V LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL LLNL ACTL ENDF B V LLNL ACTL LLNL ACTL ENDF B V LLNL ACTL LLNL ACTL 7 42 Technetium 7 a k k he s k k k kkk 43099 30y 43099 3 ly 98 90620 98 90620 LLNL ACTL LLNL ACTL 45103 30y Z 46 kkk Palladium 202006 ak k k espe k os 46110 30y 102 90600 109 90500 LLNL ACTL LLNL ACTL 7 47 he 47106 30 47106 31 47107 30
609. y specified for that decay group are then sampled Since the functionality in MCNP to produce delayed neutrons using appropriate emission data is new we include next a somewhat more expanded description A small but important fraction 190 of the neutrons emitted in fission events are delayed neutrons emitted as a result of fission product decay at times later than prompt fission neutrons MCNP users have always been able to specify whether or not to include delayed fission neutrons by using either v prompt plus delayed or prompt only However in versions of MCNP up through and including 4B all fission neutrons whether prompt or delayed were produced instantaneously and with an energy sampled from the spectra specified for prompt fission neutrons For many applications this approach is adequate However it is another example of a data approximation that is unnecessary Therefore Versions 4C and later of MCNP allow delayed fission neutrons to be sampled either analog or biased from time and energy spectra as specified in nuclear data evaluations The libraries with detailed delayed fission neutron data are listed in Table G 2 with a in the DN column The explicit sampling of a delayed neutron spectrum implemented in MCNP 4C has two effects One is that the delayed neutron spectra have the correct energy distribution they tend to be softer than the prompt spectra The second is that experiments measuring neutron de
610. y card A brief description of each one follows a Change current tally reference vector F1 current tallies measure bin angles relative to the surface normal They can be binned relative to any arbitrary vector defined with the FRV option b Gaussian energy broadening The GEB option can be used to better simulate a physical radiation detector in which energy peaks exhibit Gaussian energy broadening The tallied energy is broadened by sampling from the Gaussian E E the broadened energy the unbroadened energy of the tally a normalization constant and Gaussian width gt I The Gaussian width is related to the full width half maximum FWHM by Jis FWHM 24 n2 The desired FWHM is specified by the user provided constants a b and c where FWHM a b4E The FWHM is defined as FWHM 2 Eo 60056120439322 FWHM where is such that and f E is the maximum value of c Time convolution Because the geometry and material compositions are independent of time except in the case of time dependent temperatures the expected tally 7 t t at time t from a source particle emitted at time tis identical to the expected tally 7 0 from a source particle 2 106 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS TALLIES emitted at time 0 Thus if a calculation is performed with all source par
611. y density functions and cumulative density functions The index and the interpolation fraction r are found on the incident energy grid for the incident energy Ej such that lt Ej and Ein 4 Ej The tabular distribution at each E may be composed of discrete lines a continuous spectra or a mixture of discrete lines superimposed on a continuous background If discrete lines are present there must be the same number of lines given one per bin in each table The sampling of the emission energy for the discrete lines if present is handled separately from the sampling for the continuous spectrum if present A random number on the unit interval 0 1 is used to sample a second energy bin k from the cumulative density function If discrete lines are present the algorithm first checks to see if the sampled bin is within the discrete line portion of the table as determined by Og tT pop a Eq tte El LED If this condition is met then the sampled energy for the discrete line is interpolated between incident energy grids as E Ej E iLk fup If a discrete line has been sampled the energy sampling is finished If a discrete line has not been sampled the secondary energy is sampled from the remaining continuous background For continuous distributions the secondary energy bin k is sampled from epp op s where l iif gt rand i if and 5jis a random number
612. y it is done but also by becoming the repositories for physics knowledge MCNP represents over 500 person years of sustained effort The knowledge and expertise contained in MCNP is formidable Current MCNP development is characterized by a strong emphasis on quality control documentation and research New features continue to be added to the code to reflect new advances in computer architecture improvements in Monte Carlo methodology and better physics models MCNP has a proud history and a promising future B MCNP Structure MCNP is written in ANSI Standard Fortran 90 22 Global data is shared via Fortran modules See Appendix E for a list of data modules and their purposes The general internal structure of MCNP is as follows Initiation IMCN Read input file INP to get dimensions e Set up variable dimensions or dynamically allocated storage Re read input file INP to load input Process source Process tallies Process materials specifications including masses without loading the data files Calculate cell volumes and surface areas Interactive Geometry Plot PLOT Cross section Processing XACT Load libraries 2 4 10 3 05 CHAPTER 2 GEOMETRY DATA PHYSICS AND MATHEMATICS INTRODUCTION Eliminate excess neutron data outside problem energy range Doppler broaden elastic and total cross sections to the proper temperature if the problem temperature is higher than the library temperature Proce
613. yes Sc 45 21045 60c 44 5679 endf60 B VI2 1992 293 6 105627 10639 20 0 yes 21045 62c 44 5679 actia B VL8 X 2000 293 6 267570 22382 20 0 yes 21045 66c 44 5679 endf66a B VL2Z X 1992 293 6 256816 22383 20 0 yes Ti nat 22000 42c 47 4885 192 LLNL 1992 300 0 8979 608 30 0 yes 22000 50c 47 4676 endf5u B V 0 1977 293 6 54801 4434 200 yes 22000 50d 47 4676 dre5 0 1977 293 6 10453 263 20 0 yes 22000 51d 47 4676 drmccs B V 0 1977 293 6 10453 263 20 0 yes 22000 51 47 4676 rmccs B V 0 1977 293 6 31832 1934 20 0 yes 22000 60c 47 4676 endf60 B VLO 1977 293 6 76454 7761 200 yes 22000 61c 47 4676 actib B VL8 2000 77 0 131345 11427 200 yes 22000 62c 47 4676 actia 8 2000 2936 125641 10859 200 yes 22000 64c 47 4676 endf66d B VLO 1977 77 0 131040 11428 200 yes 22000 66c 47 4676 endf66a B VLO 1977 293 6 125336 10860 20 0 yes V nat 23000 50d 50 5040 dre5 0 1977 293 6 8868 263 20 0 23000 50 50 5040 endf5u 0 1977 293 6 38312 2265 20 0 yes 23000 51 50 5040 rmccs 0 1977 293 6 34110 1899 200 yes 23000 51d 50 5040 drmccs 0 1977 293 6 8868 263 20 0 23000 60 50 5040 endf60 B VLO 1988 293 6 167334 8957 20 0 yes 23000 62c 50 5040 actia B VL8 2000 293 6 198692 10393 20 0 yes 23000 66c 50 5040 endf66a B VLO 1988 293 6 192051 10393 20 0 yes 10 3 05 no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no
614. yes yes no yes yes no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no yes yes no no no no no no no no no no no no no no no no no no no no G 23 APPENDIX G MCNP DATA LIBRARIES NEUTRON CROSS SECTION LIBRARIES ZAID Continuous Energy and Discrete Neutron Data Libraries Maintained by X 5 AWR Ag 09 47109 42c 47109 50c 47109 50d 47109 60 47109 66 7 48 107 9692 107 9690 107 9690 107 9690 107 9690 Cd nat 48000 42 48000 50d 48000 50c 48000 51c 48000 51d Cd 106 48106 65c 48106 66c Cd 108 48108 65c 48108 66c 4 110 48110 65 48110 66 Cd 111 48111 66 4 112 48112 65 48112 66 4 113 48113 66 4 114 48114 65 48114 66 4 116 48116 65 48116 66 7 49 111 4443 111 4600 111 4600 111 4600 111 4600 105 0000 105 0000 106 9770 106 9770 108 9590 108 9590 109 9520 110 9420 110 9420 111 9300 112 9250 112 9250 114 9090 114 9090 n nat 49000 42 49000 60 49000 66 7 49 50 113 8336 113 8340 113 8340 fp 49120 42 49125 42 50120 35 50120 35 7 50 CAC 116 49
615. zero The reason is simply that the volume of the artificial sphere is infinite in a void Contributions to the detector from the other direction that is across the material will be accounted for Detectors differing only in are coincident detectors see page 2 103 and there is little cost incurred by experimenting with several detectors that differ only by in a single problem 2 Ring Detector A ring detector tally is a point detector tally in which the point detector location is not fixed but rather sampled from some location on a ring Most of the previous section on point detectors applies to ring detectors as well In MCNP three ring detector tallies FX FY and FZ correspond to rings located rotationally symmetric about the x y and z coordinate axes A ring detector usually enhances the efficiency of point detectors for problems that are rotationally symmetric about a coordinate axis Ring detectors also can be used for problems where the user is interested in the average flux at a point on a ring about a coordinate axis Although the ring detector is based on the point detector that has a 1 R singularity and an unbounded variance the ring detector has a finite variance and only a 1 R singularity where R 118 min 18 the minimum distance between the contributing point and the detector ring In a cylindrically symmetric system the flux is constant on a ring about the axis of symmetry Hence one can sample un

MCNP User Manual, Version 5

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