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The OPAL Framework - The AMAS Group

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1. This warning could be issued if the filename is mistyped or otherwise if the file couldn t be read KKK RK KKK WA RN I N Gok RRR kk kk kk ok kk kk kk kk kk kk ke ko ke ke ke THERE SEEMS TO BE SOMETHING WRONG WITH YOUR FIELDMAP file t7 Could not determine the file type Please check the section about field maps in the user manual ck ck ck ck ck ck ck ck ck ck Ck Ck CK CK CK CK CK 00e Se Se Sek kk Sk In this case OPAL Tdidn t recognise the string of characters which identify the type of field map stored in the file C 2 Types and Format The file format used for the field maps is derived from the T7 file format as produced by Superfish 43 but also ASTRA type of field maps are supported A valid field map consists of a few header lines and a rest representing regularly spaced interpolation points either in ID 2D or 3D ASTRA field maps consist of one or two header lines not supported by ASTRA and possibly non equidistant interpolation points In the case of 2D and 3D field maps the fields at a given position are calculated by linear interpolation from the nearest grid points In the case of 1D field maps a Fourier transformation is used to calculate the longitudinal derivatives of the on axis field From these the fields at any position in space are calcula
2. is Ba Mentor rarepsion s Nene acrin z Car yeaz Cae yee ma pee x From arces scat s Mean Soma emit ine Mean Sigme Emit ee a e Fre Sie screen Sice s ev sies Soroen Figure 1 4 H5PartROOT enables a variety of data analysis and post processing task on OPAL data 1 5 Output The data is stored in the H5hut file format http h5part web psi ch and can be analysed using the H5PartRoot http amas web psi ch tools H5PartROOT index html The frequency of the data output phase space and some statistical quantities can be set using the OPTION statement see 87 3 statement and the flag PSDUMPFREQ The file is named like in input file but the extension is h5 An ASCII file with statistical beam parameters is stored ina stat file An SDDS file output is in preparation 1 6 ACKNOWLEDGEMENTS 17 1 6 Acknowledgements The contributions of various individuals and groups are acknowledged in the relevant chapters however a few individuals have or had considerable influence on the development of OPAL namely Chris Iselin John Jowett Julian Cummings Ji Qiang Robert Ryne and Stefan Adam For the HSPARTROOTvisualization tool credits go to Thomas Schietinger The effort to couple FEMAXX to OPAL wa
3. KX2IPHVS SurfacePhysics TYPE z Collimator MATERIAL Graphite KXOI ECollimator L 0 09 ELEMEDGE 0 01 APERTURE 0 003 0 003 OUTEN KXOLh5 SURFACE PHYSICS KXIIPHYS 5 Slit L 0 09 ELEMEDGE 0 01 APERTURE 0 005 0 003 SURFACEPHVSICS KX2IPHVS FX16 Slit L 0 09 ELEMEDGE 0 01 APERTURE 0 005 0 003 SURFACEPHYSICS KX2IPHVS FX is a slit in x direction the APERTURE is POSITIVE the first value in APERTURE is the left part the second value is the right part FX16 is a slit in y direction the APERTURE is NEGTIVE the first value in APERTURE is the down part the second value is the up part 18 5 A Simple Test cold Gaussian beam with o oy 5 mm The position of the collimator is from 0 01 m to 0 1 m the half aperture in y direction is 3 mm Fig 18 5 shows the trajectory of particles which are either absorbed or deflected by a copper slit As a benchmark of the collimator model in OPAL Fig 18 6 shows the energy spectrum and angle deviation at z 0 1 m after an elliptic collimator 18 5 A SIMPLE TES 0 02 0 015 0 01 0 005 y m E 0 005 0 01 0 015 0 02 10 10 10 0 0 01 308 U m 01 z m Figure 18 5 The passage of protons through the collimator T 10 r r r o o FLUKA 5 OPAL 5107 4 L 3 E 5 9 20 S gs 10 F 4 4 996 L Biot 3909000005500 1 4 8
4. 107 12 6 Define Greens Function v sso y Roo xU eR e YR oS 107 12 7 Define Bounding Box Enlargement es 108 12 9 Define Geometry 4o EUr web d ber p Rod vni 108 12 9 Define Iterative Solver 55520559958 BR UY WOO gt Odo om 108 12 10Define Interpolation for Boundary 109 12 1 Dehine Lolerance CRUS UR ev ede REGI 109 12 12Define Maximal Iterations 109 12 13Define Preconditioner Behaviour 109 12 14Define the number of Energy 109 13 Wakefields 111 Wakefield Command i DAE Me E ta ee be U A 112 13 2 Define the Wakefield to be used 112 13 3 Define the wakefield 2 2 2 112 13 4 Define the number 5 2 2 2 113 13 5 Define the bunch length to be constant 113 13 6 Definetheconductivity e 113 13 7 Defin ithempeddn e 3 sodes ec RU ecu gres duse 113 13 8 Define the form of the beam pipe eA 113 13 9 Define the radius of the beam pipe 113 13 10Define the of the beam
5. 8 14 2 OPAL cYcEmode Luo om 8 15 Septum a tmm o a ia 8 16 Probe OPAI CY CL ai Ee gus dem e aad amp Bd ha xo tem OE STI Stupper OPAE CYCLhl 4 Roe ie B eer Se Pa 10 Beam Lines 9 1 9 2 Simple Beam Lines Sub lines Phvsics Commands 10 1 BEAM Command 66 67 67 68 68 68 68 68 69 69 69 69 69 70 70 70 73 73 73 75 76 80 81 81 81 83 84 86 86 86 88 89 91 91 92 93 93 94 97 97 97 99 6 CONTENTS 11 Distribution Command 101 11 1 Correlations for Gaussian Distribution 103 Example oa es And Sat 104 112 Thermal Emittance estas ween trt pie RAE RE 104 11 3 Hattop Distiibutioni ARENIS EU 105 11 344 Legacy Mod be Ss bv Dm ETE Gr Iren A eee Ses 106 12 Fieldsolver 107 12 1 Fieldsolver Command sro RE RU OE AE UY m Xs 107 12 2 Define the Fieldsolver to 107 12 3 Define Domain Decomposition ee 107 12 4 Define Number of Gridpoints 22s 107 12 5 Define Boundary Conditions
6. 6 8 2 Symbolic constants OPALrecognises a few built in mathematical and physical constants see Tab 6 8 Their names must not be used for user defined labels Additional symbolic constants may be defined see 87 4 2 to simplify their repeated use in statements and expressions 6 8 3 Variable labels Often a set of numerical values depends on a common variable parameter Such a variable must be defined as a global variable see 7 4 1 defined by one of X expression X expression VECTOR X vector expression VECTOR X vector expression When such a variable is used in an expression OPA Luses the current value of the variable When the value is a constant or an expression preceded by the delimiter it is evaluated immediately and the result is assigned to the variable as a constant When the value is an expression preceded by the delimiter the expression is retained and re evaluated whenever one of its operands changes Example L 1 0 X L D1 DRIFT L X D2 DRIFT L 2 0 X When the value of X is changed the lengths of the drift spaces are recalculated as X and 2 respectively 6 8 OPERANDS IN EXPRESSIONS Table 6 8 Predefined Svmbolic Constants OPALname Mathematical svmbol Value Unit PI 3 1415926535898 1 TWOPI 2 6 2831853071796 1 DEGRAD 180 57 295779513082 deg rad RADDEG 7 180 017453292519943 rad deg E e 2 7182818284590 1 EMASS m e 51099906e 3 GeV PMASS m p 93
7. Didn t find enough values If OPAL T expects more values on this line Found more values than expected If OPAL T expects less values on this line Found wrong type of values If OPAL T found e g characters instead of an integer number Again there seems to be something wrong with the number of grid spacings provided in the header In this example OPAL Tfound more lines than it expected Note that comments and empty lines at the end of a file are ignored such that they don t cause this warning WA RN I N Gk RK kk ck RR kk kk kk ck kk koe THERE SEEMS TO BE SOMETHING WRONG WITH YOUR FIELD MAP file t7 error msg expecting expecting on line 3 found instead found ck ck ck Ck Ck Ck C CK CK CK CK CK 00K CK Sek Sk kk kk Sk Sk kk kk Sk Ck ck ck Ck Ck Ck Ck Ck kk Sk Sk Sk kx k amp k amp x kx kx Where error msg is either _expecting_ is replaced by the types of values OPAL Texpects on the line E g it could be replaced by double double int Finally _found_ is replaced by the actual content of the line without any comment possibly following the values If line 3 of a file consists of 60 0 60 0 4 This is an other invalid comment 4 9999 OPAL Twill output 60 0 60 0 KKK KKK KK WA I N G kK KK kk kk kk ok kk kk kc koc ko ke kk kk DISABLING FIELD MAP file t7 SINCE FILE COULDN T BE FOUND ck ck ck
8. 113 13 11 Define the relaxation time of the beam pipe 113 13 12Import a wakefield from a file 113 13 13 Wake Bunctions REC UR eae BE AI 114 hok etm A SM ea i KO AN CR Ea Uta i RS 114 14 Geometry 117 Geometry Command MS E RBS wel d eue wd uve deb weit 117 142 Definethe Geometry File XP a 117 14 3 Define the Length s o area fr eR Ee emet oberg RUE RAD wea 117 14 4 Denne the Start e mpa qox ek Oa A RUN UR CA ev Pede a onum Os Tode 118 14 5 Define the Semi Major Axis 118 14 6 Define the Semi Minor Axis 118 15 Tracking 119 Ts Track Mode oe sa ace ocho De EV I Rer Ae stove Ru ce RE SEN Aun 119 15 1 4 Track Random Machine 121 CONTENTS 16 17 18 Field Emission 16 1 Field Emission Multipacting 17 1 Commands Related to Multipacting Simulation 17 2 Run Parallel Plate Benchmark 173 PostPfocessmg v6 eb ey at oe we ee Pew ae Be Physics Models Used in the Particle Matter Interaction Model 18 Enerev 20555 m oh A a RUD ee Aree ced e Pu eae 18 2 The Cou
9. EMISSION type of distribution can be used to customize the type and the parameters of sec Title Option Option Option TFS FALSE ECHO FALSE INFO FALSE Option Option Option Option PSDUMPFREQ 1 STATDUMPFREQ 1 PPDEBUG FALSE SURFDUMPFREQ 100 Set an upper limit of simulation particle number to prevent memorv overflow MAXPARTSNUM 1000000 SECONDARYFLAG 1 Using Furman Pivi s model SURFMATERIAL 0 surface material is copper Set NEMISSIONMODE false will use re normalize simulation particle approach Set the field enhancement factor FNBETA to a very small number to prevent field emission DistSurf DISTRIBUTION DISTRIBUTION SURFACEEMISSION 2 NPDARKCUR 0 INWARDMARGIN FNBETA 0 1 SECONDARYFLAG 1 NEMISSIONMODE false SURFMATERIAL 0 0 0 INWARDMARGIN seed electron positions along the inward normal w r t the boundary surface DistSurfl DISTRIBUTION DISTRIBUTION INWARDMARGIN EINITHR 0 227 SURFACERANDCREATE 0 0 NPDARKCUR 10000 For multipacting study of cyclotron cavity the axis z in geometry file is actually axis y in ParallelTTracker so we need to shift z coordinates of the geometry by specifying ZSHIFT to ma sure that the z coordinates read in by ParallelTTracke will be correct GEOMETRY FGEOM ZSHIFT 0 631 10 h5 5 0 0 DISTRS DistSurf DistSurfl string Cyclotron Multipacting Simu
10. straight reference 5 ANGLE 0 001 Deflection to the left 5 0 0 001 5 5 Deflection to the left This magnet has a straight reference ELE au BL SBEND L BL SBEND L ou 8 4 BENDING MAGNETS 79 U ele u El Figure 8 1 Visualisation of angles used to rotate the bend relative to the incoming beam where n is the normal of the face 80 CHAPTER 8 ELEMENTS 8 5 Quadrupole label QUADRUPOLE TVPE string APERTURE real vector L real Kl real K1S real The reference system for a quadrupole is a Cartesian coordinate system see Fig 77 This is a restricted feature Ka OPAL CYCL A QUADRUPOLE has three real attributes L The quadrupole length default 0 m The normal quadrupole component 25 KIS The skew quadrupole component Ki 2B FMAPFN Field maps in the 77 format can be specified This field map has to be of type 3DMagnetoStatic ELEMEDGE The edge of the field is specified absolute floor space co ordinates in m Example QPI Quadrupole L 1 20 ELEMEDGE 0 5265 FMAPFN 1T1 T7 1 0 11 8 6 SEXTUPOLE 81 8 6 Sextupole OPAL T label SEXTUPOLE TYPE string APERTURE real vector L real K2 real K2S real A SEXTUPOLE has three real attributes L The sextupole length default 0 m A thin sextupole see is defined by setting the length to zero 2 K2
11. All the three working modes of OPAL CYCL use an input file written in MAD language which will be described in detail in the following chapters For the Tune Calculation mode one additional auxiliary file with the following format is needed 72 000 2131 4 0 240 74 000 2155 1 0 296 76 000 2179 7 20319 78 000 2204 7 0 309 80 000 2229 6 0 264 82 000 2254 0 0 166 84 000 2278 0 0 025 In each line the three values represent energy FE radius and P for the SEO Static Equilibrium Orbit at starting point respectively and their units are MeV mm mrad A bash script tuning sh is shown on the next page to execute OPAL CYCLfor tune calculations 5 10 OUTPUT 43 fl bin bash rm rf tempfile rm f plotdata rm f tuningresult exec 6 FIXPO SEO N 260 Jari while read u 6 El r pr read in Energy initil R and intial Pr of each SEO from FIXPO output do rm rf tempfile echo n j echo j echo n energy tempfile echo n SEI gt gt tempfile echo gt gt tempfile echo n gt gt tempfile echo n r gt gt tempfile echo gt gt tempfile echo n gt gt tempfile echo n pr tempfile echo tempfile execute OPAL to calculate tuning frquency and store opal testcycl in commlib mpi info 0 grep gt gt tuningresult j 3 1 done exec 6 amp rm rf tempfile f post porcess exec 8 tuningresult rm f plotdata i 0 whi
12. BBOXINCR GEOMETRY ITSOLVER INTERPL TOL MAXITERS PRECMODE Specify the type of field solver If TRUE the dimension x is distributed among the processors If TRUE the dimension y is distributed among the processors If TRUE the dimension z is distributed among the processors Number of grid points in z specifying rectangular grid Number of grid points in y specifying rectangular grid Number of grid points in z specifying rectangular grid Boundary condition in z OPEN Boundary condition in y OPEN Boundary condition in z OPEN PERIODIC Defines the Greens function for the FFT Solver Enlargement of the bounding box in 96 Geometry to be used as domain boundary Type of iterative solver Interpolation used for boundary points Tolerance for iterative solver Maximum number of iterations of iterative solver Behaviour of the preconditioner 12 7 Define Bounding Box Enlargement The bounding box defines a minimal rectangular domain including all particles With BBOXINCR the bounding box can be enlarged by a factor given in percent of the minimal rectangular domain 12 8 Define Geometry The list of geometries defining the beam line boundary For further details see Chapter 14 12 9 Define Iterative Solver The iterative solver for solving the preconditioned system BICGSTAB or GMRES 12 10 DEFINE INTERPOLATION FOR BOUNDARV POINTS 109 12 10 Define Interpolation for Boundary Points The interpola
13. It mav contain functions see Tab 6 5 Parentheses indicate operator precedence if required Constant sub expressions are evaluated immediatelv and the result is stored as a constant 6 7 Operators An expression can be formed using operators see Tab 6 4 and functions see Tab 6 5 acting on operands see 86 8 Table 6 4 Real Operators in OPAL Operator Meaning result type operand type s Real operators with one operand tX unary plus returns X real real X unary minus returns the negative of X real real Real operators with two operands add X to Y real real real X Y subtract Y from X real real real X Y multiply X by Y real real real X 4 X divide X by Y real real real Xo KY power return X raised to the power Y Y gt 0 real real real Table 6 5 Real Functions in OPAL Function Meaning result type argument type s Real functions with no arguments RANF random number uniform distribution in 0 1 real GAUSS random number Gaussian distribution witho 1 real USERO random number user defined distribution real ST arc length from start of ring to the entry of the current element This function is only real available in the EALIGN command see 82 SC arc length from start of ring to the centre of the current element This function is only real available in the EALIGN command see 522 SO arc length from start of rin
14. X Horizontal position x of a particle relative to the axis of the element m PX 5 7 Horizontal canonical momentum 1 Y Horizontal position y of a particle relative to the axis of the element m PY B Horizontal canonical momentum 1 Z Longitudinal position z of a particle in floor co ordinates m PZ 2 Longitudinal canonical momentum 1 The independent variable is t s 31 32 CHAPTER 4 OPAL T 4 3 Integration of the Equation of Motion OPAL T integrates the relativistic Lorentz equation dyv dt where 7 is the relativistic factor q is the charge and m is the rest mass of the particle E and B are abbreviations for the electric field E x t and magnetic field B x t 1 Eext Esc Bext RE B 4 1 4 4 Envelope Tracker The OPAL e Envelope Tracker is an algorithm used to solve the envelope equations of a beam propagating through external fields and under the influence of its own space charge The algorithm is based on the multi slice analysis approach used in the theory of emittance compensation 62 The space charge model used can be switched between an analytic model derived and used in HOMDYN 63 and a similar model developed at PSI called Beam Envelope Tracker BET 4 5 Space Charge Space charge effects will be included in the simulation by specifying a field solver described in Chapter 12 and using the solver in the track command described in Chapter 15 By default the code does not assume any
15. 0 2 26 38 CHAPTER 5 OPAL CYCL where B B r 90 0 and 9 18 B 1 OB 1 B 1 B ro r3 r r2 Or r2 002 r3 002 1928 1B m ds uo o 0 Ho NOE mv Or Or r2 0027 All the partial differential coefficients are on the median plane and can be calculated by interpolation OPAL CYCL uses Lagrange s 5 point formula The other situation is to calculate the field on the median plane or the 3D fields of the working gap for interesting region numerically by creating 3D model using commercial software such as TOSCA ANSOFT and ANSYS during the design phase of a new machine If the field on the median plane is calculated the field off the median plane can be obtained using the same expansion approach as the measured field map as described above However the 3D fields of the entire working gap should be more accurate than the expansion approach especially at the region not so close to the median plane in Z direction In the current version we implemented the three specific type field read functions Cyclotron getFieldFromFile of the median plane fields That which function is used is controlled by the parameters TYPE of CYCLOTRON see Section 8 10 in the input file 5 41 CARBONCYCL type If TYPE CARBONCYCL the program requires the B data which is stored in a sequence shown in Fig 5 1 We Figure 5 1 2D field map on the median plane with primary direction correspo
16. 2DMagnetoStatic ZX 0 0 2 0 199 3 50 51 0 999 00000e 00 0 00000e 00 00000e 00 4 36222e 06 00000e 00 8 83270e 06 999 994 lines 00000 00 1 32490 05 00000 00 1 73710 05 00000 00 2 18598 05 eor e 47 eo Figure C 12 A 2D field map describing a magnetostatic field using 5 000 grid points in longitudinal direction times 200 grid points in transvers direction The field between the grid points is calculated with a bilinear inter polation The field is non negligible from 3 0 cm to 51 0 cm relative to ELEMEDGE and the 200 grid points in transverse direction span a length of 2 0 cm The field values are ordered in ZX orientation the index in transvers direction changes fastest on the first column the B values are stored on the second the B values 178 10 2DDynamic APPENDIX C OPAL T FIELD MAPS 2DDynamic 2 3 0 51 0 40121 1498 953425154 0 0 1 0 75 313 266 lines 0 00000 00 0 00000e 00 36222e 06 0 00000e 00 83270 06 0 00000e 00 32490 05 0 00000e 00 73710 05 0 00000e 00 18598e 05 0 00000e 00 e e 00000 00 00000 00 00000 00 00000 00 00000 00 00000 00 p 00000e 00 ISO 2 IG soe 06016 32490 05 18598 05 Figure C 13 2D field map describing a dynamic field oszillating with 1 498953425154 GHz The field map provides 4122 grid points in longit
17. logical real real Xx EY true if X is equal to Y logical real real x L y true if X is not equal to Y logical real real X amp amp Y true if both X and Y are true logical logical logical X Y true if at least one of X and Y is true logical logical logical 49 X210 Y 20 22215 6 6 Real Expressions To facilitate the definition of interdependent quantities any real value can be entered as an arithmetic expression When a value used in an expression is redefined by the user or changed in a matching process the expression is re evaluated Expression definitions may be entered in any order OPALevaluates them in the correct order before it performs any computation At evaluation time all operands used must have values assigned A real expression can occur in real arrays see 6 14 2 A real expression is built from operators see Tab 6 4 and operands see 86 8 real ref table ref primary factor term real expr real variable real array index object gt real attribute object gt real array attribute index table G place gt column name literal constant symbolic constant real ref table ref function name arguments real expression primary factor primary factor term factor term factor term term term 50 CHAPTER 6 COMMAND FORMAT real expr term real expr term l
18. 0 ME Eo k 0 56 lt 1 k 0 25 for 1 lt v lt 3 6 127 max 8 max 0 x 1 ko0 2 0 Emazx 0 l kr07 2m The secondary emission yield value for an impacting electron energy E and incident angle 0 w r t the surface normal is denoted as 0 Parameter kg and kg denotes the dependence on surface roughness Both should be assigned a default value of 1 0 which appears appropriate for typical dull surfaces in a working tube environment and lower values down to zero or higher values up to about 2 0 are only valid for specified cases 57 E naz 0 is the impacting energy when incident angle is zero and secondary yield reaches its maximum value Ep is an adjustable parameter to make the first crossover energy be fitted to the experiment data 59 is the user specified constant denote the SEY of low impacting energy The emission energy obeys the thermal energy distribution E fle ep TA TP ir 17 3 The polar angles of emitted secondaries 0 0 7 2 are with probability density cos 0 and the azimuthal angles 0 27 are with uniform probability density These emission angles of the secondary electrons is relative to the local coordinate system which is centered at the collision point and whose z axis is along the inward normal of the surface Motivated by the fact that the population of particles in simulation domain may continually grow exponen tially and lead to
19. 0 000275 2 sigmapx 0 0 corrx 0 0 sigmay 0 000275 2 sigmapy 0 0 corry 0 0 sigmat 0 0 pt 0 0 sigmapt 0 0 corrt 0 0 tRise 0 7e 12 tFall 0 7e 12 tPulseFWHM 9 9e 12 ekin 0 63 NBIN 50 DEBIN 80 where t Rise olive in Figure 1 tFall and tPulseFWHM FWHM p red in Figure 1 in seconds s define the shape of the Gauss Flattop distribution The default cutoff is 3 0 This can be changed by adding e g cutoff 4 0to the distribution command 11 3 1 Legacy Mode We provide a legacy mode for flattop distribution The following old input specification SRise 0 7e 12 SFall 0 7e 12 CRise 3 0 CFall 3 0 TFlatTop 9 9 12 0 925 TEmis TFlatTop 4 CRisex SRise 4 CFallx SFall value TFlatTop TEmis Distl DISTRIBUTION DISTRIBUTION GUNGAUSSFLATTOPTH sigmax 0 000270 2 0 sigmapx 0 0 corrx 0 0 sigmay 0 000270 2 0 sigmapy 0 0 corry 0 0 sigmat 0 0 pt 0 0 sigmapt 0 0 corrt 0 0 ekin 0 4 sigmarise 0 7 12 sigmafall 0 7e 12 flattoptime 9 9 12 0 925 cutoffrise CRise cutofffall CFall TEMISSION TEmis NBIN 10 DEBIN 80 can be replaced bv stl DISTRIBUTION DISTRIBUTION GUNGAUSSFLATTOPTH sigmax 0 000275 2 sigmapx 0 0 corrx 0 0 sigmay 0 000275 2 sigmapy 0 0 corry 0 0 sigmat 0 0 pt 0 0 sigmapt 0 0 corrt 0 0 ekin 0 4 tRise 0 7e 12 tFall 0 7e 12
20. 29 30 CHAPTER 3 TUTORIAL Chapter 4 OPAL T 4 1 Introduction OPAL T is a fully three dimensional program to track in time relativistic particles taking into account space charge forces self consistently in the electrostatic approximation and short range longitudinal and transverse wake fields OPAL T is one of the few codes that is implemented using a parallel programming paradigm from the ground up This makes OPAL T indispensable for high statistics simulations of various kinds of existing and new accelerators It has a comprehensive set of beamline elements and furthermore allows arbitrary overlap of their fields which gives OPAL T a capability to model both the standing wave structure and traveling wave structure Beside IMPACT T it is the only code making use of space charge solvers based on an integrated Green 40 function to efficiently and accurately treat beams with large aspect ratio and a shifted Green function to efficiently treat image charge effects of a cathode 39 41 For simulations of particles sources i e electron guns OPAL T uses the technique of energy binning in the electrostatic space charge calculation to model beams with large energy spread In the very near future a parallel Multi Grid solver taking into account the exact geometry will be implemented 4 2 Variables in OPAL T OPAL Tuses the following canonical variables to describe the motion of particles The physical units are listed in square brackets
21. 6 3 L Lateral Constants 4 4 vun RE Rex mie ae use e e ede 32 6 8 2 Symbolic Constants 52 6 39 35 Variable labels RD ea ee RB e e RR 52 6 8 4 Element or command attributes 53 6 8 5 Deferred Expressions and Random 53 6 3 6 Table References som eC RU m BONE So De Bi 54 6 9 Element Selection e a UAM UK UNA ee a E ee OR 54 GOT Element Selection xi ou ek eed ee IN ORO Bed Sn 54 69 2 RangeSelection x suene ck Eure Dm Rep m Bo Boe wh ees 55 6 10 Constraints 2 52 em m e EORR SUUS Re ee ie 56 Variable Names mo acere Eze CPU HAE be Ret ee x ur IR Ara 56 6 12 Regular Expressions i re Eu dep opu wu dev Ra m e Rd 56 6 13 Token List 57 6 14 A FAVS botti be gh Baa Aes eR vm a cR b A eG 57 6 14 T gt EE E Ie e Et 57 6342 Real Afr ys mee ns BE ede d Ep SE 57 6 14 3 St ng ArraysS z sb ose RE Rex OS EUR ee bus 60 6 14 4 Token List ATAY Se cc coe eden EHqG 25 60 Control Statements 61 JA Helps 5 et ve UR vie her ERR RO IR
22. A B C D E B A C D E A B 2 Omit parentheses A B C D E B A C D E A B valuated to constants immediatelv Chapter 10 Phvsics Commands 10 1 BEAM Command All OPAL commands working on a beam require the setting of various quantities related to this beam These are entered by a BEAM command label BEAM PARTICLE name MASS real CHARGE real ENERGY real PC real GAMMA real EX real EXN real EY real EYN real BCURRENT real ET real KBUNCH integer NPART real BUNCHED logical RADIATE logical DAMP logical QUANTUM logical The label is opional it defaults to UNNAMED_BEAM The particle mass and charge are defined by PARTICLE The name of particles in the machine OPAL knows the mass and the charge for the following particles POSITRON The particles are positrons MASS m CHARGE 1 ELECTRON The particles are electrons MASS m CHARGE 1 PROTON The particles are protons default MASS m CHARGE 1 ANTIPROTON The particles are anti protons MASS m CHARGE 1 HMINUS particles are h protons MASS m h7 CHARGE 1 CARBON The particles are carbons MASS m CHARGI 12 URANIUM particles are of type uranium MASS m 35 MUON The particles are of type muon MASS m CHARGE 1 DEUTERON The particles are of type deuteron MAS S mq CHARGE 1 XENON The particles of type xenon
23. D CMAKE BUILD TYPE STRING DEBUG X D TPL ENABLE SuperLUDist BOOL ONX D TPL ENABLE MPI BOOL ON D TPL ENABLE BLAS BOOL ON X D TPL ENABLE LAPACK BOOL ON D TPL ENABLE ParMETIS BOOL ON D TPL ENABLE METIS BOOL OFF D BLAS LIBRARY DIRS PATH MKL LIB DIR D BLAS INCLUDE DIRS PATH MKL INCLUDE X D BLAS LIBRARY NAMES STRING mkl blas95 1p64 X mkl intel 1p64 mkl intel thread mkl core pthread guide X 4nttp trilinos sandia gov A 4 ENABLING THE MULTIGRID SPACE CHARGE SOLVER 149 LAPACK LIBRARY DIRS PATH MKL LIB DIR X LAPACK INCLUDE DIRS PATH MKL INCLUDE LAPACK LIBRARY NAMES STRING mkl lapack X ParMETIS INCLUDE DIRS PATH PARMETIS INCLUDE ParMETIS LIBRARY DIRS PATH PARMETIS LIBRARY ParMETIS LIBRARY NAMES STRING parmetis metis ParMETIS LIBRARIES STRING parmetis metis TPL BLACS INCLUDE DIRS FILEPATH gpfs homefelsim kraus include X BLACS LIBRARY DIRS FILEPATH S MKL LIB DIR TPL BLACS LIBRARIES opt intel mkl mkl 10 2 1ib em64t libmkl blacs 1p64 a X opt intel mkl mkl 10 2 1ib em64t libmkl blacs ilp64 a X D SuperLUDist INCLUDE DIRS FILEPATH X gpfs homefelsim kraus extlib SuperLU DIST 2 5 include X D SuperLUDist LIBRARY DIRS FILEPATH X gpfs homefelsim kraus extlib SuperLU DIST 2 5 lib D SuperLUDist LIBRARY NAMES STRING superlu dist 2 5 D SuperLUDist LIBRARIES superlu dist 2 5 TPL SuperLUDist LIBRARIES X gpfs
24. MASS2m e CHARGE 20 For other particle names one may enter MASS The particle mass in GeV CHARGE The particle charge expressed in elementary charges 100 CHAPTER 10 PHVSICS COMMANDS Chapter 11 Distribution Command TODO AA will rewrite Particle distributions can be read in or generated by specifying rms beam quantities The allowed parameters are described in Table 11 3 Particle distributions are generated separately in all three phase space planes There are limited correlations between planes e g between longitudinal and transverse r51 r52 r61 r62 Besides an efficient parallel Gaus sian distribution generator based on a parallelized Method of Rejection a more general algorithm for generating distributions is available 42 The shape of the binomial distribution is governed by one parameter m By varying this single parameter one obtains the most commonly used distributions for our type of simulations as listed in Table 11 1 If NBIN is larger than one the distribution is binned in energy and for each bin a separate field solve is performed when using the electrostatic solvers Table 11 1 Different distributions specified by a single parameter m m Distribution Density Profile 0 0 Hollow shell ta r 1 r 0 5 0 5 Flat profile a 1 r2 0 5 1 1 0 Uniform i 2 7705 1 5 Elliptical 2 1 r2 95 1 1 12 2 0 Parabolic 2 1 r2 ENGI _ 1 5
25. Token list see 56 13 Array see 6 14 of Logical see 86 14 1 Real see 6 14 2 String see 56 14 3 Token lists see 56 14 4 See also 6 4 Operators see Tab 6 4 Functions see Tab 6 5 Array functions see Tab 6 7 Real functions of arrays see Tab 6 9 Operand see 86 8 Random generators see 56 8 5 String Attributes A string attribute makes alphanumeric information available e g a title file name element class name or an option It can contain any characters enclosed in single or double quotes However if it contains a quote this character must be doubled Strings can be concatenated using the amp operator see Tab 6 1 An operand in a string can also use the function STRING see Tab 6 2 String values can occur in string arrays see 86 14 Examples 48 CHAPTER 6 COMMAND FORMAT Table 6 1 String Operator in OPAL Operator Meaning result type operand types X amp Y concatenate the strings X and Y String concatenations are always eval string string string uated immediatelv when read Table 6 2 String Function in OPAL Function Meaning result tvpe argument tvpe STRING X return string representation of the value of the numeric expression X string real TITLE This is a title for the program run test CALL FILE save X 1 TWISS LINE LEP amp STRING X 1 The second exam
26. ZSTART 2 ZEND 100 WIDTH 10 0 SURFACEPHVSICS cmphvs cma2 CCollimator XSTART x3 XEND x4 YSTART y3 YEND y4 ZSTART 2 ZEND 100 WIDTH 10 0 SURFACEPHVSICS cmphvs The particles lost on the CCLLIMATOR are recorded in the ASCII file input filename loss 8 15 Septum OPAL CYCL This is a restricted feature I 3 OPAL T The particles hitting on the septum is removed from the bunch There are 5 parameters to describe a septum XSTART The x cooradinate of the start point mm XEND The x cooradinate of the end point mm YSTART The y cooradinate of the start point mm YEND The y cooradinate of the end point mm WIDTH The width of the septum mm y xend yend septum width xstart vstart Example eec2 Septum xstart 4100 0 xend 4300 0 ystart 1200 0 vend 150 0 width 0 05 The particles lost on the SEPTUM are recorded in the ASCII file input filename loss 8 16 Probe OPAL CYCL The particles hitting on the probe is recorded There are 5 parameters to describe a probe XSTART The x coordinate of the start point mm XEND The x coordinate of the end point mm YSTART The y coordinate of the start point mm 94 CHAPTER 8 ELEMENTS XEND The v coordinate of the end point mm WIDTH The width of the probe NOT used vet y xstart vstart probe width xend vend Example probl Probe xstart 4166 16 xend 4250 0 ystart 1226 85 yend 1241 3 The particles pr
27. can be chosen of course depends on the importance of space charge effects DT Initial time step for tracking default value is 1 ps STEPSPERTURN The timsteps per revolution period Only available for OPAL CYCL default value is 720 15 1 TRACK MODE 121 In OPAL Tand OPAL MAP the commond format is TRACK LINE name BEAM name MAXSTEPS value DT value In OPAL CYCL instead of setting time step the timesteps per turn should be set The commond format is TRACK LINE name BEAM name MAXSTEPS value STEPSPERTURN value Particles are tracked in parallel i e the coordinates of all particles are transformed at each beam element as it is reached OPALleaves track mode when it sees the command ENDTRACK 15 1 1 Track a Random Machine This example shows how to track a random machine i e some parameters are random variables At the moment Version 1 1 4 there seams to be a problem when having random variables in the Distribution command Option SCAN TRUE I 0 WHILE I lt 3 1 RANF x4 7 rv2 0 0 rv3 0 0 rv4 0 0 rv5 0 0 Ppo PepperPot L 200 0E 6 ELEMEDGE 6 0E 3 R 1 0E 4 PITCH 0 5E 4 NHOLX 20 NHOLY 20 XSIZE 5 0E 3 YSIZE 5 0E 3 OUTFN ppo h5 Col ECollimator L 3 0E 3 ELEMEDGE 7 0E 3 XSIZE 7 5E 4 YSIZE 7 5E 4 OUTFN Coll h5 5 1 Solenoid L 1 20 LEMEDGE 0 5315 FMAPFN 1T2 T7 8 246 05 4 rv2 SP2 Solenoid L 1 20 LEMEDGE 0 397 FMAPFN
28. define particles distribution generate Gaussion type Distl DISTRIBUTION DISTRIBUTION gauss sigmax 2 0 03 sigmapx 1 0e 7 corrx 0 0 sigmay 2 0 03 sigmapy 1 0e 7 corrv 0 0 sigmat 2 0e 03 sigmapt 1 8e 4 corrt 0 0 define parallel FFT fieldsolver parallel in x y direction Fsl FIELDSOLVER FSTYPE FFT MX 32 MX 32 MT 32 PARFFTX true PARFFTY true PARFFTT false BCFFTX open BCFFTY open BCFFTT open BBOXINCR 5 define beam parameters beaml BEAM PARTICLE PROTON 0 SPACECHARGE true NPART 1e5 BCURRENT 3 0E 3 CHARGE 1 0 BFREQ frequency select beamline Select Line 11 start tracking track line 11 beam beaml MAXSTEPS nstepxturns STEPSPERTURN nstep TIMEINTEGRATOR LF 2 run file track output turns 1 method CYCLOTRON T beam beaml fieldsolver Fs1 distribution Disti endtrack Stop To run opal on single node just use this command f opal testinj2 2 in To run opal on N nodes in parallel environment interactivelv use this command instead f mpirun opal testinj2 2 in If restart a job from the last step of an existing 25 file add a new argument like this f mpirun np opal testinj2 2 in restart 1 Figure 3 3 and 3 4 are simulation results shown by HSROOT code 3 4 3 PSI Ring Cyclotron From the view of numerical simulation the difference between Injector II and Ring cyclotron comes from two aspects B Field The structure of Ring is totally s
29. seras aban A eo URS 3 4 3 PST Rang Cyclotron 5 mal Rt pewes iu ee Pee gems Us OPAL T AT Introduction Un ES Hb sut ue ade e Eel i d pups 4 2 Nanablesim OPAL T ER Sos edet ute ia d ede ders 4 3 Integration of the Equation of Motion 4 4 Envelope Tracker eoa pote Reg edm kubi Hee Rx Sens Rd eed os 4 Space Charge oh ro dup ue mode eb AI RNC vu SE beides 4 6 Wak Fieldsa a Eun oe reden is ERROR A dd 4 Multiple Spe iesi S obese t on dese e ah eaters ie RR ans eoi e as OPAL CYCL Introd ctlom s a vet ede s ULT elt ge vis 23 2 Tracking modes o9 s eo eere SUE LN a RA ER ARM deus 5 2 1 Single Particle Tracking mode 52 2 Tune Calculation mode 5 5 ge E Yeh UA Re UE 5 2 3 Multi particle tracking 3 3 Vatiablesin OPAL CYCE Gor rU A poe V WAVE Y Xy N 5 3 1 The initial distribution in the local reference DA Field Maps xu p ea Gee A a ete S S4 CARBONGYCE types s eg bla BA Boe ee eR 13 13 13 14 15 16 17 17 19 19 21 21 21 21 22 23 24 28 31 31 31 32 32 32 33 33 CONTENTS 2 42 CY CEAEyDE estuve ERA VERDE b Greta Bre i
30. so it is a quite different implementation than that found in OPAL MAP The following commands define these elements in OPAL Tmode Label SBEND FMAPFN string L real GAP real ANGLE real KO real KOS real Kl real ROTATION real El real E2 real BETA real ELEMEDGE real DESIGNENERGY real Label RBEND FMAPFN string L real GAP real ANGLE real KO real K0S real Kl real ROTATION real El real BETA real ELEMEDGE real DESIGNENERGY real FMAPFN Field maps in the 77 format can be specified This field map has to be of type 3DMagnetoStatic not yet implemented 1DProfilel or IDProfile2 See C2 It is possible also to use a default field map FMAPN IDPROFILEl DEFAULT In this case inter nal values for the Enge function coefficients are used These are obtained from 44 The fringe field is calculated using the function 1 F z XD 1 Where D is the full gap of the magnet n is the Enge function order and 2 is the distance from the zero of the Enge function perpendicular to the edge of the dipole For this default case n 5 and the Enge coefficients are from 44 8 1 0 478959 1 911289 1 185953 1 630554 c4 1 082657 cs 0 318111 If using the default one must set GAP to declare the full gap of the magnet and one must set L This last parameter sets the distance between Enge function zeros for the entrance and exit of the dipole This effectiv
31. symmetry i e full 3D In the near future it is planed to implement also a slice 2D model This will allow the use of less numbers of macro particles in the simulation which reduces the computational time significantly The space charge forces are calculated by solving the 3D Poisson equation with open boundary conditions using a standard or integrated Green function method The image charge effects of the conducting cathode are also included using a shifted Green function method If more than one Lorentz frame is defined the total space charge forces are then the summation of contributions from all Lorentz frames More details will be given in Version 1 1 9 FFT Based Particle Mesh PM Solver More details will be given in Version 1 1 9 Interpolation Schemes More details will be given in Version 1 1 9 Iterative Space Charge Solver This is a scalable parallel solver for the Poisson equation within a Particle In Cell PIC code for the simulation of electron beams in particle accelerators of irregular shape The problem is discretized by Finite Differences Depending on the treatment of the Dirichlet boundary the resulting system of equations is symmetric or mildly nonsymmetric positive definite In all cases the system is solved by the preconditioned conjugate gradient algo rithm with smoothed aggregation SA based algebraic multigrid preconditioning More details are given in 51 Energy Binning The beam out of a ca
32. 06380 FMAPFN av3 dat TYPE SINGLEGAP FREQ frequency3 ANGLE 315 0 PHIO phi06 RMIN 830 0 RMAX 3330 0 PDIS 0 0 GAPWIDTH 0 0 Pls Line inj2 rf0 rf1 rf2 rf3 rf4 rf5 define particles distribution read from file Distl DISTRIBUTION DISTRIBUTION fromfile FNAME PartDatabase dat usset define fieldsolver useless for single particle track mode Fsl FIELDSOLVER FSTYPE NONE MX 64 MY 64 MT 64 PARFFTX true PARFFTY true PARFFTT false BCFFTX open BCFFTY open BCFFTT open define beam parameters beaml BEAM PARTICLE PROTON 0 SPACECHARGE true NPART 1 BCURRENT 0 0 select beamline Select Line 11 25 26 CHAPTER 3 TUTORIAL 13 1 65 i l 161 1 55 B i 15 4 2 ss EE a 1 22 124 126 128 1 3 1 32 1 34 1 36 x mm Figure 3 1 Reference orbit left and tune diagram right in Injector II start tracking track line 11 beam beaml MAXSTEPS nstepxturns STEPSPERTURN nstep TIMEINTEGRATOR RK 4 run file track output turns 1 method CYCLOTRON T beam beaml fieldsolver Fs1 distribution Disti endtrack Stop To run opal on a single node just use this command opal testinj2 1 in Here shows some pictures using the resulting data from single particle tracking using OPAL CYCL Left plot of Figure 3 1 shows the accelerating orbit of reference particle After
33. 1 pdef bz b z paget data table xif count eq 0 then output cvc100 ANSVS dat xSTATUS data 5 5 output xelse output cvc100O ANSYS dat append xSTATUS data 5 5 output xendif xenddo finish By running this in ANSYS you can get a fields file with the name 100 AN SY S data You need to put 6 parameters at the header of the file namely rmin mm Ar mm 6 4 A0 No total data number in each arc path of azimuthal direction and N total path number along radial direction If Ar or A0 is decimal one set its negative opposite number This is useful is the decimal is unlimited For instance if AQ 1 the fourth 3 line of the header should be 3 0 In a word the fields are stored in the following format 0 0 10 0 0 0e 00 1 0e 00 90 201 PARAMETER STATUS DATA 336 PARAMETERS DEFINED INCLUDING 17 INTERNAL PARAMETERS LOCATION VALUE 1 5 1 0 537657876 2 5 1 0 538079473 40 CHAPTER 5 OPAL CYCL 3 5 1 0 539086731 44 5 1 0 760777286 45 5 1 0 760918663 46 5 1 0 760969074 PARAMETER STATUS DATA 336 PARAMETERS DEFINED INCLUDING 17 INTERNAL PARAMETERS LOCATION VALUE d 5 1 0 704927299 2 5 1 0 705050993 3 5 1 0 705341275 5 4 3 BANDRF type If TYPE BANDRE the program requires the B data format which is same as CARBONCVCL But with BAN DRF type the program can also read in the 3D electric field s For the detail about its usage please see Sec tion8 10 5 4 4 Default PSI form
34. 106 turns the energv increases from 870 keV at the injection point to 72 16 MeV at the deflection point From theoretic view there should be an eigen ellipse for any given energy in stable area of a fixed accelerator structure Only when the initial phase space shape matches its eigen ellipse the oscillation of beam envelop amplitude will get minimal and the transmission efficiency get maximal We can calculate the eigen ellipse by single particle tracking using betatron oscillation property of off centered particle as following track an off centered particle and record its coordinates and momenta at the same azimuthal position for each revolution Figure 3 2 shows the eigen ellipse at symmetric line of sector magnet for energy of 2 MeV in Injector II Right plot of Figure 3 1 shows very good agreement of the tune diagram by OPAL CVCLand FIXPO The trivial discrepancy should come from the methods they used In FIXPO the tune values are obtained according to the crossing points of the initially displaced particle Meanwhile in OPAL CYCL the Fourier analysis method is used to manipulate orbit difference between the reference particle and an initially displaced particle The frequency point with the biggest amplitude is the betatron tune value at the given energy Following is the input file for single bunch tracking with space charge effects in Injector II examples opal cycl sc in file name testinj2 2 in Define Option parameters
35. 50 6370 frequency3 3 0 frequency turns 106 nstep 5000 define elements and beamline inj2 Cyclotron TYPE Injector2 CYHARMON 10 PHIINIT 30 0 PRINIT 0 0067 RINIT 392 5 SYMMETRY 1 0 RFFREQ 50 6370 FMAPFN ZYKL9Z NAR rf0 RFCavity VOLT 0 25796 FMAPFN Cavl dat TYPE SINGLEGAP FREQ 50 637 ANGLE 35 0 PHIO phi01 RMIN 350 0 RMAX 3350 0 PDIS 0 0 GAPWIDTH 0 0 rfl RFCavity VOLT 0 25796 FMAPFN Cavl dat TYPE SINGLEGAP FREQ 50 637 ANGLE 55 0 PHIO phi02 RMIN 350 0 RMAX 3350 0 PDIS 0 0 GAPWIDTH 0 0 rf2 RFCavity VOLT 0 25796 FMAPFN Cavl dat TYPE SINGLEGAP FREQ 50 637 ANGLE 215 0 PHIO phi03 RMIN 350 0 RMAX 3350 0 PDIS 0 0 GAPWIDTH 0 0 28 CHAPTER 3 TUTORIAL rf3 RFCavity VOLT 0 25796 FMAPFN Cavl dat TYPE SINGLEGAP FREQ 50 637 ANGLE 235 0 PHIO phi04 RMIN 350 0 RMAX 3350 0 PDIS 0 0 GAPWIDTH 0 0 rf4 RFCavity VOLT 0 06380 FMAPFN Cav3 dat TYPE SINGLEGAP FREQ 151 911 ANGLE 135 0 PHIO phi05 RMIN 830 0 RMAX 3330 0 PDIS 0 0 GAPWIDTH 0 0 rf5 RFCavity VOLT 0 06380 FMAPFN Cav3 dat TYPE SINGLEGAP FREQ 151 911 ANGLE 315 0 PHIO phi06 RMIN 830 0 RMAX 3330 0 PDIS 0 0 GAPWIDTH 0 0 11 Line inj2 rf0 rf1 rf2 rf3 rf4 rf5
36. 86 4 The command causes all beam element beam line and parameter definitions to be written on the named file Examples SAVE FILE structure SAVE Structure 77 3 MAKESEQ Statement A file containing a machine sequence can be generated in OPALby the command MAKESEQ LINE string NAME string FILE string Please note this is not yet supported for OPAL Tand OPAL CYCL The named beam line see 89 or sequence see 2 is written as a flat SEQUENCE see 622 with the given name on the named file All required elements and parameters are also written All expressions are evaluated and only their values appear in the output The command has the following attributes LINE The line for which a flat sequence is to be written NAME The name to be given to the sequence written FILE The name of the file to receive the output 70 CHAPTER 7 CONTROL STATEMENTS 7 8 IF Conditional Execution Conditional execution can be requested by an IF statement It allows usages similar to the C language if statement IF logical statement IF logical statement ELSE statement IF logical statement group IF logical statement group ELSE statement group Note that all statements must be terminated with semicolons but there is no semicolon after a closing brace The statement or group of statements following the IF is executed if the condition is satisfied If the condition is false and
37. ARCH X with h5part includedir H5hut src with h5part libdir H5hut src X with hdf5 includedir HDF5HOME include with hdf5 libdir HDF5HOME lib X with libdir L opt parmetis parmetis 3 1 L opt intel mkl mkl 10 0 1ib em64t X L opt intel intel 10 0 fce 10 0 1lib X with libs lsuperlu dist 2 0 lifcore X lparmetis lmetis X with blas mkl with lapack mkl 150 APPENDIX A INSTALLATION with trilinos includedir TRILINOS ROOT include V with trilinos libdir TRILINOS ROOT lib X enable ml solver A 5 Debug Flags Table A 1 Debug flags Name Description Default DBG_SCALARFIELD dumps scalar potential on the grid not set DBG STENCIL dumps stencil MG solver to a Matlab readable file not set DBG_CSR dump information regarding the 1D CSR calculation not set DBG_SCALARFIELD dumps the field to a file called rho_scalar The structure of the data can be deduced from the following Matlab script function scalfield RHO rhosize size RHO for i 1 rhosize 1 x RHO i 1 y RHO i 2 z RHO i 3 rhoyz y z RHO i 4 rhoxy x y RHO i 4 rhoxz x z RHO i 4 rho x y z RHO i 4 end DBG STENCIL dumps the discretization stencil to a file A dat The following Matlab code will read and store the sparse matrix in the variable A load A dat spconvert A DBG dumps a text file of the calculated 1D CSR field The first line gives the av
38. Figure 8 2 Schematic of the simplifed geometry of a cavity gap and parameters 88 CHAPTER 8 ELEMENTS Field arb units 0 2 4 6 8 10 12 14 16 18 20 Fringe Field Entrance Cavitv Field Fringe Field Exit Figure 8 3 The on axis field of S band 2997 924 MHz TRAVELINGWAVE structure The field of a single cavity is shown between its entrance and exit fringe fields The fringe fields extend one half wavelength 1 2 to either side 8 12 Traveling Wave Structure An example of a ID TRAVELINGWAVE structure field map is shown in Figure 8 3 This map is a standing wave solution generated by Superfish and shows the field on axis for a single accelerating cavity with the fringe fields of the structure extending to either side OPAL Treads in this field map and constructs the total field of the TRAVELINGWAVE structure in three parts the entrance fringe field the structure fields and the exit fringe field The fringe fields are treated as standing wave structures and are given by Eentrance r t VOLT 27 FREQ t entrance Eexit r t Etom map r cos 27 FREQ t exit where VOLT and FREQ are the field magnitude and frequency attributes see below entrance LAG the phase attribute of the element see below exit is dependent upon both LAG and the NUMCELLS attribute see below and is calculated internally by OPAL T The field of the main accelerating
39. Option ECHO FALSE Option PSDUMPFREQ 10 Option SPTDUMPFREQ 5 3 4 EXAMPLES OF BEAM LINES 0 2 OPAL cycl dt 5ps OPAE cyel g lps RIRES dt lps 0 15 l ge 4 gt s F So m 4 di tutt 01 1 oy ros OUEES S 005p 1 8 amp 15 4 E 0r 4 H N x iL Mi J amp 005 4 POE E E T 0 1 gt 4 as L BERK i HUE 0 15 1 1 i i i i i i i i 0 2 i i i i u i 2 634 634 5 635 635 5 636 636 5 637 637 5 638 638 5 25 2 1 5 1 0 5 0 05 1 5 2 r mm z mm Figure 3 2 Radial and vertical eigenellipse at 2 MeV of Injector II Option REPARTFREQ 10 Define title Title string OPAL CvciT SC test define some phvsical parameters Edes 0 000870 gamma Edes PMASS 55 beta sqrt 1 1 gamma 2 gambet gammaxbeta PO gammaxbetaxPMASS brho PMASS 1 0e9 gambet CLIGHT 101 48 4812 15 0 phi02 phi01 200 0 phi03 phi01 1800 0 phi04 phi01 2000 0 phi05 phi01 820 0 3 0 phi06 phi01 2620 0 3 0 frequency
40. Real Operators in OPA E ARES E Sn 50 Real Functions m OPAD 52524 aed ek OR ADR Rm Rp 50 Real Functions with 51 Real Functions of Arrays 52 Predefined Symbolic Constants 000 53 Real Array Functions in OPAL acting component wise 59 Default Settings for Options lox usu B uS 65 Different distributions specified by a single parameter m 101 Parameters for the DISTRIBUTION command 102 Parameters of the distribution command 103 Fieldsolver command 108 Preconditioner bahaviour command summary 109 Wakefield command summary 112 Geometry command summary 117 Commands accepted in Tracking Mode 119 Field Emission Command summary 124 Multipacting Related Command 130 Debus BLA a seb a BY 150 10 LIST OF TABLES List of Figures 1 1 1 2 1 3 3 1 3 2 3 4 3 5 5 8 1 8 2 8 3 17 1 17 2 17 3 17 4 18 1 18 2 18 3 18 4 18 5 18 6 2 C 3 Paralle
41. The normal sextupole component K E DEM The default is Om The component is positive if B is positive on the positive x axis 2 D K2S skew sextupole component n p Ee The default is Om 3 The component is negative if B is positive on the positive x axis Example S SEXTUPOLE L 0 4 K2 0 00134 The reference system for a sextupole is a Cartesian coordinate system see Fig 8 7 Octupole TODO IN OPAL T label OCTUPOLE TYPE string APERTURE real vector L real K3 real K3S real An OCTUPOLE has three real attributes L The octupole length default 0 m A thin octupole see is defined by setting the length to zero 3 K3 The normal sextupole component K The default is Om The component is positive if B is positive on the positive x axis 3 TE K3S skew sextupole component Bs E The default is 0m The component is negative if B is positive on the positive x axis Example O3 OCTUPOLE L 0 3 K3 0 543 The reference svstem for octupole is a Cartesian coordinate svstem see Fig 22 8 8 General Multipole TODO IN OPAL T A MULTIPOLE is thin lens of arbitrary order including a dipole label MULTIPOLE TYPE string APERTURE real vector L real KNORMAL real vector KSKEW real vector 82 CHAPTER 8 ELEMENTS L The multipole length default 0 m A thin multipole see 822 is defined b
42. This chapter will provide a jump start describing some of the most common used features of OPAL The complete set of examples can be found and downloaded at http amas web psi ch download TUTORIAL opal tutorial tgz Allexamples run on a single core but can be used efficiently on up to 8 cores OPAL scales in the weak sense hence for a higher concurrency one has to increase the problem size i e number of macro particles and the grid size which is beyond this tutorial 3 1 Starting OPAL opal gt CommMPI Parent process waiting for children gt CommMPI Initialization complete gt gt X X 1 gt Vo Hee A x Ww gt ANON IL JI gt b de uM gt X _ _ OPAL gt OPAL gt This is OPAL Object Oriented Parallel Accelerator Library Version 1 1 9 SVN version 13640 c PSI http amas web psi ch OPAL gt OPAL gt Please send cookies goodies or other motivations wine and beer to the OPAL developers opal lists psi ch OPAL gt Time 15 41 41 date 29 03 2012 gt 3 2 Restart Mode At the moment we always restart from the last time step in the restart fn opal input in restartfn input h5 restart 1 3 3 Autophase Example This is a partial complete example First we have to set OPALin AUTOPHASI and for example set the nominal phase to 3 5 deg 21 mode as described in Section 7 3 22 CHAPTER 3 TU
43. Ue cv 107 i L i L L L L L 1 GeV particle 5 107b e o 5 T 0 1 2 3 4 5 6 7 8 9 10 angle deg L bu Hae gta E ACE Ao xd d ia Teo A i3 KA m S T MA A b lig cie de gt 0 10 20 30 40 50 60 70 E MeV Figure 18 6 The energy spectrum and scattering angle at z 0 1 m 80 141 142 CHAPTER 18 PHVSICS MODELS USED IN THE PARTICLE MATTER INTERACTION MODEL Appendix A Installation OPAL and all its flavours are based on several packages which are all installable using cmake or the configure make install trilogy OPAL is also preinstalled on several HPC clusters including the FELSIM and Merlin clusters at PSI The prein stalled version can be accessed using the module command module load opal Due to some incompatibilities between the Intel compiler and the Gnu libraries vou have to use GCC 4 5 in combination with Intel 12 1 Next we describe the installation process for the GNU 4 6 3 compiler 1 Build and install OPAL on Mac amp Linux A 1 1 Supporting Libraries Several libraries and tools must be present before starting with the actual OPAL installation process described in A 1 3 The following packages are maybe already installed Please check the versions carefully and do not
44. a round metallic beam pipe that can be calculated numerically see Sections 13 2 13 11 Since this also limits the applications of wakefields we also provide a way to import a discretized wakefield from a file see Section 13 12 The wakefield of a round metallic beam pipe with radius a can be calculated by inverse FFT of the beam pipe impedance There are known models for beam pipes with DC and AC conductivity The DC conductivity of a metal is given by ope 13 1 with n the density of conduction electrons with charge e 7 the relaxation time and m the electron mass The AC conductivity a response to applied oscillation fields is given by TDC CAO 13 2 1 iwT with w denoting frequencv of fields The longitudinal impedance with DC conductivitv is given bv 1 2 Zrac k 13 3 az a where QE sign k 13 4 with c denoting the speed of light and k the wave number The longitudinal wake can be obtained by an inverse Fourier transformation of the impedance Since Re Zz k drops at high frequencies faster than I m Z y k cosine transformation can be used to calculate the wake The following equation holds in both the DC and AC case 107122 Re y U Re Zi k costs 13 5 with Zz k either representing Zr or k depending on the conductivity With help of the Panofsky Wenzel theorem k Zi k 22 13 6 we deduce t
45. alive get the address of R P a new particle in collimator label 1 5 dead Yes _ write to file label 1 No scattering and integration Figure 18 3 The diagram of CollimatorPhysics in OPAL 18 3 THE FLOW DIAGRAM OF COLLIMATORPHVSICS CLASS IN OPAL calculate the number of particles in partColArrav loop over another n 1 steps in partColArrav No particle alive get the address of R P Yes track it as in a drift write to file label 1 scattering and integration Figure 18 4 The diagram of CollimatorPhysics in OPAL Continued 139 140 CHAPTER 18 PHVSICS MODELS USED IN THE PARTICLE MATTER INTERACTION MODEL 18 3 1 The Substeps Small step is needed in the routine of CollimatorPhysics If alarge step is given in the main input file in the file CollimatorPhysics cpp it is divided by a integer number n to make the stepsize using for the calculation of collimator physics less than 1 01e 12 s As shown by Fig 18 3 and Fig 18 4 in the previous section first we track one step for the particles already in the collimator and the newcomers then another n 1 steps to make sure the particles in the collimator experiencr the same time as the ones in the main bunch Now if the particle leave the collimator during the n 1 steps we track it as in a drift and put it back to the main bunch when finishing n 1 steps 18 4 Example of an Input File KXIIPHYS SurfacePhysics
46. arrav term arrav term arrav term wow arrav expr arrav expr able column range p y column real expr teger teger integer y dex select real expr name ion arguments w array primary array factor array factor arrav term arrav term 6 COMMAND FORMAT Example a atb a4t2xb There are also three functions allowing the generation of real arravs TABLE Generate an arrav of expressions TABLE n2 expression implies TABLE 1 n2 1 expression TABLE n1 n2 expression implies TABLE n1 n2 1 expression TABLE nl n2 n3 expression These expressions all generate an array with n2 components The components selected by n1 n2 n3 are filled from the given expression a C pseudo code for filling is int i for i nl i lt n2 i n3 alil expression i In each generated expression the special character hash sign is replaced the current value of the index Jis Example 6 14 ARRAVS Table 6 9 Real Arrav Functions in OPAL acting component wise Function Meaning result tvpe argument tvpe TRUNC X truncate X towards zero discard fractional part real array real array ROUND X round X to nearest integer real array real array FLOOR X return largest integer not greater than X real array real array CEIL X
47. as an operand in another expression 6 8 6 Table References Values can be extracted from a table with the syntax table name Q place gt column name Here table name denotes a table see Chapter 77 place denotes a table row see 6 9 1 and column name denotes the name of a column in the table Example TWISS E gt BETX denotes the horizontal beta function at the end of table TWISS 6 9 Element Selection Many OPALcommands allow for the possibility to process or display a subset of the elements occurring in a beam line or sequence This is not yet available in I 3 OPAL Tand OPAL CYCL 6 9 1 Element Selection A place denotes a single element or the position following that element It can be specified bv one of the choices object name index The name verb object name is the name of an element line or sequence and the integer index is its occurrence count in the beam line If the element is unique index can be omitted S denotes the position before the first physical element in the full beam line This position can also be written 0 E denotes the position after the last physical element in the full beam line Either form may be qualified by one or more beam line names as described by the formal syntax place element name element name integer 5 line name 1 omitted index defaults to one Examples assume the following defi
48. dat re spectively The data is stored in the global cylindrical coordinate system which can be used to check the property of the closed orbit Tune calculation mode The tunes v and v of each energy are stored in a ASCII file with name tuningresult Multi particle tracking mode The intermediate phase space data of all particles and some interesting parameters including RMS envelop size RMS emittance external field time energy length of path number of bunches and tracking step are stored in the H5hut file format http h5part web psi ch and can be analyzed using the H5PartRoot http amas web psi ch tools H5PartROOT index html The frequency of the data output can be set using the PSDUMPFREQ option of OPTION statement see 87 3 The file is named like the input file but the extension is h5 The intermediate phase space data of centeral particle with ID of 0 and an off centering particle with ID of 1 are stored in an ASCII file The file s name is combined by the input file name without extension and trackOrbit dat The frequency of the data output can be set using the SPTDUMPFREQ option of OPTION statement see 7 3 Chapter 6 Command Format All flavours of OPALusing the same input language the MADlanguage The language dialect here is ajar to MAD9 for hard core MAD8users there is a conversion guide It is the first time that machines such as cyclotrons proton and electron linacs can be described within the same
49. e ea d 7 9 IF Conditional Bxec tion 2e RUN A a erc de Ue De ARP Gu cmn CS HE HA en T9 WHILE Repeated 2 see be ees is br xp Ser RES 7 10 MACRO Macro Statements Elements 8 1 Element Input Format e sre 8 2 Common Attributes forall Elements 8 3 DEES paces som ete nk aire Re ed ak a ey eo ty P RU be REM RUE e 84 Bending Magnets 6 sss Ro ER ua 8 5 Quadrupole nono Re RES EAS Ee hub ed 8 6 Sextupole eR Bero RUE RUE RUE ee 8 7 O t ple oed ene a EIN RR SERV Brie CERE uere 8 8 General Multipole cow ERE Eng se EXT RV I NUS ee v 8 9 Sol noid V ii eue qe ur eve x uen 8 10 Gyelotron Ba a E se A le 8 11 RF Cavities OPAL T OPAL CYCL 8 114 OPA Ezrmode bozza exem Dae qup reus 8 112 OPAL CYCLImode ieu puce TR ponn URS SOR 8 12 Traveling Wave Structure 222525225 RUE ok ERES 5 15 MOnILOfS 255 405 potu eto ee Rege d EA ey esp Som qr om ge iore e p ien 8 14 Collimatots 6 le we wh C URUR ele qe uere bad l CERES Ue ede 8 14 1 OPAT Tmode 241 4 54e mens B ma mla BR
50. element aperture It is ignored by OPAL but it can be used in other programs WAKEF Defines the type of wake to be applied WT WL or WTL for transverse longitudinal or both other elements can have arbitrary additional attributes which are not defined below Such attributes must have a name different from all defined attributes and single real values Only the TYPE attribute is used by OPAL but the SAVE command see 7 7 2 saves all attributes 8 3 DRIFT SPACES 75 8 3 Drift Spaces label DRIFT TYPE string APERTURE real vector L real A DRIFT space has one real attribute L The drift length default 0 m Examples DRI DRIFT L 1 5 DR2 DRIFT L DR1 gt L TYPE DRF The length of DR2 will always be equal to the length of DR1 The reference system for a drift space is a Cartesian coordinate system see Fig 27 This is a restricted feature OPAL CYCL OPAL Tdrifts are implicitly given if no field is present 76 CHAPTER 8 ELEMENTS 8 4 Bending Magnets Two different type keywords are recognised for bending magnets they are distinguished only by the reference system used RBEND is a rectangular bending magnet It has parallel pole faces and is based on a Cartesian reference system see Fig SBEND is a sector bending magnet Its pole faces meet at the centre of curvature of the curved reference system see Fig Using a RBEND or SBEND in OPAL Tmode requires a field map
51. homefelsim kraus extlib SuperLU DIST 2 5 lib libsuperlu dist 2 5 a X SCALAPACK INCLUDE DIRS FILEPATH S MKL INCLUDEJ SCALAPACK LIBRARY DIRS FILEPATH S MKL LIB DIRJ SCALAPACK LIBRARY NAMES STRING mkl scalapack lp64 QUUUUUUUUUUUUU 1 KJ Didasko ENABLE TESTS OFF Didasko ENABLE EXAMPLES OFF D Trilinos ENABLE TESTS BOOL OFF V SEXTRA ARGS STRILINOS ROOT D D D D Trilinos ENABLE Belos BOOL ON D Trilinos ENABLE Epetra BOOL ON D Trilinos ENABLE EpetraExt BOOL ON D Trilinos ENABLE Ifpack BOOL ON D Trilinos ENABLE ML BOOL ON X D Trilinos ENABLE Amesos BOOL ON D Amesos ENABLE BLACS BOOL ON D Amesos ENABLE SuperLUDist BOOL ON D Amesos ENABLE SCALAPACK BOOL ON D Trilinos ENABLE Amesos superlu BOOL ONN D Trilinos ENABLE AztecOO BOOL ON X D Trilinos ENABLE Teuchos BOOL ON X D Trilinos ENABLE Aztecoo Teuchos BOOL ON D Trilinos ENABLE Teuchos Extended BOOL ON D Trilinos ENABLE Isorropia BOOL ON D Trilinos ENABLE Isorropia Epetraext BOOL ON D Trilinos ENABLE Didasko BOOL OFF X D D Finally execute the following configure command i e on the FELSIM cluster CXX mpicxx configure with classic includedir CLASSIC ROOT src with classic libdir CLASSIC ROOT src with doom includedir DOOM ROOT with doom libdir DOOM X with ippl includedir IPPL ROOT src with ippl libdir IPPL ROOT lib S IPPL
52. mm MBTC The maximal B field of trim coil kG SLPTC The slope of the rising edge kG mm This is a restricted feature OPAL CYCL 86 CHAPTER 8 ELEMENTS 8 11 Cavities OPAL T and OPAL CYCL For an RFCAVITY the three modes have four real attributes in common label RFCAVITY APERTURE real vector L real VOLT real LAG real L The length of the cavity default 0 m VOLT The peak RF voltage default 0 MV The effect of the cavity is VOLT sin 27 LAG HARMON fot LAG The phase lag rad default 0 8 11 1 OPAL Tmode Using a RF Cavity in OPAL t mode the following additional parameters are defined FMAPFN Field maps in the 77 format can be specified ELEMEDGE The edge of the field is specified absolute floor space co ordinates in m TYPE Type specifies STANDING default or SINGLE GAP structures FREQ Defines the frequency of the RF Cavity in units of MHz A warning is issued when the frequency of the cavity card does not correspond to the frequency defined in the FMAPEN file The frequency of the cavity card overrides the frequency defined in the FMAPEN file APVETO If TRUE this cavity will not be auto phased instead the actual phase on the element is used Example standing wave cavity which mimics a DC gun gun RFCavity L 0 018 VOLT 131 1 052 2 658 FMAPFN 1T3 T7 ELEMEDGE 0 00 TYPE STANDING FREQ 1 0e 6 Example of a two frequency standing wave cavity rfl RFCavity
53. premier super computer The instructions below work but you may want to modify them depending on where you prefer various codes and libraries to be located or if you are on a similar Cray system A 2 1 bash profile ext File Edit the bash profile ext file in your home directory Add the following lines if NERSC HOST hopper then export PATH S PATH S HOME hopper bin f Module files module load cmake module load gsl module load hdf5 parallel module load zlib Note we encountered in some cases a problem when the build directory is under IPPL ROOT 21f you can not checkout the sources send an email to andreas adelmann psi ch 3We encountered in some cases a problem when the build directory is under SOPAL ROOT 146 APPENDIX module swap PrgEnv pgi PrgEnv gnu fi source SHOME bashrc INSTALLATION 2 22 bashrc ext File Edit the bashrc ext file in your home directory Add the following lines if NERSC HOST then f For OPAL export export export export export export export fi HDF5 INCLUD HDF5 LIBRAR H5hut HOME GSL PREFIX IPPL ROOT OPAL ROOT CLASSIC ROO hopper 1 E PATH SCRAY HDF5 DIR hdf5 parallel gnu include Y PATH SCRAY HDF5 DIR hdf5 parallel gnu lib hopper extlib H5hut 1 99 8 GSL DIR HOME hopper extlib ippl HOME svnwork OPAL T OPAL ROOT classic 5 0 These environment variables need to be set so we can build OPAL When you are done
54. provide in the file we linearly interpolate the available function values The files are specified in the SDDS Self Describing Data Sets Whenever a file is specified OPAL will use the wakefield found in the file and ignore all other commands related to round beam pipes lnttp www aps anl gov Accelerator Systems Division Operations Analysis manuals GettingStartedWithSDDS HTML GettingStartedWithSDDS html 114 CHAPTER 13 WAKEFIELDS 13 13 Wake Functions Three types of wake functions are implemented so far transverse and longitudinal geometric wakes and the CSR wake The general input format is label WAKE TYPE string NBIN real CONST LENGTH bool CONDUCT string ZO real FORM string RADIUS real SIGMA real TAU real FILTERS string array CONST LENGTH CONDUCT Z0 FORM RADIUS SIGMA and TAU are only used in the geometric wakes TYPE The type of wake function either TRANSV SHORT RANGE LONG SHORT RANGE or 1D CSR NBIN Not implemented yet Number of bins to be used for line density if different from space charge solver grid CONST LENGTH CONDUCT Z0 FORM RADIUS SIGMA TAU FILTERS Array of names of filters to be applied onto the longitudinal histogram of the bunch to get rid of the noise and to calculate derivatives the filters smoothers are applied to the line density in the order they appear in the array The last filter is also used for calculating the derivatives The actual filters have to be defined elsew
55. random number generator RANDOM is a portable 48 bit generator Three quasi ran dom generators are available 1 HALTON 2 SOBOL 3 NIEDERREITER For details see the GSL reference manual 18 5 FINEEMISSION During emission of the beam from a cathode the time step of the integration is set to a new value until all of the particles are emitted This new value is determined two different ways depending on whether this OPTION command is true or false 1 TRUE The longitudinal distribution of the initial beam is represented internally has a histogram with N bins The number of bins is determined by N NBIN x SBIN where N BIN is the number of energy bins used to calculate the beam space charge and SBIN is the number of sampling bins per energy bin see Chapter 11 The integration time step is set so that one histogram bin is emitted each time step Therefore it takes N steps to emit the entire beam 2 FALSE In this case the integration time step is set so that one entire energy bin is emitted each time step This typical results in a very coarse emission time step with the entire beam being emitted in N BIN steps Once the entire beam is emitted the time step is reset to the value defined in the input file By using this option one can obtain fine time step emission without using many energy bins As the number of energy bins is increased so is the space charge calculation time Additionally a large number of energy bins is not always ne
56. should have two lines 1 0 001 0 001 0 001 0 001 0 001 0 001 35 36 CHAPTER 5 OPAL CYCL The number in the first line is the total number of particles In the second line the data represents 2 pz y py Z pz in the local reference frame Their units are described in section 5 3 Please don t try to run his mode in parallel environment You should believe that a single processor of 21 century is capable of doing the single particle tracking 5 2 2 Tune Calculation mode In this mode two particles are tracked one with all data is set to zero is the reference particle and another one is an off centering particle which is off centered in both r and z directions Working in this mode OPAL CYCL can calculate the betatron oscillation frequency v and v for different energies to evaluate the focusing characteristics for a given magnetic field Like the single particle tracking mode the initial 6D parameters of the two particles in the local reference frame must be read from a file too In the file should has three lines DOW 0 0 0 0 0 0 0 0 0 001 0 0 0 0 0 0 0 001 0 0 When the total particle number equals 2 this mode is triggered automatically Only the element CYCLOTRON in the beam line is used and other elements are omitted if any exists Please don t try to run his mode in parallel environment either 5 2 5 Multi particle tracking mode In this mode large scale particles can be tracked simultaneously eithe
57. structure is reconstructed from the center section of the standing wave solution shown in Figure 8 3 using VOLT r t MODE x Bromma 2 cos 27 FREQ t LAG 2 MODE 3 Enom map X Y Z d FREQ t HLAG F MODE where d is the cell length and is defined 4 MODE is an attribute of the element see below When calculating the field from the map Eg om map X z the longitudintal position is referenced to the 8 13 MONITORS 89 start of the cavitv fields at In this case starting at z 5 0 cm If the longitudinal position advances past the end of the cavity map 3 15 0 cm in this example an integral number of cavity wavelenths is subtracted from the position until it is back within the map s longitudinal range A TRAVELINGWAVE structure has seven real attributes one integer attribute one string attribute and one boolean attribute label TRAVELINGWAVE APERTURE real vector L real VOLT real LAG real FMAPFN string ELEMEDGE real FREQ real NUMCELLS integer MODE real L The length of the cavity default 0 m In OPAL Tthis attribute is ignored the length is defined by the field map and the number of cells VOLT The peak RF voltage default 0 MV The effect of the cavity 15 VOLT sin LAG 27 FREQ t LAG The phase lag rad default 0 FMAPEN Field maps in the 77 format can be specified ELEMEDGE The edge o
58. tPulseFWHM 9 9 12 0 925 NBIN 10 DEBIN 80 LEGACYMODE TRUE and should produce the same results Make sure to enable the LEGACYMODE option to create the flattop distribu tion in legacy mode Chapter 12 Fieldsolver TODO will rewrite 12 1 Fieldsolver Command See Table 12 1 for a summary of the Fieldsolver command 12 2 Define the Fieldsolver to be used At present only a FFT based solver is available Future solvers will include Finite Element solvers and a Multi Grid solver with Shortley Weller boundary conditions for irregular domains 12 3 Define Domain Decomposition The dimensions in z y and z can be parallel TRUE or serial FALSE The default settings are parallel in z and serial in x and y 12 4 Define Number of Gridpoints Number of grid points in x y and 2 for a rectangular grid 12 5 Define Boundary Conditions Two boundary conditions can be selected independently among x y namely OPEN and for 2 OPEN amp PERI ODIC In the case you select for z periodic you are about to model a DC beam 12 6 Define Greens Function Two Greens functions can be selected INTEGRGREEN GREEN The integrated Green s function is described in 40 107 108 CHAPTER 12 Table 12 1 Fieldsolver command summarv HELDSOLVER Command Purpose FIELDSOLVER Specify a fieldsolver FSTYPE PARFFTX PARFFTY PARFFTZ MX MY MZ BCFFTX BCFFTY BCFFTZ GREENSF
59. the corresponding input quantities 2 the energy integral of d d E is guaranteed to equal 3 the energy of any given emitted electron is guaranteed not to exceed the primary energy and 4 the aggregate energy of the electrons emitted in any multielectron event is also guaranteed not to exceed the primary energy This model contains built in SEY curves for copper and stainless steel and the only thing user need to set is to choose the material type i e copper or stainless steel as long as the surface material of user s RF structure has the same SEY curve as built in SEY curves Although a set of parameters in the model can be adjusted to model different SEY curves without breaking the 125 126 CHAPTER 17 MULTIPACTING 2 5 0 500 1000 1500 2000 2500 Impact energv eV Figure 17 1 Tvpical SEX curve a Surface normal n Incident electron Backscattered electron 2 Rediffused electron True secondaries A eS Figure 17 2 Sketch map of the secondary emission process above mentioned mathematical self consistency it is easier to use Vaughan s formula based secondary emission model if user has to model a different SEY curve The Vaughan s secondary emission model is based on a secondary emission yield formula 57 58 E 0 Smax 9 ve for v lt 3 6 17 2a Suas 0 1125 9 75 fora gt 8 6 17 2b E 0 forv lt 0 17 2c where v Emax
60. the pattern Entering SHOW alone displays help on the SHOW command Examples SHOW SHOW NAME QD L SHOW QD L 61 62 CHAPTER 7 CONTROL STATEMENTS 7 1 3 WHAT Command The WHAT statement displavs all object names matching a given regular expression It has three formats WHAT Give help on the WHAT command WHAT NAME label Show definition of label WHAT label Shortcut for the second format label is an identifier see 86 2 If it is non blank displays the object label in a format similar to the input statement that created the object Entering WHAT alone displays help on the WHAT command Examples WHAT WHAT NAME QD WHAT QD 7 22 STOP QUIT Statement The statement STOP or QUIT terminates execution of the OPALprogram or when the statement occurs in a CALL file see 87 7 1 returns to the calling file Any statement following the STOP or QUIT statement is ignored 7 3 OPTION Statement The OPTION command controls global command execution and sets a few global quantities OPTION ECHO logical INFO logical TRACE logical VERIFY logical WARN logical SEED real TELL logical PSDUMPFREQ integral STATDUMPFREQ integral SPTDUMFREQ integral REPARTFREQ integral REBINFREQ integral The first five logical flags activate or deactivate execution options ECHO Controls printing of an echo of input lines on the standard error file INFO If th
61. use older ones For a Linux installation you can skip macport and Xcode related software e macport from www macports org e Xcode http developer apple com TOOLS Xcode e automake 1 10 2 e autoconf 2 64 e libtool 2 2 e cmake 2 8 4 A 1 2 Environment Variables Assuming IPPL and OPAL resides in SHOME svnwork the following environment variables must be set ac cordingly export OPAL ROOT HOME svnwork OPAL export CLASSIC ROOT SOPAL ROOT classic 5 0 export H5hut HOME svnwork H5hut export IPPL ROOT HOME svnwork ippl export IPPL PREFIX SIPPL ROOT build 143 144 Build Install gcc 4 6 3 Mac APPENDIX A INSTALLATION sudo port install gcc46 Build Install gsl 1 14 Mac sudo port install gsl Build Install OpenMPI openmpi 1 4 3 Mac amp Linux CXX g F77 gfortran configure Build Install HDF5 1 8 7 Mac amp Linux configure eenable parall Libraries have been install usr local lib If vou ever happen to want in a given directorv LIBD lel prefix usr local led in to link against installed libraries R you must either use libtool and specify the full pathname of the library or use the LLIBDIR flag during linking and do at least one of the following add LIBDIR to the DYLD LIBRARY PATH environment variable during execution See any operating system documentation about shared libraries for more information such
62. values in transvers direction for each longi tudinal grid point are calculated The field is non negligible from 60 0 cm to 60 0 cm relative to ELEMEDGE in longitudinal direction The 200 grid points span a length of 2 0 cm in radial direction From the 107000 field values 5 000 complex Fourier coefficients are calculated whereof only 40 are kept to calculate the off axis field values OPAL Tnormalizes the field values internally such that max Bonaxis 1 0 T 170 APPENDIX C OPAL T FIELD MAPS AstraMagnetostatic AstraMagnetostatic 40 3 0000000 01 0 0000000 00 2 9800000 01 2 9075045 05 2 9600000 01 5 9367702 05 2 9400000 01 9 0866460e 05 2 9200000e 01 1 2374798e 04 2 9000000e 01 1 5799850e 04 2 9000000e 01 1 5799850e 04 2 9200000e 01 1 2374798e 04 2 9400000e 01 9 0866460e 05 2 9600000e 01 5 9367702 05 2 9800000 01 2 9075045 05 3 0000000 01 0 0000000e 00 Figure C 4 A 1D field map describing a magnetostatic field using n non equidistant grid points in longitudinal direction From these values n equidistant field values are computed from which in turn n 2 complex Fourier coefficients are calculated In this example only 40 Fourier coefficients are kept to calculate the off axis field values The z position of the sampling is in the 1 column in meters the corresponding longitudinal on axis magnetic field amplitude is in the 274 column As with the 1DMagnetoStatic field maps OPAL Tnormal
63. 0 002 gamma Edes PMASS 55 beta sqrt 1 1 gamma 2 gambet gammaxbeta gammaxbetaxPMASS brho PMASS 1 0e9 gambet CLIGHT value gamma brho Edes beta gambet 01 48 4812 15 0 phi02 phi01 200 0 phi03 phi01 1800 0 phi04 phi01 2000 0 phi05 phi01 820 0 3 0 phi06 phi0l 4 2620 0 x3 0 turns 106 nstep 5000 define elements and beamline inj2 Cyclotron TYPE Injector2 CYHARMON 10 PHIINIT 30 0 PRINIT 0 0067 RINIT 392 5 SYMMETRY 1 0 RFFREQ frequency FMAPFN ZYKL9Z NAR rf0 RFCavity VOLT 0 25796 FMAPFN avl dat TYPE SINGLEGAP FREQ frequency ANGLE 35 0 01 RMIN 350 0 RMAX 3350 0 PDIS 0 0 GAPWIDTH 0 0 rfl RFCavity VOLT 0 25796 FMAPFN avl dat TYPE SINGLEGAP FREQ frequency ANGLE 55 0 PHIO phi02 RMIN 350 0 RMAX 3350 0 PDIS 0 0 GAPWIDTH 0 0 rf2 RFCavity VOLT 0 25796 FMAPFN avl dat TYPE SINGLEGAP FREQ frequency ANGLE 215 0 PHIO phi03 RMIN 350 0 RMAX 3350 0 PDIS 0 0 GAPWIDTH 0 0 rf3 RFCavity VOLT 0 25796 FMAPFN avl dat TYPE SINGLEGAP FREQ frequency ANGLE 235 0 PHIO phi04 RMIN 350 0 RMAX 3350 0 PDIS 0 0 GAPWIDTH 0 0 rf4 RFCavity VOLT 0 06380 FMAPFN av3 dat TYPE SINGLEGAP FREQ frequency3 ANGLE 135 0 PHIO phi05 RMIN 830 0 RMAX 3330 0 PDIS 0 0 GAPWIDTH 0 0 rf5 RFCavity VOLT 0
64. 0000000 00 Figure C 6 A ID field describing dvnamic field using n non equidistant grid points in longitudinal di rection From the n non equidistant field values n equidistant field values are computed from which in turn n 2 complex Fourier coefficients are calculated In this example only 40 Fourier coefficients are kept to calculate the off axis field values The z position is in the 1 column in meters the corresponding longitudinal on axis elec tric field amplitude is in the 2 column OPAL Tnormalizes the field values such that max Egnaxis 1 MV m In the header only the first and the third line of a corresponding IDDvnamic field map is needed since the infor mation on the longitudinal dimension is contained in the first column OPAL Tdoes not provide a FAST version of this map type 7 IDPROFILEI IDPROFILE2 173 C 7 1IDProfilel amp 1DProfile2 The field maps IDProfilel and 1DProfile2 are different from the rest since no actual fields are stored but a profile They are used to represent the fringe fields of various elements The actual fields used in an OPAL Tsimulation are calculated using Enge functions 44 In turn the Enge functions are declared in two different ways A IDProfilel field map gives the coefficients of the Enge function explicitly A 1DProfile2 field map stores the profile itself From this profile the Enge coefficients are calculated by solving a least square equation On the first line afte
65. 1 3 517 ELEMEDGE 6 074 SCREEN Monitor L 0 01 ELEMEDGE 7 3867 OUTFN Screen h5 FIND1 Line FINLBO2 MSLAC40 FINDI MQ10 FINDI MQ20 SCREEN Distl DISTRIBUTION DISTRIBUTION gauss sigmax 1 0e 03 sigmapx 1 0e 4 corrx 0 5 sigmay 2 0 03 sigmapy 1 0e 4 corry 0 5 sigmat 3 0e 03 sigmapt 1 0e 4 corrt 0 0 Fs2 FIELDSOLVER FSTYPE FFT MX 32 MY 32 MT 64 PARFFTX false PARFFTY false PARFFTT true BCFFTX open BCFFTY open BCFFTT open BBOXINCR 1 0 GREENSF INTEGRATED PARTICLE ELECTRON pc PO NPART 1e5 BFREQ 1498 953425154e6 BCURRENT 0 299598 CHARGE 1 Select Line FIND1 track line FIND1 beam beaml MAXSTEPS 10000 DT 1 0e 12 run method PARALLEL T beam beaml fieldsolver Fs2 distribution Disti endtrack Stop 3 4 2 PSI Injector II Cyclotron Injector II is a separated sector cyclotron specially designed for preacceleration inject 870 keV extract 72 MeV of high intensity proton beam for Ring cyclotron It has 4 sector magnets two double gap acceleration cavities represented by 2 single gap cavities here and two single gap flat top cavities Following is an input file of Single Particle Tracking mode for PSI Injector II cyclotron examples opal cycl in Title string OPAL CvclT test Option TFS FALSE Option ECHO FALSE Option PSDUMPFREQ 100000 Option SPTDUMPFREQ 5 3 4 EXAMPLES OF BEAM LINES define some phvsical parameters Edes
66. 18 9 Py Py 2400 18 10 18 2 2 Large Angle Rutherford Scattering 25 Ps a da Generate a random number 1 if amp lt Te Pu a dat 725 Ps ajd gem 0 0047 sampling the large angle Rutherford scattering The cumulative distribution function of the large angle Rutherford scattering is Ps a da F a Jag Ps e do alo E 18 11 dee Ps a da where is a random variable So i i a 2 54 UH 18 12 18 3 THE FLOW DIAGRAM OF COLLIMATORPHVSICS CLASS IN OPAL 137 Generate a random variable P3 if P gt 0 5 Oru 25 2260 18 13 else Oru 725 2283 18 14 The angle distribution after Coulomb scattering is shown in Fig 18 2 The line is from Jackson s formula and the points are simulations with Matlab For a thickness of As le 4 m 0 0 5349a in degree P P 0 Figure 18 2 The comparison of Coulomb scattering with Jackson s book 18 3 The Flow Diagram of CollimatorPhysics Class in OPAL 138 CHAPTER 18 PHVSICS MODELS USED IN THE PARTICLE MATTER INTERACTION MODEL bunch in the regio Qf collimator Yes loop over particles in bunch particle alive get the value of R P particle in collimatorz Y es Yes No scattering and integration record particle in partColArray label 0 mark the particle to remove calculate the number of particles in partColArrav dt dtbunch n loop over particles in partColArrav No particle
67. 1T3 T7 1 615e 05 rv3 SP3 Solenoid L 1 20 LEMEDGE 0 267 FMAPFN 1T3 T7 1 016e 05 4 rv4 5 4 Solenoid L 1 20 FMAPFN 1T3 T7 SP5 Solenoid L 1 20 FMAPFN 1T3 T7 LEMEDGE 0 157 4 750 05 rv5 LEMEDGE 0 047 0 0 CQ Dd Co Dd Co Dd Co Dd Co Hd gun RFCavity L 0 013 FMAPFN IT1 T7 TYPE STANDING VOLT 47 51437343 rv1 LEMEDGE 0 00 REQ 1 0e 6 xa op value I rvl rv2 rv3 rv4 rv5 11 Line gun Ppo spl sp2 sp3 sp4 sp5 SELECT Line 11 122 CHAPTER 15 TRACKING TRACK line 11 beam beaml MAXSTEPS 500 DT 2 0e 13 RUN method PARALLEL T beam beaml fieldsolver Fs1 distribution Distl ENDTRACK SYSTEM mkdir p scan0 6 STRING I SYSTEM mv scan 0 h5 scan 0 stat scan 0 lbal scan0 amp STRING I I EVAL I41 0 Chapter 16 Field Emission Field emission is a major source of both dark current particles and primarv incident particles in secondarv emis sion The Fowler Nordheim F N formula we use here to predict the emitted current densitv is given in 16 1 52 53 2 Bo 3 2 J r t MA exp 555 A m 16 1 where J r t stands for emitted electric current density in position r and time t The Greek letters y 8 denote the work function of the surface material and the local field enhancement factor respectively The parameter E is the electric field in the normal direction of surface The parameters A and B a
68. 7 1 shows a typical SEY curve Here the horizontal axis is the energy of impacting electron the vertical axis is the SEX value 6 defined as 56 TOS 17 1 where 10 is the incident electron beam current and 1 is the secondary current i e the electron current emitted from the surface Usually the SEY value appeared in an SEY curve is the measured SEY with normal incident i e the impacting electron is perpendicular to the surface The energy and E are the first crossover energy and the second crossover energy respectively where the SEY value 6 exceed and fall down to 6 1 at the first time Obviously only the energy range of gt 1 i e E can contribute to multipacting Both Furman Pivi s probabilistic secondary emission model 56 and Vaughan s formula based secondary emission model 57 have been implemented in OPA Land have been benchmarked see Section 17 2 The Furman and Pivi s secondary emission model calculates the number of secondary electrons that result from an incident electron of a given energy on a material at a given angle see Figure 17 2 For each of the generated secondary electrons the associated process true secondary rediffused or backscattered is recorded as is sketched in Figure 17 2 This model is mathematically self consistent which means that 1 when averaging over an infinite number of secondary emission events the reconstructed and d d E are guaranteed to agree with
69. 74 APPENDIX C OPAL T FIELD MAPS Origin of Enge Function Origin of Enge Function Figure C 8 FIXME The location and definitions of the Enge function coefficients for a sector bend and its corresponding design path 6 7 3 0 0 72 0 2 0 1000 DAO 2350 3250 0 00000 00 36222 06 83270 06 9 lines 32490 05 73710 05 18598 05 po 90 pex Figure C 9 A 1D field map describing the fringe field of an element using 7 Enge coefficients for the entrance fringe field and 8 Enge coefficients for the exit fringe field polynomial order 6 and 7 respectively The element has a gap height of 3 0 cm the entrance fringe field is non negligible from 6 0 cm and reaches the core strength at 2 0 cm relative to ELEMEDGE The origin of the Enge function for the entrance fringe field is at 2 0 cm relative to ELEMEDGE The exit fringe field is non negligible up to 32 0 cm from ELEMEDGE and starts to deviate from the core strength after 24 0 cm from ELEMEDGE The origin of the Enge function for the exit fringe field is at 28 0 cm from ELEMEDGE The values 1000 in line 2 and 0 in line 3 do not have any meaning C 7 IDPROFILEI amp IDPROFILE2 175 lez 6 y 3 0 0 2 0 2 0 1000 24 9 28 0 32 0 O 00000 00 36222 06 83270 06 995 lines 32490 05 73710e 05 18598e 05 Noy J fos HS em Figure C 10 A 1D field map describing the f
70. 827231 GeV HMMASS m h 939277 GeV CMASS Me 12 0 93 1494027 GeV UMASS Mu 238 0 931494027 GeV MMASS my 0 1057 GeV DMASS md 2 0 931494027 GeV XEMASS Tae 124 0 931494027 GeV CLIGHT 299792458 m s 6 8 4 Element or command attributes 53 In arithmetic expressions the attributes of physical elements or commands can occur as operands They are named respectively by element name attribute name command name attribute name If they are arrays they are denoted by element name attribute name index command name attribute name index Values are assigned to attributes in element definitions or commands Example DI DRIFT L 1 0 D2 DRIFT L 2 0 D1 gt L D1 L refers to the length L of the drift space D1 6 8 5 Deferred Expressions and Random Values Definition of random machine imperfections requires evaluation of expressions containing random functions These are not evaluated like other expressions before a command begins execution but sampled as required from 54 CHAPTER 6 COMMAND FORMAT the distributions indicated when errors are generated Such an expression is known as a deferred expression Its value cannot occur as an operand in another expression Example ERROR EALIGN CLASS QUADRUPOLE DX SIGMAxGAUSS elements in range are assigned independent random displacements sampled from a Gaussian distribution with standard deviation SIGMA The quantity ERROR PDX must not occur
71. 9 Distl DISTRIBUTION DISTRIBUTION GUNGAUSSFLATTOPTH sigmax 0 00054 sigmapx 0 0 corrx 0 0 sigmay 0 00054 sigmapy 0 0 corrv 0 0 sigmat 0 0 pt 0 0 sigmapt 0 0 corrt 0 0 tRise 0 5e 12 tFall 0 5e 12 tPulseFWHM 9 9e 12 cutoff 3 0 NBIN 50 DEBIN 80 ELASER 4 6 SIGLASER 0 001 W 4 6 FE 7 0 AG 84 11 3 Distribution taattop FWHMp d PWHMg FWHMr tr 90 50 10 3O0R 20R OR Op 20p 3op 1 tg 3 FWHMp 35 22 tg tr Figure 11 1 OPAL Gauss Flattop Distribution Figure 11 1 depicts parameters needed to specify a Gauss Flattop distribution in OPAL where c stands for cutoff P for pulse R for rise and F for fall A Gauss Flattop distribution is defined as half a Gauss plus a uniform flat top part plus half a Gauss with the parameters and tgattop For practical reasons we replace these three parameters with the following measurable parameters 10 2In cg 1 68690 tp 1 686907 and FWHMp tfattop 21 2 oR oL 106 CHAPTER 11 DISTRIBUTION COMMAND The emission time tg with a given cutoff c in terms of input parameters is given by 1 1 tg c FWHMp 3 WHMpr a WHMr COR COR c 21 2 FWHMp WHMP In OPAL this distribution be specified the following distribution command thermal emittance enabled Distl DISTRIBUTION DISTRIBUTION GUNGAUSSFLATTOPTH sigmax
72. 9 Figure 14 3D field map describing a dvnamic field oszillating with 1 498953425154 GHz The field map provides 4122 grid points in z direction times 228 grid points in x direction and 152 grid points in v direction The field between the grid points is calculated with a bilinear interpolation The field is non negligible between 3 0 to 51 0 cm relative to ELEMEDGE the 228 grid points in x direction range from 1 5 cm to 1 5 and the 152 grid points in y direction range from 1 0 cm to 1 0 cm relative to the design path The field values are ordered in XYZ orientation the index in z direction changes fastest then the index in y direction while the index in x direction changes slowest This is the only orientation that is implemented The columns correspond to Ez Ey Ez By By and B 180 APPENDIX C OPAL T FIELD MAPS Bibliographv 1 The Graphical Kernel System GKS ISO Geneva July 1985 International Standard ISO 7942 2 B Autin and Y Marti Closed Orbit Correction of Alternating Gradient Machines using a small Number of Magnets CERN ISR MA 73 17 CERN 1973 3 D P Barber K Heinemann H Mais and G Ripken A Fokker Planck Treatment of Stochastic Particle Motion within the Framework of a Fully Coupled 6 dimensional Formalism for Electron Positron Storage Rings including Classical Spin Motion in Linear Approximation DESY report 91 146 1991 4 R Bartolini A Bazzani M Giovannozzi W Scandale a
73. 99 The following examples will break the parsing of the field maps 1DMagnetoStatic This is an invalid comment 40 60 0 60 0 4 This is an other invalid comment 9999 0 0 2 0 199 If OPAL Tencounters an error while parsing a field map it disables the corresponding element outputs a warning message and continues the simulation The following messages may be output WARN I N Gok RK RK RR RR ER RR IK THERE SEEMS TO BE SOMETHING WRONG WITH YOUR FIELD MAP file t7 There are only 10003 lines in the file expecting more Please check the section about field maps in the user manual ck ck ck ck ck ck ck ck KKK KKK KKK KKK KKK KKK KKK KKK KKK KKK KK KK KKK KKK KKK ko ko ko ko ko ko ko kk In this example there is something wrong with the number of grid spacings provided in the header of the file Make sure that you provide the number of grid spacings and not the number of grid points The two numbers always differ by 1 KKKKKKKKKKKK WA RN IN G KKK KKK KK KK ck ck kk kk kk kc kc kc k THERE SEEMS TO BE SOMETHING WRONG WITH YOUR FIELD MAP file t7 There are too many lines in the file expecting only 10003 lines Please check the section about field maps in the user manual ck ck ck ck ck ck ck ck Ck Ck CC CK CK CK CK CK CI CIS SS SS Sk Sk kk kk Sk Sk kk kk kk ck ck ck kk Ck kk kk Sk kk oko 163 164 APPENDIX C OPAL T FIELD MAPS
74. CTOR 9 1 2 3 4 Sy Tr 8 9 10 43 Circular definitions are not allowed but redefinitions by assignment are allowed Logical Variables BOOL variable name logical expression This statement creates a new global variable variable name and discards any old variable with the same name Its value depends on all quantities occurring in 1ogical expression see 86 5 Whenever an operand changes in logical expression a new value is calculated The definition may be thought of as a mathe matical equation However OPAL is not able to solve the equation for a quantity on the right hand side Example BOOL FLAG X 0 Circular definitions are not allowed but redefinitions by assignment are allowed 7 4 2 Symbolic Constants OPAL recognises a few build in built in mathematical and physical constants see Tab 6 8 Additional constants can be defined by the command REAL CONST label CONSTANT real expression which defines a constant with the name label The keyword REAL is optional and 1 1 must be unique An existing symbolic constant can never be redefined The real expression is evaluated at the time the CONST definition is read and the result is stored as the value of the constant Example CONST IN 0 0254 conversion of inches to metres 7 4 3 Vector Values A vector of expressions is established by a statement REAL VECTOR vector name vector expression 7 4 PARAMETE
75. E 1 3 FREQ 1498 956 LAG 248 0 360 0 8 13 Monitors A MONITOR detects all particles passing it and writes the position the momentum and the time when they hit it into an H5hut file Furthermore the exact position of the monitor is stored It has always a length of 1 cm consisting of 0 5 cm drift the monitor of zero length and another 0 5 cm drift This is to prevent OPAL Tfrom missing any particle The positions of the particles on the monitor are interpolated from the current position and momentum one step before they would passe the monitor 90 CHAPTER 8 ELEMENTS OUTFN The filename into which the monitor should write the collected data The file is an HShut file ELEMEDGE The position of the monitor is specified absolute floor space co ordinates in m This is the position at which the data is collected This is a restricted feature Ka OPAL CYCL 8 14 COLLIMATORS 91 8 14 Collimators Three tvpes of collimators are defined ECOLLIMATOR Elliptic aperture RCOLLIMATOR Rectangular aperture CCOLLIMATOR Radial rectangular collimator in cyclotrons label ECOLLIMATOR TYPE string APERTURE real vector L real XSIZE real YSIZE real label RCOLLIMATOR TYPE string APERTURE real vector L real XSIZE real YSIZE real Either type has three real attributes L The collimator length default 0 m XSIZE The horizontal half aperture default unlimited XSIZE The vertical half aperture default unlimited For e
76. E VER But 61 Td HELP Command irsi orari a REDEEM RERO 61 7 1 2 SHOW Command 61 TASS WHAT Command 5 5 sia eere eh De Ar aoe a RR UA 62 7 22 STOP QUIT Statement ue Rx eere bog ep de eee Exe eee A 62 7 3 OPTION Statement sse o omo 545465864054 6 ISO 62 TA Parameter Statements 5 3 55 a ae eme ee ox ed dg 64 7 4 4 Variable Definitions 64 74 2 Symbole Constants possc san eb Wu ba mr intu sg 66 CONTENTS 74 32 Vector Val es se Te det pe ex vens Ar e P HE Bk Bee 7 4 4 Assignmentto Variables 7 4 5 VALUE Output of Expressions 7456 l ele MES ere XEG uere NE 7 5 Miscellaneous Commands del ECHO Statement kr e Dg SONUS GU RT S p 7 5 2 SYSTEM Execute System Command 7 5 3 SYSTEM Command under 7 6 TITLE Statement Maur TER M ENDS RE AD Rar es 757 Handing mr BA LA eR uem Dee s eene ds Jb GALL Statement rad shies Wa ga ped edu DU EN SE 7 12 SAVE Statement i loeo oo Be ADR RASA ES TAs MAKESEO Statement uU DE AE ea oe
77. Figure 17 4 Time evolution of electron number predicted bv theoretical model and OPAL simulation using Vaughan s secondarv emission model with both constant simulation particle approach and real emission particle approach at f 1640MHz Vo 120V d Imm To run the parallel plate benchmark simulation user need to set the option PPDEBUG in the input file true 132 CHAPTER 17 MULTIPACTING The input file and the geometry file needed by the parallel plate benchmark simulation can be found in the regres sion test folder 17 3 POSTPROCESSING 133 17 3 PostProcessing In the general case not only in multipacting simulations OPALwill dump the 6D phase space and statistical information of the particles in the simulation domain into a h5 file The dump frequency i e after how many time steps the particle information will be saved can be specified with the option PSDUMPFREQ Setting Option PSDUMPFREQ 1 dumps the information in each time step A utility tool hSToVtk converts the n5 file to the Visualization Toolkit VTK legacy format The number of VTK files equals to the number of time steps in h5 file These VTK files together with a VTK file automatically generated by the geometry class of OPAL which contains the geometry of the RF structure under study can be visualized using for example with Paraview 61 The animation and clip feature of Paraview is very useful to visualize the particle motion inside the RF structure For simulatio
78. IGMA Material constant dependent on the beam pipe material in Q m TAU Material constant dependent on the beam pipe material in s FNAME Specify a file that provides a wakefunction 13 2 Define the Wakefield to be used The WAKE statement defines data for a wakefunction on an element 13 3 Define the wakefield type Used to specify the wakefunction 13 4 DEFINE THE NUMBER OF BINS 113 13 4 Define the number of bins The number of bins used in the calculation of the line densitv 13 5 Define the bunch length to be constant With the CONST LENGTH flag the bunch length can be set to be constant 13 6 Define the conductivity The conductivity of the bunch which can be set to either AC or DC 13 7 Define the impedance The impedance Zo of the beam pipe in 13 8 Define the form of the beam pipe The form of the beam pipe can be set to ROUND 13 9 Define the radius of the beam pipe The radius of the beam pipe in m 13 10 Define the c of the beam pipe The c of the beam pipe material constant see 13 1 13 11 Define the relaxation time 7 of the beam pipe The 7 defines the relaxation time and is needed to calculate the impedance of the beam pipe see 13 1 13 12 Import a wakefield from a file Since we only need values of the wakefunction at several discreet points to calculate the force on the particle it is also possible to specify these in a file To get required datapoints of the wakefield not
79. L 0 54 VOLT 19 961 LAG 193 0 360 0 FMAPFN 1T3 T7 ELEMEDGE 0 129 TYPE STANDING FREQ 1498 956 rf2 RFCavity L 0 54 VOLT 6 250 LAG 136 0 360 0 FMAPFN 1T4 T7 ELEMEDGE 0 129 TYPE STANDING FREQ 4497 536 8 11 2 OPAL CYCLmode Using a Cavity standing wave in OPAL CvCLmode the following parameters are defined FMAPEN Defines name of file which stores normalized voltage amplitude curve of cavity gap in ASCII format See data format in Section5 4 VOLT Sets peak value of voltage amplitude curve in MV TYPE Defines Cavity type SINGLEGAP represents cyclotron type cavity FREQ Sets the frequency of the RF Cavity in units of MHz 8 11 RF CAVITIES OPAL T AND OPAL CVCL 87 RMIN Sets the radius of the cavity inner edge in mm RMAX Sets the radius of the cavity outer edge in mm ANGLE Sets the azimuthal position of the cavity in global frame in degree PDIS Set shift distance of cavity gap from center of cyclotron in mm If its value is positive the shift direction is clockwise namely shift towards the smaller azimuthal angle GAPWIDTH Set gap width of cavity in mm PHIO Set initial phase of cavity in degree Example of a RF cavity of cyclotron rf0 RFCavity VOLT 0 25796 FMAPFN Cavl dat TYPE SINGLEGAP FREQ 50 637 RMIN 350 0 RMAX 3350 0 ANGLE 35 0 PDIS 0 0 GAPWIDTH 0 0 PHIO phi01 Fig 8 2 shows the simplifed geometry of a cavity gap and its parameters machine center
80. LA FEL Report 1997 01 50 J E Clendenin T Kotseroglou G A Mulhollan D T Palmer J F Schmerge Reduction of thermal emittance of RF guns NIM A 455 2000 198 201 51 A Adelmann and P Arbenz and Y Ineichen A Fast Parallel Poisson Solver on Irregular Domains Applied to Beam Dynamic Simulations 0907 4863v1 arXiv 2009 52 Y Feng and J P Verboncoeur Transition from Fowler Nordheim field emission to space charge limited current density Phys Plasmas 13 073105 2006 53 R H Fowler and L Nordheim Electron Emission in Intense Electric Fields Proc R Soc London Ser A 119 173 1928 54 J H Han Dynamics of Electron Beam and Dark Current in Photocathode RF Guns PhD Thesis Desy 2005 Available Online on http www library desy de preparch desy thesis desy thesis 05 045 pdf 55 C Wang and A Adelmann and Y Ineichen A Field Emission and Secondary Emission Model in OPAL Proc of HB2010 MOPD55 2010 56 M A Furman and M T F Pivi Probabilistic model for the simulation of secondary electron emission Phys Rev ST Accel Beams 5 124404 2002 57 J Rodney M Vaughan A New Formula for Secondary Emission Yield IEEE Trans on Electron Devices 36 9 1963 1989 58 J Rodney M Vaughan Secondary Emission Formulas IEEE Trans on Electron Devices 40 4 830 1993 59 C Vicente and M Mattes and D Wolk and H L Hartnagel and J R Mosig and D Raboso FEST3D A Simulation Tool for Multipacto
81. N SQRT LOG SIN COS ABS TAN ASIN ACOS ATAN TGAUSS USER1 ATAN2 AX IN OD POW APPENDIX B OPAL LANGUAGE SYNTAX function of array VMIN VMAX VRMS VABSMAX Real variables and constants real prefix real definition symbolic constant real name object name table reference empty REAL REAL CONST CONST real prefix real name real expression expression evaluated real prefix real name real expression expression ratained TWOPI U EGRAD RADDEG ti EMASS PMASS CLIGHT real name identifier identifier table name 8 place gt column name 157 158 table name column name Logical expressions logical expression and expression relation logical name relation operator APPENDIX B OPAL LANGUAGE SVNTAX identifier identifier and expression logical expression and expression relation and expression amp relation logical name TRUE FALSE real expression relation operator real expression identifier 159 Logical variables logical prefix BOOL BOOL CONST logical definition logical prefix logical name logical expression expression evaluated logical prefix logical name logical expression expression retained String expressions string expression String identifier taken as a string string expression am
82. O SEX will be if energy is less than VEZERO in Vaughan s model 12 5 eV VSEYZERO in Vaughan s model 0 5 VSEYMAX maa in Vaughan s model 2 22 VEMAX Energy related to maxr in Vaughan s model 165 eV VKENERGY The roughness of surface for impact energy in Vaughan s model 1 0 VKTHETA The roughness of surface for impact angle in Vaughan s model 1 0 SURFMATERIAL The material type for Furman Pivi model 0 copper 1 stainless steel 0 17 2 RUN PARALLEL PLATE BENCHMARK 131 17 2 Run Parallel Plate Benchmark Both the Furman Pivi s model and Vaughan s model have been carefully benchmarked in both re normalize sim ulation particle approach and real simulation particles approach against a non stationary multipacting theory 60 The OPALsimulation results and the theory match very well see figure 17 3 and figure 17 4 theory H OPAL const particlesii OPAL real emission normalized particle number i 0 10 20 30 40 50 60 time ns Figure 17 3 Time evolution of electron number predicted by theoretical model and OPAL simulation using Furman Pivi s secondary emission model with both constant simulation particle approach and real emission par ticle approach at f 200M Hz Vo 120V d 5mm theory OPAL const particles OPAL real emission Normalized Particle Number 1 0 0 5 1 1 5 2 2 5 3 3 5 4 4 5 5 time ns
83. R STATEMENTS 67 The keyword REAL is optional It creates a new global vector vector name and discards any old vector with the same name Its value depends on all quantities occurring in vector expression see 6 14 Whenever an operand changes in vector expression a new value is calculated The definition may be thought of as a mathematical equation However OPAL is not able to solve the equation for a quantity on the right hand side Example VECTOR A AMPL 2 5e 3 3 4e 2 0 4 5e 8 VECTOR A ON TABLE 10 1 Circular definitions are not allowed 7 4 4 Assignment to Variables A value is assigned to a variable or vector by using the function EVAL real expression When seen this function is immediately evaluated and replaced by the result treated like a constant variable name EVAL real expression This statement acts like a FORTRAN or C assignment The real expressionor vector expression is evaluated and the result is assigned as a constant to the variable or vector on the left hand side Finally the expression is discarded The EVAL function can also be used within an expression e g vector name TABLE range EVAL real expression vector name EVAL real expression A sequence like the following is permitted UU some definitions X20 create variable X with value zero WHILE X lt 0 10 TWISS LINE uses X 0 0 01 0 10 X EVAL X 01 increment variab
84. Rn e Bxamples 2 ge m RR mim E dee tme ni E OPAL Language Syntax OPAL T Field Maps CL Introduction z s suum Re Ant JIE A dex P WO IDE Ug ee ee 52 Types and Format gt o nie we ORO Aedes eU A TRIES C3 1DMagnetoStafiC eR Ren RU CUR SNe ROT e d CA AstraMagnetostatic ES 1DDynamie pes xn nec Re m EG m kk Eg ea pe xq S 6 AstraDynamlIC Re be yop uu Ue QUU Re EUR RO e ugs UU e C IPProtilelit 1DProhle2 i v aue woe eb WHEN EUER vede s dies d C8 2DBl ctroStatiC sa odo sony Se eS Ee Por hee be ee ease ee eee PR ea Ee 29 2DMasgnetoStatlC zs Be boats BE Sat kG CAO 2DDyt amiC ss aud OR Pes ER Hee Oa Seed ee ue CAT SD Dynan x hbase 123 124 125 128 131 133 135 135 136 136 136 137 140 140 140 143 143 143 143 145 145 145 146 146 148 148 150 150 151 153 CONTENTS List of Tables 7 1 11 1 11 2 11 3 12 1 12 2 14 1 15 1 16 1 17 1 Physical Units 225225525 SEA ee GA Pe a ees 20 String Operatorin OPAL 222502255506 el US RR 48 String Functionin OPAT i 4 XO ow pa NU Re 48 Logical Operatorsin 49
85. STALLATION Using pre build Binaries Pre build binaries are available for SL Linux 2 16 and Mac OS X 10 6 7 6 10 7 3 at the following download page http amas web psi ch download OPAL 4 Enabling the Multigrid Space Charge Solver Please note The Multigrid space charge solver is not vet capable of emitting a beam from the cathode Xou are advised to use the FFT space charge solver for studies with particle emission The following packages must be pre installed mkl 10 0 em64t parmetis SuperLUDist If using CMake you can enable the solver with cmake D ENABLE ML SOLVER TRUE S OPAL and make sure the TRILINOS INCLUDE PATH en vironment variable points to the directory containing the Trilinos header files If no Trilinos version 710 6 is available download and build the source code from the Trilinos webpage The following Trilinos packages are required e epetra and epetraext e ml and ml parmetis3x e amesos and amesos superludist e ifpack e teuchos and teuchos extended e aztecco and aztecoo teuchos e galeri e belos To enable these packages run cmake with the following arguments CC mpicc CXX mpicxx CPP mpicxx F77 mpif77 cmake prefix path to install DCMAKE INSTALL PREFIX PATH path to install DCMAKE CXX FLAGS STRING DMPICH IGNORE CXX SEEK fPIC DCMAKE C FLAGS STRING DMPICH IGNORE CXX SEEK fPIC DCMAKE Fortran FLAGS STRING fPIC
86. TORIAL Option FINSS RGUN AUTOPHASE 4 3 5 180xPi The cavitv would be defined like FINSS RGUN RFCavitv L 0 17493 VOLT STANDING FINSS RGUN dat ELEMEDGE 0 0 LAG FINSS RGUN phi 100 0 FREQ 2998 0 with FINSS RGUN phi defining the off crest phase Now a normal TRACK command can be executed A file containing the values of maximum phases is created and has the format like 1 FINSS RGUN 2 22793 with the first entry defining the number of cavities in the simulation 3 4 Examples of Beam Lines Title string OBLA Gun Option Option Option Edes 1 0E 9 TFS FALSE PSDUMPFREQ 10 FALSE gamma Edes EMASS EMASS beta sqrt 1 gambet gamma x brho 55 value gamma L KS ELEMEDGE 5 1 5 0 000 SP2 Solenoid SP3 Solenoid gun RFCavitv ELEMEDGE 112 Line rf 1498 956e6 Solenoid L 1 20 1 gamma 2 beta gammaxbetaxEMASS 1 0e9 gambet field file name v0 betax xCLIGHT Iz 6 5E 12 value v0 1z v0 phvsical element length field scaling factor VOLT 102 28 CLIGHT brho Edes beta gambet real string physical start of the element on the floor ELEMEDGE 0 5335 ELEMEDGE 0 399 ELEMEDGE 0 269 LI L 1 20 L 1 20 P ESO 4011 20 00 TYPE STANDING g
87. X Vi PY 21 21 T2 pro py2 22 pz2 UN PLN UN PYN ZN PZN where N is the number of particles the vector z yi zi describes the position of the i th particle and the vector px pz its momentum in as defined in section 4 2 and section 5 3 11 1 Correlations for Gaussian Distribution Experimental To generate gaussian initial distribution with dispersion first we generate the uncorrelated gaussian inputs matrix R R1 Rn The mean of R is 0 and the standard deviation squared is 1 Then we correlate R The correlation coefficient matrix in x px t p phase space reads x t pt 104 CHAPTER 11 DISTRIBUTION COMMAND 1 Cx 151 r61 Cx 1 r52 r62 rbl r52 1 Ct 61 762 ci 1 The Cholesky decomposition of the symmetric positive definite matrix is then the correlated distribution is R Note This correlation works for the moment only with the gaussian distribution 11 1 1 Example Let the initial correlation coefficient matrix be 1 0 756 0 023 0 496 0 756 1 0 385 0 042 0 023 0 385 1 0 834 0 496 0 042 0 834 1 then the corresponding distribution command read Dist DISTRIBUTION DISTRIBUTION gauss sigmax 4 796e 03 sigmapx 231 0585 corrx 0 756 sigmay 23 821e 03 sigmapy 1 6592e 03 corrv 0 999 t 0 466e 02 sigmat 0 466e 02 pt 72e6 sigmapt 74 7 corrt 0 834 r6l 0 496 r62 0 042 r5120 023 r5220 385 11 2 Thermal Emittance The thermal emittanc
88. YCL Example LIST COLUMN X 12 6 V 12 6 where X 12 6 and Y 12 6 are two token lists and X 12 6 X 12 6 isa token list array 6 14 Arrays An attribute array is a set of values of the same attribute type see 86 3 Normally an array is entered as a list in braces value value The list length is only limited by the available storage If the array has only one value the braces can be omitted value 6 14 1 Logical Arrays For the time being logical arrays can only be given as a list The formal syntax is logical array ji legical last j logical list logical expr l logical list logical expr Example true true a b false x y 88 y gt z true false 6 14 2 Real Arrays Real arrays have the following syntax array ref array variable object gt array attribute table ref ROW table place ROW table place column list COLUMN table column 58 columns column list column real list index select arrav primarv arrav factor arrav term arrav expr COLUMN t column column lis column column list string real expr on real list integer integer in integer in real list TABLE array ref table ref array function array express in array primary array factor array factor array term array term
89. aces all occurrences of the corresponding formal name The actuals are separated by commas Example macro definitions SHOWIT X MACRO SHOW NAME X 7 10 MACRO MACRO STATEMENTS SUBROUTINES DOIT MACRO DYNAMIC LINE RING FILE DYNAMIC OUT macro calls SHOWIT PI DOIT 71 72 CHAPTER 7 CONTROL STATEMENTS Chapter Elements 81 Element Input Format phvsical elements are defined statements of the form label kevword attribute attribute where label Is the name to be given to the element in the example itis an identifier see 56 2 kevword Is a keyword see 86 2 it is an element type keyword in the example QUADRUPOLE attribute normally has the form attribute name attribute value attribute name selects the attribute from the list defined for the element type keyword in the example L and K1 It must be identifier see 6 2 attribute value gives ita value see 86 3 in the example 1 8 and 0 015832 Omitted attributes are assigned a default value normally zero Example QF QUADRUPOLE L 1 8 Kl 0 015832 8 2 Common Attributes for all Elements The following attributes are allowed on all elements TYPE A string value see 86 4 It specifies an engineering type and can be used for element selection 73 74 CHAPTER 8 ELEMENTS APERTURE A real vector with an arbitrary length which describes the
90. achine design One mode is the single particle tracking mode which is a useful tool for the preliminary design of a new cyclotron It allows one to compute basic parameters such as reference orbit phase shift history stable region and matching phase ellipse The other one is the tune calculation mode which can be used to compute the betatron oscillation frequency This is useful for evaluating the focusing characteristics of a given magnetic field map In additions the widely used plugin elements including collimator radial profile probe septum trim coil field and charge stripper are currently implemented in OPAL CYCLThese functionalities are very useful for designing commissioning and upgrading of cyclotrons and FFAGs 5 2 Tracking modes According to the number of particles defined by the argument NPART in BEAM see Section 10 1 OPAL CYCL works in one of the following three operation modes automatically 5 2 1 Single Particle Tracking mode In this mode only one particle is tracked either with acceleration or not Working in this mode OPAL CYCL can be used as a tool during the preliminary design phase of a cyclotron The 6D parameters of a single particle in the initial local frame must be read from a file To do this in the OPAL input file the command line DISTRIBUTION See section 11 should be defined like this Disti DISTRIBUTION DISTRIBUTION fromfile FNAME PartDatabase dat where the file Part Database dat
91. ack a beam line see 89 or sequence see 82 and a beam see 510 1 must be selected The time step DT and the maximal steps to track MAXSTEPS or ZSTOP should be set This command causes OPAL to enter tracking mode in which it accepts only the track commands see Tab 15 1 Several tracks can be defined in a sequence and all parameters are always local to the actual step The attributes of the command are 119 120 LINE The label of a preceding LINI E see 59 or S CHAPTER 15 TRACKING EQUE NC E see 82 no default BEAM The named BEAM command defines the particle mass charge and reference momentum default UNNAMED BEAM MAXSTEPS The maximal number of timesteps default value is 10 ZSTOP Defines a z location m after which the simulation stops when SPOS gt ZSTOP The initial value for ZSTOP is 1E6 m TIMEINTEGRATOR Define the time integrator Currently only available in OPAL CYCL The valid options are RK 4 LF 2 and MTS e RK 4 the fourth order Runge Kutta integrator This is the default integrator for OPAL CYCL e LF 2 the second order Boris Buneman leapfrog like integrator Currently LF 2 is only availabe for multi particles with without space charge For single particle tracking and tune calculations use the RK 4 for the time being e MTS the multiple time stepping integrator Considering that the space charge fields change much slower than the externa
92. andard mapping Physica D56 253 1992 27 H Mais and G Ripken Theory of Coupled Synchro Betatron Oscillations DESY internal Report DESY M 82 05 1982 28 M Meddahi Chromaticity correction for the 108 60 lattice CERN SL Note 96 19 AP 1996 29 J Milutinovic and S Ruggiero Comparison of Accelerator Codes for a RHIC Lattice AD AP TN 9 BNL 1988 30 B W Montague Linear Optics for Improved Chromaticity Correction LEP Note 165 CERN 1979 31 G Ripken Untersuchungen zur Strahlf hrung und Stabilit t der Teilchenbewegung in Beschleunigern und Storage Ringen unter strenger Ber cksichtigung einer Kopplung der Betatronschwingungen DESY internal Report R1 70 4 1970 32 F Ruggiero Dynamic Aperture for LEP 2 with various optics and tunes Proc Sixth Workshop on LEP Performance Chamonix 1996 ed J Poole CERN SL 96 05 DI 1996 pp 132 136 33 L C Teng Concerning n Dimensional Coupled Motion FN 229 FNAL 1971 34 U V lkel Particle loss by Touschek effect in a storage ring DESY 67 5 DESY 1967 35 R P Walker Calculation of the Touschek lifetime in electron storage rings 1987 Also SERC Daresbury Laboratory preprint DL SCI P542A 36 P B Wilson Proc 8th Int Conf on High Energy Accelerators Stanford 1974 37 A Wrulich and H Meyer Life time due to the beam beam bremsstrahlung effect PET 75 2 DESY 1975 38 Birdsall Langdon Plasma Physics via computer simulation Pag
93. aracters Example a zA Z denotes the choice of any letter Allows zero or more repetitions of the preceding item Example A Z denotes a string of zero or more upper case letters character Removes the special meaning of character Example denotes a literal asterisk other characters stand for themselves The pattern A Za z A Za z0 9 illustrates all possible unquoted identifier formats see 56 2 Since identifiers are converted to lower case after reading they will match the pattern Wla 0 9 1 Examples for pattern use SELECT PATTERN D SAVE PATTERN K QD R1 6 13 TOKEN LIST 57 The first command selects all elements whose names have exactly three characters and begin with the letter D The second command saves definitions beginning with the letter K containing the string OD and ending with the string R1 The two occurrences of x each stand for an arbitrary number including zero of any character and the occurrence V stands for a literal period 6 13 Token List In some special commands LIST see 2 an attribute cannot be parsed immediately since some information may not yet be available during parsing Such an attribute is entered as a token list and it is parsed again when the information becomes available Token lists can occur in token list arrays see 56 14 4 This is not yet available in K OPAL Tand OPAL C
94. arger of X Y real real real MIN X Y return the smaller of X Y real real real MOD X Y return the largest value less than Y which differs from X by a multiple real real real of Y USER2 X Y random number user defined distribution with two parameters real real real Care must be used when an ordinary expression contains a random generator It may be re evaluated at unpredictable times generating a new value However the use of a random generator in an assignment expression is safe Examples D DRIFT L 0 01xRANF a drift space with rand length mav change during execution P EVAL 0 001 TGAUSS X Evaluated once and stored as a constant 52 CHAPTER 6 COMMAND FORMAT Table 6 7 Real Functions Arravs OPAL Function Meaning result type operand type VMAX X Y return largest array component real real array VMIN X Y return smallest array component real real array VRMS X Y return rms value of an array real real array VABSMAX X Y return absolute largest array component real real array 6 8 Operands in Expressions A real expression may contain the operands listed in the follolwing subsections 6 8 1 Literal Constants Numerical values are entered like FORTRAN constants Real values are accepted in INTEGER or REAL format The use of a decimal exponent marked by the letter D or E is permitted Examples 1 10 35 314 1592 2
95. at If the value of TYPE is other string rather than above mentioned the program requires the data format like PSI format field file ZYKL9Z NAR and SO3AV NAR which was given by the measurement We add 4 parameters at the header of the file namely rmin mm Ar mm Onin A0 If Ar or A0 is decimal one can set its negative opposite number This is useful is the decimal is unlimited For instance if AQ 1 the fourth line of the header should be 3 0 1900 0 20 0 0 0 73 10 LABEL SO3AV CFELD FIELD NREC 141 NPAR 3 LPAR 7 IENT 1 IPAR l 3 141 135 30 8 8 70 LPAR 1089 IENT 2 IPAR 2 0 100000000 01 0 190000000 04 0 200000000 02 0 000000000E 00 0 333333343E 00 0 506500015E 02 0 600000000E 01 0 938255981E 03 0 100000000E 01 0 240956593E 01 0 282477260 01 0 340503168E 01 0 419502926 01 0 505867147 01 0 550443363E 01 0 570645094 01 0 579413509 01 0 583940887 01 0 586580372 01 0 588523722 01 5 4 5 user s own fieldmap You should revise the function or write your own function according to the instructions in code to match your own field format if it is different to above types For more detail about the parameters of CYCLOTRON please refer to Section 8 10 5 5 RF FIELD 41 5 5 RF field 5 5 1 Read RF voltage profile The RF cavities are treated as straight lines with infinitely narrow gaps and the electric field is a 6 function plus a transit time correction the two gap cavity is treated as two
96. atively coarse mesh with some 110 000 tetrahedra the difference between the analytical and the numerical solution was usually smaller than 1 percent 2 Using an adaptively refined mesh the difference between analytical and numerical solutions decreased below 1 pro mille The mesh is shown in the figure 1 3 3 It is thereofore imperative to usa a tetrahedral mesh which has been refined around the beam axis It is definitely more efficient to use local refinement based on physical argument than simply refine the complete mesh in a uniform manner We are now working towards benchmarking more complicated shapes in order to assess requirements w r t to meshes and modeling geometry so that we achieve the same or better accuracy as has been obtained from field maps that were computed with Superfish like solvers based on azimuthal symmetry 16 CHAPTER 1 INTRODUCTION Figure 1 3 We show the discretization of a pillbox shaped cavity geometry into a tetrahedral mesh The mesh has been adaptively refined so that the region around the cylinder axis is decomposed into smaller tetrahedra than those which are further away from the axis X HSPanROOT X HsPartROOT eoo X HSPartROOT Ele Options He line plot distr step 125 EI z pz distr stop 100 Gun test 2 P1 h5 Gun test 2 P1 h5 pz By Gun test 2 P1 hs e z m rad Entries 50000 Mean x 0 0132 Meany 1 702 RMS x 0 001686 RMS y 0 08248
97. atively thick absorbers such that the number of collisions is large the energy loss distribution is shown to be Gaussian in form For nonrelativistic heavy particles the spread of the Gaussian 135 136 CHAPTER 18 PHVSICS MODELS USED IN THE PARTICLE MATTER INTERACTION MODEL distribution is calculated bv L An 2 As 18 3 where p is the density As is the thickness 18 2 The Coulomb Scattering The Coulomb scattering is treated as two independent events the multiple Coulomb scattering and the large angle Rutherford scattering Using the distribution given in Classical Electrodynamics by J D Jackson the multiple and single scattering distributions can be written 1 2 Py o do ue da 18 4 1 da P s a da 20422173 18 5 0 OM where a 625172 726 the transition point is 0 2 5 200 3 500 g _ 13 6MeV zw As Xoll 0 038 In As Xojl 18 6 where p is the momentum As is the stepsize and is the radiation length 18 2 1 Multiple Coulomb Scattering Generate two independent Gaussian random variables with mean zero and variance one 21 and 22 If 2500 gt 3 506 start over Otherwise z1Asbo V12 22A580 2 18 7 Dr Dar 2200 18 8 Generate two independent Gaussian random variables with mean zero and variance one 24 and z4 If 2400 gt 3 506 start over Otherwise y y z3As00 v 12 24 A500 2
98. ay literal real expression array name object name gt array attribute identifier REAL VECTOR array prefix array name array expression array prefix array name array expression array expression constraint operator array expression real name object name gt attribute name 162 Places place Ranges range Token lists token list token list arrav Regular expressions regular expression APPENDIX B OPAL LANGUAGE SVNTAX element name element name integer 5 integer line name place place place place anvthing except comma token list token list array token list UNIX regular expression Appendix C OPAL T Field Maps C 1 Introduction In this chapter details of the different tvpes of field maps in OPAL Tare presented The possibilitv to add com ments almost evervwhere in the files is common to all field maps Comments are initiated bv a ff and contain the rest of a line Comments are accepted at the beginning of the file between the lines and at the end of a line If in the following sections two values are shown on one line then they have to be on the same line They should not be separated by a comment and consequently be on different lines Three examples of valid comments f This is valid a comment IDMagnetoStatic 40 This is an other valid comment 60 0 60 0 9999 f and this is also a valid comment 050 250 1
99. ble column implies all rows COLUMN table column range 60 CHAPTER 6 COMMAND FORMAT This generates array containing the selected or all rows of the named column 6 14 3 String Arrays String arrays can only be given as lists of single values For permissible values String values see 96 4 Example A Xyz A amp STRING X 6 14 4 Token List Arrays Token list arrays are always lists of single token lists Example 12 8 12 8 Chapter 7 Control Statements 7 1 Getting Help 7 1 1 HELP Command A user who is uncertain about the attributes of a command should try the command HELP which has three formats HELP Give help on the HELP command HELP NAME label List funct and attr types of label HELP label Shortcut for the second format label is an identifier see 56 2 If itis non blank OPALprints the function of the object 1abe1 lists its attribute types Entering HELP alone displays help on the HELP command Examples HELP HELP NAME TWISS HELP TWISS 7 1 22 SHOW Command The SHOW statement displays the current attribute values of an object It has three formats SHOW Give help on the SHOW command SHOW NAME pattern Show names matching of pattern SHOW pattern Shortcut for the second format patternisan regular expression see 86 12 If it is non blank OPALdisplays all object names match ing
100. ction Those two lines are omitted in the ASTRA compatible field maps On the sixth line follows the first line with field values as described above Even though there is no secondary direction in the ID case the header of a ID field map is equal to its 2D equivalent the elements can be provided with a boolean attribute FAST which has only an effect in conjunction with a 1D field map The code then generates internally a 2D field map and the field strengths are interpolated as in the case of 2D and 3D field maps instead of being calculated using the Fourier coefficients The fourth line determines the transverse dimension and the grain size of the produced mesh 168 APPENDIX C OPAL T FIELD MAPS pz By 7826 F pz By 7869 E 27825 l f 2 7868 E 2 7809 l 27824 F L 27823 L L 2 7867 823 2 7808 E 27822 2 7866 F 2 7807 L 2 7821 l L 1 2 7865 4 2 782 F l 27006 ta 0 d roo A 4 pica dri iei E ggg 0 01 0 015 0 02 0 01 0 015 0 02 0 01 0 015 0 02 z m z m z m a ID b ID FAST c 2D Figure C 2 The longitudinal phase space after a gun simulation using a 1D field map on axis field of the gun a ID field map on axis field of the gun in combination with the FAST switch and a 2D field map of the gun generated by Poisson Superfish i As a general warning be wise when you choose the type of field map to be u
101. d 2 stop false No matter what the value of STOP is the particles hitting on the STRIPPER are recorded in the ASCII file input filename loss 96 CHAPTER 8 ELEMENTS Chapter 9 Beam Lines The accelerator to be studied is known to OPAL as a sequence of phvsical elements called a beam line A beam line is built from simpler beam lines whose definitions can be nested to anv level A powerful svntax allows to repeat or to reflect pieces of beam lines Formally a beam line is defined by a LINE command label LINE member member label see 56 2 gives a name to the beam line for later reference Each member may be one of the following e An element label e A beam line label e A sub line enclosed in parentheses Beam lines can be nested to any level 91 Simple Beam Lines The simplest beam line consists of single elements label LINE member member Example L LINE A B C D A D 92 Sub lines Instead of referring to an element a beam line member can refer to another beam line defined in a separate command This provides a shorthand notation for sub lines which occur several times in a beam line Lines and sub lines can be entered in anv order but when a line is used all its sub lines must be known Example L LINE A B S B A S A B S LINE C D E 97 98 This example produces the following expansion steps 1 Replace sub line S CHAPTER 9 BEAM LINES
102. d in the bend plane of the magnet even when the magnet is rotated ROTATION When setting the bend angle we assume a positive bend in the x plane If one wants to bend plane other than the horizontal or x plane the magnet needs to be rotated about the 2 axis This is set via the ROTATION parameter A bend magnet is defined to have zero rotation if it has a purely y field and bends particles in the positive direction toward the negative x axis A magnet rotated by 90 will have a field in the x direction and bend particles in the positive y direction A magnet rotated by 180 will have a field in the y direction and bend particles in the negative direction toward the positive x axis And so on Angles that are not multiples of 90 will bend in both planes Another way to set the magnet rotation is via the KO and KOS parameters However in this case the rotation of the bend is defined by the direction of the field For instance a positive value for KO and a zero value of KOS gives a 0 rotation A positive value of KOS and a zero value of KO gives a rotation of 45 And so on When inputing magnet parameters in this way one must be careful because the signs of the entrance and exit angles may not be consistent with bend the direction of the magnet especially when bending negative particles E1 Edge angle for the magnet entrance This is the angle between the design beam trajectory and the face of the bend E1 0 for a perpendicu
103. d mathematical models and evolving computer power available on the desktop and in super computer centers OPAL runs on your laptop as well as on the largest HPC clusters available today The OPAL framework makes it easy to add new features in the form of new C classes OPAL comes in the following flavours e OPAL MAP More details will be given in Version 1 1 9 e OPAL CYCL e OPAL T e OPAL E OPAL MAP tracks particles with 3D space charge using split operator techniques and is a proper subset of MAD9P In the future a linear space charge mode will become available allowing the user to track moments of the distribution OPAL CYCL tracks particles with 3D space charge including neighbouring turns in cyclotrons with time as the independent variable OPAL T is a superset of IMPACT T 40 and can be used to model guns injectors and complete excluding the undulator It should be noted that not all features of OPAL are available in all flavours The following icon OPAL T means that a feature is not yet available in OPAL T Similar icons are used for the other flavours 1 2 Parallel Processing Capabilities OPAL is built to harness the power of parallel processing for an improved quantitative understanding of particle accelerators This goal can only be achieved with detailed 3D modelling capabilities and a sufficient number of 13 14 CHAPTER 1 INTRODUCTION Table 1 1 Parameters Parallel Performance Example Distribut
104. e 340 341 39 G Fubaiani J Qiang E Esarey W P Leemans G Dugan Space charge modeling of dense electron beams with large energy spreads Acclerators and Beams 9 064402 2006 BIBLIOGRAPHV 183 40 J Qiang S Lidia D Ryne and C Limborg Deprey A Three Dimensional Quasi Static Model for High Brightness Beam Dvnamics Simulation Lawrence Berkelev National Laboratorv Paper LBNL 59098 http repositories cdlib org Ibnl LBNL 59098 41 J Qiang S Lidia R D Ryne C Limborg Deprey Phys Rev Special Topics Accel Beams 9 044204 2006 42 W Joho private discussions 43 J H Billen L M Young POISSON SUPERFISH LA UR 96 1834 Los Alamos National Laboratory 2004 44 J E Spencer H A Enge Split Pole Magnetic Spectrograph for Precision Nuclear Spectroscopy Nucl Instr Meth 49 1967 181 193 45 J M Sanz Sern and M P Calvo Numerical Hamiltonian Problems Chapman and Hall 1994 46 E Forest Phys Lett A 158 p99 1991 47 P Arbenz R Geus and S Adam Solving Maxwell eigenvalue problems for accelerating cavities Physical Review Special Topics Accelerators and Beams 4 pp 022001 1 022001 10 2001 48 P Arbenz M Becka R Geus U Hetmaniuk and T Mengotti On a Parallel Multilevel Preconditioned Maxwell Eigensolver PARCO 32 2 pp 157 165 2006 doi 10 1016 j parco 2005 06 005 49 K Fl ttmann Note on the thermal emittance of electrons emitted by Cesium Telluride photo cathodes TES
105. e calculation is based on 49 50 where Ej hw the probability for a photon of energy exiting an electron to a final state energy Ey is Epn hw x N Ej Ni Ep Epn hw with 11 1 N f is the density of final state and Epp is the density of initial state Two cases no scattering non equilibrum and scattering equilibrium e e and e phonon collisions can be distinguished In OPALthe non equilibrum case is considered and a uniform radial distribution is assumed hence Trms 3 V Photoemission from a metal involves fist the absorption of a photon with hw gt 11 2 where A is the reduced work function The reduction is a function of the applied electric field e A ev eE 4reo 11 3 Soon we can generate distributions form virtual cathode images 11 3 FLATTOP DISTRIBUTION 105 Electrons are emitted isotropic into the half sphere with Ekin hw Particles with angel larger than Ymar arccos Exin will pass the potential barrier Pz psinpcosb o O Pmarl 0 10 11 4 and p moey 1 11 5 The following parameters defines the thermal emittance ryms material such as Cu Fe Cs2Te y the laser energy given by fw and the electric field E which enters in the Schottky effect calculation This is a example of an OPAL distribution definition with thermal emittance similar to the example in 50 p 19
106. e dynamic field map 172 C 7 The profile of a rectangular bend and its corresponding design path 173 C 8 FIXME The location and definitions of the Enge function coefficients for a sector bend and its corresponding design 174 C 9 Example of a IDProfilel field 174 C 10 Example ofa IDProfile2 field 175 C 11 Example of a 2DElectroStatic field map 176 C 12 Example of a 2DMagnetostatic field map 177 C 13 Example of a 2DDvnamic field map 178 C 14 Example of a 3DDvnamic field map 179 Chapter 1 Introduction 1 4 Aim of OPAL and History OPAL is a tool for charged particle optics in accelerator structures and beam lines Using the MAD language with extensions OPAL is derived from MAD9P and is based on the CLASSIC class library which was started in 1995 by an international collaboration IPPL Independent Parallel Particle Layer is the framework which provides parallel particles and fields using data parallel ansatz OPAL is built from the ground up as a parallel application exemplifying the fact that HPC High Performance Computing is the third leg of science complementing theory and the experiment HPC is made possible now through the increasingly sophisticate
107. eded for an accurate simulation depending on the type of injector being modeled ENABLEHDFS If true default HDF5 read and write is enabled ASCIIDUMP If true instead of HDF5 ASCII output is generated for the following elements Probe Collimator Monitor Stripper Foil and global losses The last attribute requests listing of the current settings TELL If true the current settings are listed Examples OPTION ECHO FALSE TELL OPTION SEED 987456321 7 4 Parameter Statements 7 41 Variable Definitions OPAL recognises several types of variables 7 4 PARAMETER STATEMENTS Table 7 1 Default Settings for Options 65 ECHO true INFO true TRACE false WARN true VERIFY false SEED 123456789 PSDUMPFREQ 10 SPTDUMPFREQ 1 REPARTFREQ 10 FINEEMISSION true CZERO false TELL false VERIFY false STATDUMPFREQ 10 RNGTYPE RANDOM EBDUMP false RDUMP 0 100 RHODUMP false SCSOLVEFREQ 1 EFDUMP false SCAN false AUTOPHASE 0 PPDEBUG false SURFDUMPFREQ z 1 PSDUMPEACHTURN false PSDUMPLOCALFRAME false CSRDUMP false ENABLEHDF5 true ASCIIDUMP false Real Scalar Variables REAL variable name real expression The kevword REAL is optional For backward compatibilitv the program also accepts the form variable name real expression This statement creates a new global variable variable name and discards any old va
108. ely sets the magnet length See Figure C 7 and Figure C 8 Both the entrance and the exit use the same Enge function for the fringe fields When using the default OPAL Twill adjust the extend of the fringe field calculation to be reasonable values That is it extends the fringe fields outside the magnet until the field is 1074 the field at the center of the magnet The fringe calcuation is extended inside the magnet in a similar fashion Be careful if using a large gap This can lead to funny magnet field profiles if it is on the order of the magnet L Finally this default option is implemented in order to make it easier to include bends in a simulation without having to generate field maps for each one This should give you reasonable results But be aware that at some point you will want to replace the default with profiles from your own magnets as the your design moves forward 8 4 BENDING MAGNETS 77 L This parameter is ignored if the element has a field map defined If FMAPN IDPROFILEl DEFAULT then L must be defined and is the distance between the entrance and exit Enge polvnomial zeros in meters See Figure C 7 and Figure C 8 GAP This parameter is ignored if the element has a field map defined If FMAPN IDPROFILEl DEFAULT then GAP must be defined and is the full gap of the magnet in meters ANGLE Since OPAL Tuses a field map we must specify a scaling factor for that map There are two ways to do thi
109. eometry command summary Command Purpose GEOMETRY Specify a geometry FGEOM Specifies the HSFED geometry file LENGTH Specifies the length of the geometry S Specifies the start of the geometry A Specifies the semi major axis of the elliptic base area B Specifies the semi minor axis of the elliptic base area 14 2 Define the Geometry File The HSFED file containing the surface mesh of the geometry 14 3 Define the Length The length of the specified geometry in m 117 118 14 4 Define the Start The start of the specified geometry in m 14 5 Define the Semi Major Axis The semi major axis of the ellipse in m 14 6 Define the Semi Minor Axis The semi minor axis of the ellipse in m CHAPTER 14 GEOMETRY Chapter 15 Tracking Table 15 1 Commands accepted in Tracking Mode name expression START RUN TSAVE ENDTRACK Command Purpose TRACK Enter tracking mode LINE Label of LINE or SEQUENCE BEAM Label of BEAM DT Initial time step for tracking MAXSTEPS The maximal number of time steps 25 Defines a z location m after which the simulation stops when SPOS p ZSTOP STEPSPERTURN The timsteps per revolution period TIMEINTEGRATOR Defines the time integrator used in OPAL CYCL Parameter relation Define initial conditions Run particles for specified number of turns or steps Save end conditions Leave tracking mode 15 1 Track Mode Before starting to tr
110. eometry it can model It is therefore possible to consider arbitrary shapes and their inclusion in beam dynamics and particle tracking calculations Given a mesh of a 3 dimensional geometry femaxx computes eigenomdal field decompositions The user then specifies sampling locations for the electromagnetic eigenfields At present sampling locations are specified in terms of a cylinder shape i e the user indicates the cylinder axis the radial cylinder vector and the number of sampling locations in axial radial and azimuthal directions Once the eigenmodal solution has been computed the fields are sampled at these locations and stored in the T7 file format for subsequent use in OPAL Considerable effort has been spent for the validation and benchmarking of beam dynamics calculations based on T7 field maps computed with femaxx A pillbox cavity i e a cylinder shape with a radius r 4 7cm and height h 3 cm has been chosen for benchmarking purposes due to the availability of an analytical solution The analytical resonance frequency of the dominant mode is 2 441 GHz We have compared two cases with OPAL 1 The analytical solution has been sampled within a cylinder vol ume stored into a T7 file and used in an OPAL run 2 the same pillbox shaped geometry has been discretization into tetrahedra and the eigenmodal fields were calculated with femaxx These two cases were then compared resulting in the following conclusions 1 Using a rel
111. ep Default value is 1 Making less steps per turn and increasing this value is the recommended way to reduce space charge solve frequency RHODUMP If true the scalar p field is saved each time a phase space is written There exists a reader in Visit with versions greater or equal 1 11 1 EFDUMP If true the electric field from the space charge is saved each time a phase space is written EBDUMP If true the electric and magnetic field on the particle is saved each time a phase space is written CSRDUMP If true the electric csr field component line density and the derivative of the line density is written into the data directory AUTOPHASE A phase scan of all n rf elements is performed if AUTOPHASE is greater than zero AUTOPHASE finds the maximum energy in a way similar to the code Astra 1 find the phase for maximum energy of the i th cavity 2 track is continued with LAG to the element i 1 3 if i lt n goto 1 For connivence a file input fn phases with the phases corresponding to the maximum energies is written A AUTOPHASE value of 4 gives Astra comparable results An example is given in see 83 3 SCAN If true one can simulate in a loop several machines where some variables can be random variables Find an example at 15 1 1 64 CHAPTER 7 CONTROL STATEMENTS CZERO ff true the distributions are generated such that the centroid is exactly zero and not statistically depen dent RNGTYPE The default
112. erage position of the beam bunch Subsequent lines list z position of longitudinal mesh with respect to the head of the beam bunch line density and the derivative of the line density Note that currently the line density derivative needs to be scaled by the inverse of the mesh spacing to get the correct value The CSR field is dumped at each time step of the calculation Each text file is named Bend Name from input file CSRWake time step number in that bend starting from 1 txt A 6 OPALasa Library An OPAL library can be build by specifying DBUILD LIBOPAL in the cmake process The OPAL libraey is currently used in the opt pilot a multi objective optimization package 64 A 7 EXAMPLES 151 A 7 Examples When checking out the OPAL framework you will find the opal Tests directory and moreover a subdirectory called RegressionTests There several input files can be found which are run every day to check the validity of the current version of OPAL This is a good starting point to learn how to model accelerators with the various flavours of OPAL More examples will be given in subsequent chapters enjoy 152 APPENDIX A INSTALLATION Appendix B OPAL Language Svntax Words in italic font are svntactic entities and characters in monospaced font must be entered as shown Comments are given in bold font Statements comment identifier integer string command kevword label attribute list an
113. erial 4 65 eV FNBETA Field enhancement factor 8 for F N emission 50 0 FNFIELDTHR Field threshold for F N emission 30 0 MV m FNMAXEMI Maximum Number of electrons emitted from a single triangle in each time step 10 Chapter 17 Multipacting Multiple electron impacting multipacting is a phenomenon in radio frequencv RF structure that under certain conditions material and geometrv of the RF structure frequencv and level of the electromagnetic field with or without the appearance of the magnetic field electrons secondary emission yield SEY coefficient will be larger than one and lead to exponential multiplication of electrons Besides the particle tracker in OPAL the computational model for solving multipacting problem contains an accurate representation of 3D geometry of RF structure by using triangulated surface mesh see Chapter 14 and Chapter 16 an efficient particle boundary collision test scheme two different secondary emission models and necessary post processing scripts As we use a triangulated surface mesh to represent the RF structure our particle boundary collision test scheme is based on line segment triangle intersection test An axis aligned boundary box combined with surface triangle inward normal method is adopted to speedup the particle boundary collision test 55 The SEY curve is a very important property of the surface material for the development of a multipacting in a RF structure Figure 1
114. f o PT pz see Chapter on Notation SIGM APT Pt see Chapter on Notation mx Defines the transverse distribution see Table 11 1 my Defines the transverse distribution see Table 11 1 mt Defines the longitudinal distribution see Table 11 1 CORRX Defines the x pz correlation CORRY Defines the y py correlation CORRT Defines the t pz correlation DistFile DISTRIBUTION DISTRIBUTION FROMFILE FNAME Dist inpdistlfinitecur dat XMULT 0 06816207 YMULT 0 06816207 TMULT 1 0xbetax0 06816207 PXMULT 1 gambet PVMULT 1 gambet PTMULT 1 0 beta 2 gamma The file with the data has to have the following format 11 1 CORRELATIONS FOR GAUSSIAN DISTRIBUTION EXPERIMENTAL 103 Table 11 3 Parameters of the distribution command Parameter Purpose TEMISSION Defines the length of the emission process s NBIN How many energy bins begin used For accurate results this should be around 10 for an RF photoinjector and around 40 for a DC photoinjector SBIN How many samples per energy bin to use when constructing the time histogram of the distribution The default value is 100 DEBIN Defines a energy band dE MeV If the maximal energy difference between all bins are smaller than d E all bins are merged into one bin ELASER Laser energy eV SIGLASER Sigma of uniform laser spot size m W Workfunction of material eV FE Fermi energy eV AG Acceleration Gradient MV m N 21 P
115. f the field is specified absolute floor space co ordinates in m This is the position of the front edge of the first TRAVELINGWAVE cavity In the simulation the actual field will extend 4 wavelength in front of this position FREQ Defines the frequency of the traveling wave structure in units of MHz A warning is issued when the fre quency of the cavity card does not correspond to the frequency defined in the FMAPEN file The frequency defined in the FMAPEN file overrides the frequency defined on the cavity card NUMCELLS Defines the number of cells in the tank The cell count should not include the entry and exit half cell fringe fields MODE Defines the mode in units of 27 for example 5 stands for a 3 structure FAST If FAST is true and the provided field map is in 1D then a 2D field map is constructed from the 1D on axis field see section C 2 To track the particles the field values are interpolated from this map instead of using an FFT based algorithm for each particle and each step default FALSE APVETO If TRUE this cavity will not be auto phased instead the actual phase on the element is used Use of a traveling wave requires the particle momentum P and the particle charge CHARGE to be set on the rele vant optics command before any calculations are performed Example of a L Band travelling wave structure lrf0 TravelingWave L 0 0253 VOLT 14 750 NUMCELLS 40 ELEMEDGE 2 73066 FMAPFN INLB 02 RAC Ez MOD
116. g to the exit of current the element This function is only real available in the EALIGN command see 82 6 7 OPERATORS 51 Table 6 6 Real Functions with OPAL TRUNC X truncate X towards zero discard fractional part real real ROUND X round X to nearest integer real real FLOOR X return largest integer not greater than X real real CEIL X return smallest integer not less than X real real SIGN X return sign of X 1 for X positive 1 for X negative 0 for X zero real real SORT X return square root of X real real LOG X return natural logarithm of X real real EXP X return exponential to the base e of X real real SIN X return trigonometric sine of X real real COS X return trigonometric cosine of X real real ABS X return absolute value of X real real TAN X return trigonometric tangent of X real real ASIN X return inverse trigonometric sine of X real real ACOS X return inverse trigonometric cosine of X real real ATAN X return inverse trigonometric tangent of X real real TGAUSS X random number Gaussian distribution with 1 truncated at X real real USERI X random number user defined distribution with one parameter real real EVAL X evaluate the argument immediately and transmit it as a constant real real Real functions with two arguments ATAN2 X Y return inverse trigonometric tangent of Y X real real real MAX X Y return the l
117. gnetoStatic if the file describes a 3D magnetostatic field map Not implemented yet 166 APPENDIX C OPAL T FIELD MAPS r primarv direction secondary direction 2 primarv direction 2 secondarv direction a XZ orientation b ZX orientation Figure 1 Ordering of points for 2D field maps in T7 files 3DDynamic if the file describes a 3D dynamic electromagnetic field map In the case of the 1DDynamic 1DMagnetoStatic IDElectroStatic AstraMagnetostatic and the AstraDynamic field maps one finds in addition one integer number on the first line of the file describing the number of Fourier coefficients to be used in the calculation of the derivative of the on axis field In the case of 2D and 3D field maps an additional string has to be provided describing the orientation of the field map For 2D field maps this can either be XZ if the primary direction is in z direction and the secondary in r direction ZX if the primary direction is in r direction and the secondary in z direction For 3D field maps this can be XYZ if the primary direction is in z direction the secondary in x direction and the tertiary in y direction Each line after the header corresponds to a grid point of the field map This point can be referred to by two indices in the case of a 2D field map and three indices in the case of a 3D field map respectively Each column describes either E Ep Bz
118. gure 1 2 the comparison between IMPACT T and OPAL T is shown This example is part of the regression test suite that is run every night The inputfile is found in Section 22 1 4 FIELD MAPS FROM THE FEMAXX 3D EIGENMODE SOLVER 15 0 5 r 4 06 QGunimpactT32B h5 1 GunimpactT32B h5 1 Gun test 2 P2 h5 4 C Gun test 2 P2 h5 1 0 4 m s 0 5 S 1 o 4 E 0 4 0 3 7 1 03 9 H 4 0 2 1 T L C 1 X 02 L 2 0 1 F 4 0 1 oF J 0 i sede i 0 0 01 0 02 0 03 0 0 01 0 02 0 03 SPOS m SPOS m Figure 1 2 Comparison of energy and emittance in x between IMPACT Tand OPAL T 1 4 Field Maps from the Femaxx 3D Eigenmode Solver TODO AA will rewrite Electromagnetic field maps for beam dynamics calculations originate from a number of different electromag netic solvers e g Superfish and similar codes Here we describe the current status of work in progress which will eventually allow the usage of field maps that have been computed with the femaxx 3 dimensional electromagnetic eigenmodal solver 47 48 The femaxx code computes electromagnetic eigenmodes of resonant cavities of arbitrary 3 dimensional shape and boundary conditions Unlike Superfish and similar 2 dimensional codes femaxx is not restricted in the kind of g
119. h effects in the simulation to quantitatively study its impact on the beam dynamics In OPAL CYCL we developed a new fully consistent algorithm of multi bunches simulation We implemented two working modes namely AUTO and FORCE In the first mode only a single bunch is tracked and accelerated at the beginning until the radial neighboring bunch effects become an important factor to the bunches beheaver Then the new bunches will be injected automatically to take these effects into accout In this way we can save time and memory sufficiently and more important we can get higher precision for the simulation in the region where neighboring bunch effects are neglectable In the other mode multi bunches simulation starts from the injection points This mode is appropriate for the machines in which this effects is unneglectable since the injection point In the space charge calculation for multi bunches the computation region covers all bunches Because the energy of the bunches is quite different it is inappropriate to use only one particle rest frame and a single Lorentz transformation any more So the particles are grouped into different energy bins and in each bin the energy spread is relatively small We apply Lorentz transforming calculate the space charge fields and apply the back Lorentz transforming for each bin separately Then add the field data together Each particle has a ID number to identify which energy bin it belongs to 5 9 Input
120. he solenoid field points in the direction of increasing s The reference svstem for a solenoid is a Cartesian coordinate svstem see Fig 77 Using a solenoid in OPAL t mode the following additional parameters are defined FMAPFN Field maps in the 77 format can be specified ELEMEDGE The edge of the field is specified absolute floor space co ordinates in m Example SP1 Solenoid L 1 20 ELEMEDGE 0 5265 KS 0 11 FMAPFN 1T1 T7 84 CHAPTER 8 ELEMENTS 8 10 Cyclotron label CYCLOTRON TYPE string CYHARMON int PHIINIT real PRINIT real RINIT real SYMMETRY real RFFREQ real FMAPFN string A CYCLOTRON object includes the main characteristics of a cyclotron the magnetic field and also the initial condition of the injected reference particle and it has currently the following attributes TYPE The data format of field map Currently three formats are implemented CARBONCYCL CYCIAE AVFEQ FFAG BANDRF and default PSI format For the details of their data format please read Section 5 4 CYHARMON The hamonic number of the cyclotron h RFFREQ The RF system f unit MHz default 0 The particle revolation frquency fre frf h Filename for the magnetic field map SYMMETRY Defines symmetrical fold number of the B field map data RINIT The initial radius of reference particle unit mm default 0 PHINIT The initial azimuth of reference particle unit degree default 0 PRINIT Initial radial
121. he transversal wakefield from 13 5 ET E Wr s 10 Re 7 ZL k cos ks dk 13 7 0 111 112 CHAPTER 13 WAKEFIELDS To calculate the integrals in 13 5 and 13 7 numericallv the Simpson integration schema with equidistant mesh spacings is applied This leads to an integration with small Ak with a big N which is computational not optimal with respect to efficiencv Since we calculate the wakefield usuallv just once in the initialization phase the overall performance will not be affected from this 13 1 Wakefield Command See Table 13 1 for a summary of the Wakefield command NOTE Currently when using wakefields the domain can only be parallelized in z direction Please adapt the parallelization in the FieldSolver accordingly Fsl FIELDSOLVER MX 32 32 32 PARFFTX false PARFFTY false PARFFIT true BCFFTX open BCFFTY open BCFFTT open BBOXINCR 0 GREENSF INTEGRATED FSTYPE FFT Table 13 1 Wakefield command summary CONST LENGTH Command Purpose WAKE Specify a wakefield TYPE Specify the wake function 1D CSR LONG SHORT RANGE TRANSV SHORT RANGE LONG TRANSV SHORT RANGE NBIN Number of bins used in the calculation of the line density TRUE if the length of the bunch is considered to be constant CONDUCT Conductivity AC DC 20 Impedance of the beam pipe in FORM The form of the beam pipe ROUND RADIUS The radius of the beam pipe in m S
122. here 13 14 Filters Filters can be defined which then are applied to the line density of the bunch The following smoothing filters are implemented Savitzky Golay Stencil FixedFFTLowPass RelativFFTLowPass The input format for them is label FILTER TYPE string NFREQ real THRESHOLD real NPOINTS real NLEFT real NRIGHT real POLYORDER real TYPE The type of filter Savitzky Golay Stencil FixedFFTLowPass RelativFFTLowPass NFREQ Only used in FixedFFTLowPass the number of frequencies to keep THRESHOLD Only used in RelativeFFTLowPass the minimal strength of frequency compared to the stronges to consider NPOINTS Only used in Savitzky Golay width of moving window in number of points NLEFT Only used in Savitzky Golay number of points to the left NRIGHT Only used in Savitzky Golay number of points to the right POLYORDER Only used in Savitzky Golay polynomial order to be used in least square approximation 13 14 FILTERS 115 The Savitzkv Golav filter and the ones based on the FFT routine provide a derivative on a natural way For the Stencil filter a second order stencil is used to calculate the derivative An implementation of the Savitzky Golay filter can be found in the Numerical Recipes The Stencil filter uses the following two stencil consecutively to smooth the line density 2 To fi at 24 gt fi 24 34 fi 24 fire 7 fina 9 fi T fi g 24 f 1434 fi 24 figi 7 figo KA 96 For
123. independent single gap cavities the spiral gap cavity is not implemented yet For more detail about the parameters of cyclotron cavities see Section 8 11 2 The voltage profile of a cavity gap is read from ASCII file Here is an example 6 0 00 VERES 2 40 0 20 0 65 2 41 0 40 0 98 0 66 0 60 0 88 105 9 0 80 0 43 2 65 1 00 250 205 The number in the first line means 6 sample points and in the following lines the three values represent the normalized distance to the inner edge of the cavitv the normalized voltage and its derivative respectivelv 5 5 2 Read RF fieldmap The 3D RF fieldmap can be read from h5part type file This is useful for modeling the central region electric fields which usually has complicate shapes For the detail about its usage please see Section8 10 Please note that in this case the E field is treated as a part of CYCLOTON element rather than a independent RFCAVITY element 5 6 Particle Tracking and Acceleration The precision of the tracking methods is vital for the entire simulation process especially for long distance tracking jobs OPAL CYCL uses a 4th order Runge Kutta algorithm and the second order Leap Frog scheme The 4th order Runge Kutta algorithm needs 4 the external magnetic field evaluation in each time step 7 During the field interpolation process for an arbitrary given point the code first interpolates Formula B for its counterpart on the median plane and then expands
124. ion Particles Mesh Greens Function Time steps Gauss 3D 10 10243 Integrated 10 m 9 38 P4 m oa 078 gt 7 c 0 7 9 9 MEN a 2 a ty 0 5 4 us o 5 KA o 0 4 G 0 2 1024 2048 4096 8192 Total m X Integrationl wd Particle Pushed sess Self Fields e Integration2 Gi Figure 1 1 Parallel efficiency and particles pushed per us as a function of cores simulation particles to obtain meaningful statistics on various quantities of the particle ensemble such as emit tance slice emittance halo extension etc The following example is exemplifying this fact Figure 1 1 shows the parallel efficiency time as a function of used coresfor a test example with parameters given in Tab 1 1 The data where obtained on a Cray XT5 at the Swiss Center for Scientific Computing 1 3 Quality Management Documentation and quality assurance are given our highest attention since we are convinced that adequate doc umentation is a key factor in the usefulness of a code like OPAL to study present and future particle accelera tors Using tools such as a source code version control system subversion source code documentation Doxy gen check out for instance ParallelTTracker and the extensive user maunal you are now enjoying we are committed to providing users as well as co developers with state of the art documentation to OPAL One example of an non trivial test example is the PSI DC GUN In Fi
125. is option is turned off OPAL suppresses all information messages It also affects the gnu out and eb out files in case of OPAL CYCL simulations TRACE When the TRACE option is on OPAL writes additional trace information on the standard error file for each executable command This information includes the command name and elapsed CPU time before and after the command VERIFY If this option is on OPAL gives a message for each undefined variable or element in a beam line WARN If this option is turned off OPAL suppresses all warning messages SEED Selects a particular sequence of random values A SEED value is an integer in the range 0 999999999 default 123456789 SEED can be an expression If SEED 1 the time is used as seed and the generator is not portable anymore See also random values see 86 8 5 7 3 OPTION STATEMENT 63 PSDUMPFREQ Defines after how many time steps the phase space is dumped into the H5hut file Default value is 10 STATDUMPFREQ Defines after how many time steps we dump statistical data such as RMS beam emittiance to the stat file The default value is 10 Currently only available for OPAL T SPTDUMPFREQ Defines after how many time steps we dump the phase space of single particle It is always useful to record the trajectory of reference particle or some specified particle for primary study Its default value is 1 Defines after how many time steps we do particles repartition to ba
126. issue the command source S HOME bash profile A 2 3 OPAL To install OPAL you will need to perform the following steps 1 Install HShut 2 Install IPPL 3 Install OPAL Install HShut 1 mkdir p hopper extlib mkdir svnwork 2 3 SHOME svnwor 4 Get the source code k Nurl svntssh savannah02 psi ch repos H5hut src tags 1 99 9 H5hut 1 99 9 5 cd H5hut 1 99 9 6 autogen h export HDFSROOT SCRAV HDF5 DIR hdf5 parallel gnu T configure prefix HOME hopper extlib H5hut 1 99 9 enable parallel CFLAGS std c99 A 2 XE6 INSTALLATION 147 8 make 9 make install Install IPPL 1 cd SHOME svnwork 2 Get source code svn co username username svntssh savannah02 psi ch repos ippl src trunk ippl 3 cd ippl 4 mkdir build export IPPL_ROOT HOME svnwork ippl export IPPL PREFIX SIPPL ROOT build rm f CMakeCache txt CXX mpicxx cmake DCMAKE BUILD TYPE RELEASE DCMAKE INSTALL PREFIX SIPPL PREFIX SIPPL ROOT 5 make 6 make install 7 Add the export statements to your bashrc file Install OPAL 1 cd 2 cd svnwork 3 Get the source code svn co username username svntssh savannah02 psi ch repos opal src OPAL 4 cd SOPAL ROOT 5 cmake SOPAL ROOT 6 makeNverb T mkdir HOME hopper bin 8 cp src opal HOME hopper bin 148 APPENDIX A IN
127. izes the field values to max Bonaxis 1 0 T In the header only the first line is neaded since the information on the longitudinal dimension is contained in the first column Furthermore OPAL Tdoes not provide a FAST version of this map type 5 IDDVNAMIC 171 C 5 1DDynamic 1DDynamic 40 3 0 57 2054999 1498 953425154 2 0 2 0 195 0 00000e 00 36222 06 83270 06 4 994 lines 32490 05 23 73 0895 18598e 05 Figure 5 A ID field map describing dvnamic field using 57000 grid points in longitudinal direction If the FAST switch is set in the input deck 200 values in transvers direction for each longitudinal grid point are calculated The field is non negligible from 3 0 cm to 57 0 cm relative to ELEMEDGE in longitudinal direction The 200 grid points span a length of 2 0 cm in radial direction From the 5 000 field values 2500 complex Fourier coefficients are calculated whereof only 40 are kept to calculate the off axis field values 172 C 6 AstraDynamic APPENDIX C OPAL T FIELD MAPS 29972 OR S OF AstraDynamic 40 924 0000000e 00 0007941 04 9991114 04 872996062 05 1L o9 740 85 VE 01 Le 9 0 198916525 0 OS APA OG ee Onl 60 Ea 59 y N Gal 09 i 0000000 00 8090000 04 6553000 04 4103000 04 4295000 03 1306000 03 4103000 04 6553000 04 8090000 04
128. l efficiency and particles pushed per us as a function of cores Comparison of energy and emittance in x between IMPACT Tand Tetrahedral mesh of a pillbox shaped cavity Reference orbit left and tune diagram right in Injector M Radial and vertical eigenellipse at 2 MeV of Injector Il Energy Vs time left and external B field Vs trackstep Right only show for about 2 turns Vertical phase at different energy from left to right 0 87 MeV 15 MeV 35 MeV Reference orbit left and tune diagram right in Ring cyclotron 2D field map on the median plane with primary direction corresponding to the azimuthal direction secondary direction to the radial direction Visualisation of angles used to rotate the bend relative to the incoming beam where n is the normalobthedace mecs gr 5 a Ge WOM D Bur yu RE ee Schematic of the simplifed geometry of a cavity gap and parameters The on axis field of an S band TRAVELINGWAVE OPAL Gauss Flattop Distribution 2 les Typical SEY CUVE vce be ee ee oh ly eo ee ted Pw weg Rs Sketch map of the secondary emission process Time evolution of electron number predicted by theoretical m
129. l fields in cyclotrons the space charge can be calculated less frequently than the external field interpolation so as to reduce time to solution The outer step determined by STEPSPERTURN is used to integrate space charge effects A constant number of substeps per outer step is used to query external fields and to move the particles The number of substeps can be set with the option MTSSUBSTEPS and its default value is 1 When using this integrator the input file has to be rewritten in the units of the outer step For example extracts of the inputfile suited for LF 2 or RK 4 read Option PSDUMPFREQ 100 Option REPARTFREQ 20 Option SPTDUMPFREQ 50 turns 5 nstep 3000 TRACK LINE 11 BEAM beaml1 MAXSTEPS nstepxturns STEPSPERTURN nstep TIMEINTEGRATOR LF 2 RUN METHOD CYCLOTRON T BEAM beaml FIELDSOLVER Fs1 DISTRIBUTION Dist1 ENDTRACK and should be transformed to Option MTSSUBSTEPS 10 Option PSDUMPFREQ 10 Option REPARTFREQ 2 Option SPTDUMPFREQ 5 turns 5 nstep 300 TRACK LINE 11 BEAM beaml MAXSTEPS nstepxturns STEPSPERTURN nstep TIMEINTEGRATOR MTS RUN METHOD CYCLOTRON T BEAM beaml FIELDSOLVER Fs1 DISTRIBUTION Dist1 ENDTRACK In general all step quantities should be divided by MTSSUBSTEPS In our first experiments on PSI injector II cyclotron simulations with reduced space charge solving frequency by a factor of 10 lie still very close to the original solution How large MTSSUBSTEPS
130. lance the computational load of the computer nodes Its default value is 10 REBINEREQ Defines after how many time steps we update the energy Bin ID of each particle For the time being Only available for multi bunch simulation in OPAL CYCL Its default value is 100 PSDUMPEACHTURN Control option of phase space dumping If true dump phase space after each turn For the time being this is only use for multi bunch simulation in OPAL CYCL Its default set is false PSDUMPLOCALFRAME Control option whether the phase space data is dumped in the global Cartesian frame or in the local Cartesian frame If true in local frame otherwise in global Cartesian frame Only available for OPAL CYCL Its default set is false Note that restarting run cannot be launched by reading in phase space data in local frame SCSOLVEFREQ If the space charge field is slowly varying w r t external fields this option allows to change the frequency of space charge calculation i e the space charge forces are evaluated every SCSOLVEFREQ step and then reused for the following steps Affects integrators LF 2 and RK 4 of OPAL CYCL Its default value is 1 Note as the multiple time stepping MTS integrator maintains accuracy much better with reduced space charge solve frequency this option should probably not be used anymore MTSSUBSTEPS Only used for multiple time stepping MTS integrator in OPAL CYCL Specifies how many substeps for external field integration are done per st
131. language in the same simulation framework 6 1 Statements and Comments Input for OPALis free format and the line length is not limited During reading input lines are normally printed on the echo file but this feature can be turned off for long input files The input is broken up into tokens words numbers delimiters etc which form a sequence of commands also known as statements Each statement must be terminated by a semicolon and long statements can be continued on any number of input lines White space like blank lines spaces tabs and newlines are ignored between tokens Comments can be introduced with two slashes and any characters following the slashes on the same line are ignored The convention for comments x isalso accepted The comment delimiters and x can be nested this allows to comment out sections of input In the following descriptions words in lower case stand for syntactic units which are to be replaced by actual text UPPER CASE is used for keywords or names These must be entered as shown Ellipses are used to indicate repetition The general format for a command is keyword attribute attribute label keyword attribute attribute It has three parts 1 The label is required for a definition statement Its must be an identifier see 86 2 and gives a name to the stored command 2 The keyword identifies the action desired It must be an identifie
132. lar face and E1 gt 0 if the face is rotated anticlockwise from this perpendicular position as seen from above y 2 0 on to the plane See Figure Figure 77 and Figure 8 1 E2 Edge angle for the magnet exit This parameter is not used for an RBEND element as it is fixed by the entrance angle E1 and the rectangular geometry of the magnet E2 gt 0 if the exit face of the magnet is rotated anticlockwise from the position where the design trajectory is perpendicular to the exit face See Figure BETA Analogous to E1 but slighlty more complicated This is a rotation of the magnet about the x axis See Figure 8 1 78 CHAPTER 8 ELEMENTS ELEMEDGE The edge of the field is specified in floor coordinates from the cathode in m If one uses IDProfilel or IDProfile2 field files this is the location of the zero of the Enge function for the entrance fringe field see C 2 Fora 3DMagnetoStatic map it is the location of the start of that map DESIGNENERGY Energy of the reference particle If the magnet strength is set With KO and or KOS this is set as the energy of the reference trajectory through the magnet and therefore sets the reference beam bend angle It is used to calculate the radius of the circular path in the y 0 plane The radius in turn is needed in the calculation of the CSR wakefield The design energy is also used to track a single particle through the bend while initializing the elements DESIGNENERGY fixes the
133. lation example ke r 17 1 COMMANDS RELATED TO MULTIPACTING SIMULATION Box RFCavitv PLENGTH 1 262 VOLT GEOMETRV ge FMAPFN ELEMEDGE 0 FAST true FREQ 44 6 LAG 0 0 DX 0 DY 0 DZ 0 1 CyciaeEM h5 This element is used to model the magnetic field in the valley of a cyclotron where the RF cavity is installed Mag CYCLOTRONVALLEY FMAPFN CyciaeMagReal h5 ELEMEDGE 0 DX 0 Benchmark Line Box Mag Fsl FIELDSOLVER FSTYPE NONE MX 32 MY 32 MT 256 PARFFTX true PARFFTY PARFFTT false BCFFTX BCFFTY open BCFFTT BBOXINCR 0 1 GREENSF qb 0 2e 9 bfreq 300 bcurrent qbxbfreq DY 0 DZ 0 true open open INTEGRATED beaml BEAM PARTICLE ELECTRON pc PO NPART 2000 BFREQ bfreq BCURRENT bcurrent CHARGE Select Line Benchmark track line Benchmark beam beaml MAXSTEPS 23000 DT 4e 12 ZSTOP 3 run method PARALLEL T beam beaml 1 fieldsolver Fs1 MULTIPACTING true endtrack Quit 129 130 CHAPTER 17 MULTIPACTING Table 17 1 Multipacting Related Command Summarv Command Purpose Default VW Velocity scalar in Maxwellian Dist 1 0 m s VVTHERMAL Thermal velocity in Maxwellian Dist 7 268929821 x 109 m s SECONDARYFLAG Secondary model type 0 none 1 Furman Pivi 2 Vaughan 0 NEMISSIONMODE Emit real No secondaries or not true VEZER
134. le i lt N 1 do read u 8 a b urli d read u 8 aa bb uzi dd echo url Suzi gt gt plotdata i i41 done exec 8 amp rm f tuningresult To start execution just run tuning sh which uses the input file testcycl in and the auxiliary file FIX PO SEO The output file is plotdata from which one can plot the tune diagram 5 10 Output Single Particle Tracking mode The intermediate phase space data is stored in an ASCII file which can be used to the plot the orbit The file s name is combined by input file name without extension and trackOrbit dat The data are stored in the global Cartesian coordinates The frequency of the data output can be set using the option SPTDUMPFREQ of OPTION statement see 87 3 44 CHAPTER 5 OPAL CYCL The phase space data per STEPSPERTURN a parameter in the TRACK command steps is stored in an ASCII file The file s name is a combination of input file name without extension and a fter EachTurn dat The data is stored in the global cylindrical coordinate system Please note that if the field map is ideally isochronous the reference particle of a given energy take exactly one revolution in STEPPERTURN steps Otherwise the particle may not go through a full 360 in STEPPERTURN steps There are 3 ASCII files which store the phase space data around 0 7 8 and 7 4 azimuths Their names are the combinations of input file name without extension and Angle0 dat Anglel dat and Angle2
135. le X by 0 01 CANNOT use X X 01 7 4 5 VALUE Output of Expressions The statement VALUE VALUE expression vector evaluates a set of expressions using the most recent values of any operands and prints the results on the standard error file Example A 4 VALUE VALUE TABLE 5 A Pl 5 P2 7 VALUE VALUE P1 P2 P1 P2 3 These commands give the results 68 CHAPTER 7 CONTROL STATEMENTS value 0 1 2 4 0 4 8 12 16 value P1 P2 P1 P2 3 5 7 32 This commands serves mainlv for printing one or more quantities which depend on matched attributes It also allows use of OPAL as a programmable calculator One mav also tabulate functions 7 4 6 H5merge With the H5merge utility H5hut tools H5PartMerge src H5merge cpp I can prune h5 files With this feature you can hence restart from every time step H5merge bigfile h5 0 100 input h5 The first 100 steps from the file bigfile h5 are copied into the file input h5 from which the simulation can be restarted as shown above The H5merge utility comes with H5hut 7 5 Miscellaneous Commands 7 51 ECHO Statement The ECHO statement has two formats ECHO MESSAGE message ECHO message shortcut message is a string value see 6 4 It is immediately transmitted to the ECHO stream 7 5 2 SYSTEM Execute System Command During an interactive OPAL session the command SYSTEM allows to exec
136. lliptic apertures XSIZE and 5 denote the half axes respectivelv for rectangular apertures thev denote the half width of the rectangle Optically a collimator behaves like a drift space but during tracking it also introduces an aperture limit The aperture is checked at the entrance If the length is not zero the aperture is also checked at the exit Example COLLIM ECOLLIMATOR L 0 5 XSIZE 0 01 5 2 0 005 The reference system for a collimator is a Cartesian coordinate system see Fig 77 8 14 1 OPAL Tmode The RCOLLIMATOR and CCOLLIMATOR are not supported at the moment A ECOLLIMATOR detects all parti cles which are outside the aperture defined by XSIZE and YSIZE The lost particles are saved into an H5hut file defined by OUTFN The ELEMEDGE defines the location of the collimator and L the length OUTEN filename into which the monitor should write the collected data The file is an H5hut file ELEMEDGE The position of the monitor is specified absolute floor space co ordinates in m This is the position at which the data is collected Example Col ECOLLIMATOR L 1 0E 3 ELEMEDGE 3 0E 3 XSIZE 5 0E 4 5 2 5 0 4 11 5 92 CHAPTER 8 ELEMENTS 8 14 2 OPAL cYCLmode Only CCOLLIMATOR is available for OPAL CYCL This element is radial rectangular collimator which can be used to collimate the radial tail particles So when a particle hit this c
137. lomb Scattering s sses o ore OR ue MUR Rugs RAW Ry Sa 18 2 1 Multiple Coulomb 18 2 2 Large Angle Rutherford 18 3 The Flow Diagram of CollimatorPhysics Class in OPAL 18 3 1 The Substeps 55503 as Soe Si ee ee be Ti e L 18 4 Example of an Input Fil i drst 3808 eko gone web S Y Low em RR 1835 A Simple TEST sa ck ome Roe ee th On U E BIE bab ele Eee wes Installation Build and install OPAL amp Linux Al Supporting Libraries sose 86 ko Rok kou AE ee os 1 2 Environment Variables A 1 3 Installmg OPAL 22225855226 6 Ne uum pd uus 2 Cray XE6 Installation 2 a0 ee Be RU RA MU ee A2 T sbasbisprofile ext Fle e oos ES RSS 2 2 bashrc extFile io uon ere L eR me ia iti ues bs 2 5 OPALE S E NES A E S AMEN A 3 Using pre build Binaries 2 A 4 Enabling the Multigrid Space Charge AS Debug Blas 5i sce af om Saadeh Bet a Ue EM Bob we S EUER amp AG OPAL asa se ee eo i pos RU p X t
138. m Em PAUL SCHERRER INSTITUT PSI PR 08 02 The OPAL Framework Object Oriented Parallel Accelerator Library Version 1 1 9 User s Reference Manual Andreas Adelmann Achim Gsell Christof Kraus PSI Yves Ineichen IBM Steve Russell LANL Yuanjie Bi Chuan Wang Jianjun Yang CIAE Hao Zha Thinghua University Suzanne Sheehy Chris Rogers RAL and Christopher Mayes Cornell Abstract OPAL is a tool for charged particle optics in accelerator structures and beam lines Using the MAD language with extensions OPAL is derived from MAD9P and is based on the CLASSIC class library which was started in 1995 by an international collaboration IPPL Independent Parallel Par ticle Layer is the framework which provides parallel particles and fields using data parallel ansatz OPAL is built from the ground up as a parallel application exemplifying the fact that HPC High Performance Computing is the third leg of science complementing theory and the experiment HPC is made possible now through the increasingly sophisticated mathematical models and evolving com puter power available on the desktop and in super computer centres OPAL runs on your laptop as well as on the largest HPC clusters available today The OPAL framework makes it easy to add new features in the form of new C classes It comes in the following flavours OPAL CYCL tracks particles with 3D space charge including neighbouring turns in cyclotrons with time as the inde
139. mi National Accelerator Laboratory July 1981 American Institute of Physics 1982 17 D A Edwards and L C Teng Parametrisation of linear coupled motion in periodic systems IEEE Trans on Nucl Sc 20 885 1973 181 182 BIBLIOGRAPHV 18 M Giovannozzi Analvsis of the stabilitv domain of planar svmplectic maps using invariant manifolds CERN PS 96 05 PA 1996 19 H Grote GXPLOT User s Guide and Reference Manual LEP TH Note 57 CERN 1988 20 LEP Design Group Design Study of a 22 to 130 GeV Colliding Beam Machine LEP CERN ISR LEP 79 33 CERN 1979 21 M Hanney J M Jowett and E Keil BEAMPARAM A program for computing beam dynamics and performance of e e storage rings CERN LEP TH 88 2 CERN 1988 22 R H Helm M J Lee P L Morton and M Sands Evaluation of synchrotron radiation integrals IEEE Trans Nucl Sc NS 20 1973 23 F James MINUIT A package of programs to minimise a function of n variables compute the covariance matrix and find the true errors program library code D507 CERN 1978 24 E Keil Synchrotron radiation from a large electron positron storage ring CERN ISR LTD 76 23 CERN 1976 25 D E Knuth The Art of Computer Programming Volume 2 Addison Wesley second edition 1981 Semi numerical Algorithms 26 J Laskar C Froeschl and A Celletti The measure of chaos by the numerical analysis of the fundamental frequencies Application to the st
140. momenta of reference particle P y default 0 MINZ The minimal vertical extent of the machine unit mm default 10000 0 MAXZ The maximal vertical extent of the machine unit mm default 10000 0 MINR Minimal radial extent of the machine unit mm default 0 0 MAXR Minimal radial extent of the machine unit mm default 10000 0 During the tracking the particle r z 0 will be deleted if MINZ z MAXZ or MINR r MAXR and it will be recorded in the ASCII file input f ilename loss Example ring Cyclotron TYPE RING CYHARMON 6 PHIINIT 0 0 PRINIT 0 000240 RINIT 2131 4 SYMMETRY 8 0 RFFREQ 50 650 FMAPFN s03av nar MAXZ 10 MINZ 10 MINR 0 MAXR 2500 If TYPE is set to BANDRF the 3D electric field map of RF cavity will be read from external h5part file and 4 extra arguments need to specified RFMAPFN The filename for the electric fieldmap in h5part binary format RFPHI The Initial phase of the electric field map rad ESCALE The maximal value of the electric fieldmap MV m SUPERPOSE An option whether all of the electric field maps are superposed The is valid when more than one electric field map is read default true Example for single electric field map 8 10 CYCLOTRON 85 COMET Cyclotron TYPE BANDRF CYHARMON 2 PHIINIT 71 0 PRINIT prO RINIT r0 SYMMETRY 1 0 FMAPFN Tosca map txt RFPHI Pi RFFREQ 72 0 RFMAPFN efield h5part ESCALE 1 06E 6 We can have more tha
141. n ees IS UE IPS 39 9453 pd im uhr dte eb eite 40 5 4 4 Default PSI format 40 5 4 5 usersownfieldmap 22 2 2 2 5 44 44 4 40 25 37 RE field Ged ees ke wok A Gare eet 41 3 Read RE voltage profile sos tu gts sas bob ek 41 35 52 Read 3D RF fieldmap 0 5 5 54 ea ER 41 5 6 Particle Tracking and Acceleration 41 9 7 EEG utei eg EI p E 41 5 8 Multrbunches s ueS 2222 5 22 eR UE S xov gt ee a us 42 29 gt ue Weis PNE ue a A OWE 42 5 10 O tp t is chart ROG tan EUR E e SCIRE ERR 43 Command Format 45 6 1 Statements and Comments 22s 45 6 2 Iden fiers or Labels RARE due Wee RE 46 6 3 Command Attribute Types 46 64 Sting Attributes us v Rep Tx eee ete eee i tede eb t 47 6 55 Logical EXpreSsIOnS c S B Ren 48 6 6 Real Expressions piocs t Rp Ren um Roe G8 Som eR Rege Rue dep Anji p 49 6 75 Operators s xke ueber E Rap ended uve 50 6 87 Operands m Expressions 9o bs oper b 52
142. n one RF field maps Example for multiple RF field maps COMET Cyclotron TYPE BANDRF CYHARMON 2 PHIINIT 71 0 PRINIT pr0 0 SYMMETRY 1 0 FMAPFN Tosca map txt RFPHI Pi 0 Pi 0 RFFREQ 72 0 72 0 72 0 72 0 RFMAPFN el h5part e2 h5part e3 h5part e4 h5part ESCALE 1 06E 6 3 96E 6 1 3E 6 1 E 6 SUPERPOSE true In this example SUPERPOSE is set to true Therefore if a particle locates in multiple field regions all the field maps are superposed if SUPERPOSE is set to false then only one field map which has highest priority is used to do interpolation for the particle tracking The priority ranking is decided by their sequence in the list of RFMAPEN argument i e el h5hart has the highest priority and e4 h5hart has the lowest priority For RF cavity another way is reading the RF voltage profile in the RFCAVITY element see Section8 11 and just do a momentum kick when a particle crosses the RF gap In the center region of the compact cyclotron the electric field shape of complicated and pay significant impact on the transverse beam dynamics hence a simple momentum Kick is not enough In this case we need to read 3D field map to do precise simulation In additions the simplified trim coil field model is also implemented so as to do fine tuning on the magnetic field A trim coil can be defined by 4 arguments TCRI Tthe inner radius of the trim coil mm TCR2 Tthe outer radius of the trim coil
143. nd E Todesco Tune evaluation in simulations and experiments CERN SL 95 84 AP 1995 5 J D Bjorken and S K Mtingwa Particle Accelerators 13 pg 115 6 E M Bollt and J D Meiss Targeting chaotic orbits to the Moon through recurrence Phys Lett A204 373 1995 7 P Bramham and H Henke private communication and LEP Note LEP 70 107 CERN 8 Karl L Brown A First and Second Order Matrix Theory for the Design of Beam Transport Systems and Charged Particle Spectrometers SLAC 75 Revision 3 SLAC 1972 9 Karl L Brown D C Carey Ch Iselin and F Rothacker TRANSPORT A Computer Program for Designing Charged Particle Beam Transport Systems CERN 73 16 revised as CERN 80 4 CERN 1980 10 A Chao Evaluation of beam distribution parameters in an electron storage ring Journal of Applied Physics 50 595 598 1979 11 A W Chao and M J Lee SPEAR II Touschek lifetime SPEAR 181 SLAC October 1974 12 M Conte and M Martini Particle Accelerators 17 1 1985 13 E D Courant and H S Snyder Theory of the alternating gradient synchrotron Annals of Physics 3 1 48 1958 14 Ph Defert Ph Hofmann and R Keyser The Table File System the C Interfaces LAW Note 9 CERN 1989 15 M Donald and D Schofield A User s Guide to the HARMON Program LEP Note 420 CERN 1982 16 A Dragt Lectures on Nonlinear Orbit Dynamics 1981 Summer School on High Energy Particle Accelera tors Fer
144. nding to the azimuthal direction secondary direction to the radial direction need to add 6 parameters at the header of a plain kGauss data file namely rmin mm Ar mm 121 A 6 No total data number in each arc path of azimuthal direction and N total path number along radial direction If Ar or A0 is decimal one can set its negative opposite number For instance if A0 1 the fourth line of the header should be set to 3 0 Example showing the above explained format 3 0e 03 10 0 0 0 3 0 300 161 1 414 03 3 884 02 1 779e 01 3 743 03 5 999 02 2 090 01 8 517 03 8 580 02 2 392 01 1 221 02 1 150 01 2 682 01 2 296 02 1 461 01 2 964 01 5 4 FIELD MAPS 39 3 245 01 3 534 01 3 843 01 4 184 01 4 573 01 5 4 2 CXCIAE tvpe If TYPE CYCIA the program requires data format given by ANSYS 10 0 This function is originally for the 100 MeV cyclotron of CIAE whose isochronous fields is numerically computed by by ANSYS The median plane fields data is output by reading the APDL ANSYS Parametric Design Language script during the post processing phase you may need to do minor changes to adapt your own cyclotron model postl resume solu db csys l nsel s loc x 0 nsel r loc y 0 nsel r loc z 0 PRNSOL B COMP 5 5 1 rsvs l xdo count 0 200 path cyc100 Ansvs 2 5 45 ppath 1 0 Olxcount 0 1 ppath 2 0 0lxcount sqrt 2 0 01 count sqrt 2
145. nitions 6 9 ELEMENT SELECTION 55 M MARKER S LINE C M D L LINE A M B 2x8 A M B SURVEY LINE L The line L is equivalent to the sequence of elements A M B C M D C M D A M B Some possible place definitions are C 1 The first occurrence of element C S The beginning of the line L M 2 The second marker M at top level of line L i e the marker between second A and the second B KE The end of line L S 1 M 1 The marker M nested in the first occurrence of S 6 9 2 Range Selection A range in a beam line see 89 is selected by the following syntax range place place place This denotes the range of elements from the firstplace to the second place Both positions are included A few special cases are worth noting e When placel refers to a LINE see 89 the range starts at the beginning of this line e When place2 refers to a LINE see 89 the range ends at the ending of this line e When both place specifications refer to the same object then the second can be omitted In this case and if place refers to a LINE see 9 the range contains the whole of the line Examples Assume the following definitions M MARKER S LINE C M D L LINE A M B 2x8 A M B The line L is equivalent to the sequence of elements A M B C M D C M D A M B Examples for range selections S E The full range or L A 1V A 2 2111 through A 2 both incl
146. ns involving the geometry multipacting and field emission OPAL will also dump the position and current of incident particles into another h5 file with the name _Surface h5 where the asterisk stands for the base name of the user s OPALinput file If we need this surface loss data during post processing we should specify the dump frequency in the option SURFDUMPFREO with a positive integer in the OPALinput file otherwise the default value of the option is SURFDUMPFREQ 1 and the x Surface h5 will not be generated Another utility tool hSSurfaceVtk convert Surface h5 file to VTK files For multipacting simulation these VTK files can be used to visualize the hot spots of the RF structure where multipacting happens The above mentioned utility tools are based on H5hut library and will soon be available in the distribution Some of the boundary geometry related simulations like the multipacting simulation using re normalizing particle number approach or dark current simulations where the current of field emitted particles from a single triangle has been re normalized as the model predicted current has exceeded the user defined upper limit the current weight of simulation particles varies and each simualtion particle stands for more physical particles than the initial simulation particles In these cases instead of using simulation particles we count the number of effective particles defined as the ratio of total current in simulation over
147. nt is valid for field emission A SURFAC GE attached to the T EMISSION type of distribution defined in DISTRIBUTION command should be OMETRY command And users can customize dark current simulation by specifying the value of the work function p local field enhancement factor 8 and other parameters present in 16 1 and 16 2 in the SURFAC T E ISSION type of distribution definition in input file See the following example input file and Table 16 1 for a summary of the field emission related command in the SURFACEEMISSION type of distribution definition DistSurf DISTRIBUTION DISTRIBUTION SURFACEEMISSION NPDARKCUR 0 INWARDMARGIN 0 0 FNBETA 30 FNMAXEMI 2 FNFIELDTHR 0 1 ge GEOMETRY FGEOM New Gun h5 20 0 DISTR DistSurf ZSHIFT 0 0 FINSSGUN RFCavity 1 0 175 VOLT 100 0 RF GUN PSI fieldmap T7 GEOMETRY ge ELEMEDGE 0 0 TYPE STANDING FREQ 2997 922938148 ldots Table 16 1 Field Emission Command summary Command Purpose Default Empirical constant A for F N emission model 1 54 10 6 F NB Empirical constant B for F N emission model 6 83 x 109 FNY Constant for image charge effect parameter y E 3 795 x 1075 FNVYZERO Zero order constant for v y function 0 9632 FNVYSECOND Second order constant for v y function 1 065 FNPHIW Work function of gun surface mat
148. ntal multiple time stepping MTS variant of the Boris Buneman leapfrog method which evaluates space charge only every N th step thus greatly reducing computation time while usually being still accurate enough 5 8 Multi bunches Issues The neighboring bunches problem is motivated by the fact that for high intensity cyclotrons with small turn separation single bunch space charge effects are not the only contribution Along with the increment of beam current the mutual interaction of neighboring bunches in radial direction becomes more and more important especially at large radius where the distances between neighboring bunches get increasingly small and even they can overlap each other One good example is PSI 590 MeV Ring cyclotron with a current of about 2mA in CW operation and the beam power amounts to 1 2 MW A upgrade project for Ring is in process with the goal of 1 8 MW CW on target by replacing four old aluminum resonators by four new copper cavities with peak voltage increasing from about 0 7 MV to above 0 9 MV After upgrade the total turn number is reduced from 200 turns to less then 170 turns Turn separation is increased a little bit but still are at the same order of magnitude as the radial size of the bunches Hence once the beam current increases from 2 mA to 3 mA the mutual space charge effects between radially neighboring bunches can have significant impact on beam dynamics In consequence it is important to cover neighboring bunc
149. obed on the PROBE are recorded in the ASCII file input f ilename loss Please note that these particles are not deleted in the simulation however they are recorded in the loss file 8 17 Stripper OPAL CYCL A stripper element strip the electron s from a particle The particle hitting the stripper is recorded in the file which contains the time coordiantes and mumentum of the particle at the moment it hit the stripper The charge and mass are changed Its has the same geometry as the PROBE element Please note that the stripping physics in not included yet There are 9 parameters to describe a stripper XSTART The x cooradinate of the start point mm XEND The x cooradinate of the end point mm YSTART The y cooradinate of the start point mm YEND The y cooradinate of the end point mm WIDTH The width of the probe NOT used yet OPCHARGE Charge number of the outcoming particle Negative value represents negative charge OPMASS Mass of the outcoming particles GeV c OPYIELD Yield of the outcoming particle the outcome particle number per income particle the default value is 1 STOP If STOP is true the particle is stopped and deleted from the simulation Otherwise the outcoming particle continues to be tracked along the extraction path 8 17 STRIPPER OPAL CYCL 95 Example particle stripping probl Stripper xstart 4166 16 xend 4250 0 ystart 1226 85 yend 1241 3 opcharge 1 opmass PMASS opyiel
150. odel and OPAL simulation using Furman Pivi s secondary emission model with both constant simulation particle approach and real emission particle approach at f 200M Hz Vo 120V d 5MM Time evolution of electron number predicted by theoretical model and OPAL simulation using Vaughan s secondary emission model with both constant simulation particle approach and real emission particle approach at f 1640MHz 120V d 1mm The comparison of stopping power with PSTAR The comparison of Coulomb scattering with Jackson s book The diagram of CollimatorPhysicsin OPAL The diagram of CollimatorPhysics OPAL Continued The passage of protons through the collimator The energy spectrum and scattering angle at z 0 1 M The longitudinal phase space after a gun simulation using a 1D field map on axis field of the gun a 1D field map on axis field of the gun in combination with the FAST switch and a 2D field map of the gun generated by Poisson Superfish Example of a IDMagnetostatic field map 12 LIST OF FIGURES CA Example of an ASTRA compatible magnetostatic field 170 C 5 Example ofa IDDvnamic field map 171 C 6 Example of an ASTRA compatibl
151. ollimator it will be absorbed or scattered the algorithm is based on the Monte Carlo method Pleased note when a particle is scattered it will not be recored as the lost particle If this particle leave the bunch it will be removed during the integration afterwards so as to maintain the accuracy of space charge solving XSTART The x cooradinate of the start point mm XEND The x cooradinate of the end point mm YSTART The y cooradinate of the start point mm YEND The y cooradinate of the end point mm ZSTART The vertical cooradinate of the start point mm Default value is 100 mm ZEND The vertical cooradinate of the end point mm Default value is 100 mm WIDTH The width of the septum mm SURFACEPHYSICS Surfacephysics is an attribute of the element Collimator physics is a only a kind of sur facephysics It can be applied to any element If the type of Surfacephysics is Collimator the material is defined here The material Graphite and are defined untill now If this is not set the surface physics module will not be activated The particle hitting collimator will be recorded and directly deleted from the simulation y Example 1 0 0 2 0 0 3 200 0 4 205 0 1 215 0 2 220 0 3 0 0 4 0 0 cmphys surfacephysics TVPE Collimator MATERIAL Cu cmal CCollimator XSTART x1 XEND x2 YSTART yl YEND y2 8 15 SEPTUM OPAL CYCL 93
152. on generator see Section11 is specified in the local reference frame which is an Cartesian coordinates During run time the 6 phase space variables y 2 Px Py p are transformed to the global Cartesian coordinates before particle tracking starts X 00 y sin 0o ro 0 Y xsin 00 y 00 ro sin 0o 2 2 PX px pro cos 00 peo 0 PY pz pro sin 00 py peo 0 PZ p 5 4 Field Maps In OPAL CYCL the magnetic field on the median plane is read from an ASCII type file The field data should be stored in the cylinder coordinates frame because the field map on the median plane of the cyclotron is usually measured in this frame There are two possible situations One is the real field map on median plane of the exist cyclotron machine using measurement equipment Limited by the narrow gaps of magnets in most cases with cyclotrons only vertical field B on the median plane z 0 is measured Since the magnetic field data off the median plane field components is necessary for those particles with z Z 0 the field need to be expanded Z direction According to the approach given by Gordon and Taivassalo by using a magnetic potential and measured B on the median plane at the point r 0 z in cylindrical polar coordinates the 3th order field can be written as OB 1 B r 0 z2 z 5r 62 Cr zOB 123 0 2 r 00 cow cd 5 4
153. oo Gaussian oe 55 exp Ma JE exp 22 There also special distribution commands 1 GUNGAUSSFLATTOPTH will create a distribution that is uniform transverselv The longitudinal profile has a Guassian rise and fall with a flat top distribution in between More details are given in Section 11 3 This distribution has thermal emittance as defined at 11 2 2 ASTRAFLATTOPTH is the same like GUNGAUSSFLATTOPTH except it uses a low noise Hammerslev generator in the longitudinal direction The following example reads in a distribution from a file and scales the coordinates 101 102 CHAPTER 11 DISTRIBUTION COMMAND Table 11 2 Parameters for the DISTRIBUTION command Parameter Purpose DISTRIBUTION FROMFILE or GAUSS or BINOMINAL GUNGAUSSFLATTOPTH ASTRAFLATTOPTH FNAME Specifies the filename of a particle distribution to be read in XMULT Scales the x coordinate x X MULT xx PXMULT Scales the px coordinate pr PX MULT px YMULT Scales the y coordinate y Y MULT PYMULT Scales the py coordinate py PY MULT x pu TMULT Scales the t coordinate t TMULT xt PTMULT Scales the pt coordinate pt PIT MULT pt SIGM AX amp see Chapter on Notation SIGM D see Chapter on Notation SIGM AY y see Chapter on Notation SIGMAPY Py see Chapter on Notation SIGMAT t see Chapter on Notation TRANSVCUTOFF Defines the transverse cut off of GUNGAUSS 3D in units o
154. or H in the 2D case and Ez Ey Ez By By or B in the 3D case By primary secondary and tertiary direction is meant the following see also Figure C la and Figure C 1b e the index of the primary direction increases the fastest the index of the tertiary direction the slowest e the order of the columns is accordingly if the z direction in an electrostatic field map is the primary direction then E is on the first column on the second For all other cases it s analogous For the 2D dynamic case in XZ orientation there are four columns E an unused column and in this order In the other orientation the first and the second column and the third and fourth column are interchanged On the second line of the header of a 1D 2D or 3D T7 type of field map the beginning and the end of the electromagnetic field relative to the physical element in primary direction is written in centimeters Also written on the second line is the number of mesh spacings corresponding to the number of grid points minus 1 For the ASTRA compatible field maps this line is omitted On the third line is the frequency For static cases this line is omitted The frequency is on the second line of a AstraDynamic field map C 2 TYPES AND FORMAT 167 The fourth line corresponds to the second line but in secondary direction and the fifth accordingly for the tertiary direction In the case of a 1D or 2D the fifth line is omitted since there is no tertiary dire
155. p string String constants string prefix STRING string definition o string prefix string name string expression expression evaluated string prefix string name string expression expression retained 160 Real arrav expressions arrav expression arrav term array factor array primary table generator first last step table row APPENDIX B OPAL LANGUAGE SYNTAX array term array term array term array expression 4 array term array expression array term array factor array term x array factor array term array factor array primary array factor array primary array literal array reference table generator row reference column reference real function array expression array expression ABLE last real expression ABLE first last real expression ABLE first last step real expression integer integer integer table name place row reference column reference column list array literal array reference array name Real array definitions array prefix array definition Constraints constraint constraint operator Variable references variable reference 161 ROW table name place ROW table name place column list COLUMN table name column name COLUMN table name column name range column name column list column name real expression arr
156. pages as the ld 1 and 1d so 8 manual H5hut 1 99 9 Mac amp Linux The tarball can be found at svntssh savannah02 psi ch repos H5hut src tags 1 99 9 Now we can build and install the package configure enable parallel CFLAGS std c99 make make install Install IPPL Mac amp Linux 1 cd HOME svnwork 2 Get source code svn co username username svntssh savannah02 psi ch repos ippl src trunk ippl A 2 XE6 INSTALLATION 145 3 cd ippl 4 mkdir build export IPPL ROOT HOME svnwork ippl export IPPL PREFIX SIPPL ROOT build rm f CMakeCache txt CXX mpicxx cmake DCMAKE BUILD TYPE RELEASE DCMAKE INSTALL PREFIX SIPPL PREFIX SIPPL ROOT 5 make 6 make install 7 Add the export statements to your bashrc file A 1 3 Installing OPAL The following svn checkout cd OPAL ROOT svntssh savannah02 psi ch repos opal src will get you the trunk of the repository Now install OPAL mkdir build cd build CXX mpicxx cmake DCMAKE BUILD TYPE RELEASE SOPAL ROOT Use DCMAKE BUILD TYPE DEBUG to enable g 2 Cray XEG Installation These notes are for installing OPAL on Hopper at the National Energy Research Scientific Computing Center NERSC NERSC is an open science computing center sponsored by the U S Department of Energy and located at Lawrence Berkely Laboratory LBL Hopper is a Cray XE6 system and at the time of this writing is their
157. pendent variable OPAL T is a superset of IMPACT T 40 and can be used to model guns injectors and complete XFEL s excluding the undulator It should be noted that not all features of OPAL are available in all flavours The icon K OPAL T means that a feature is not yet available in OPAL T Similar icons are used for the other flavours Release Date February 13 2013 Contents Introduction ht AmrofOPAlL and History 054 kx ue veg AR Rue 1 2 Parallel Processing 1 3 Quality Management i dotes Rue ba pow 1 4 Field Maps from the Femaxx 3D Eigenmode 1 5 Output ze eu Ke b mS uw ue OER ue 1 6 Acknowledgements lt 4 A i write A Ili 17 ise specs eub mb hoe s e ele ek Conventions DA Physical Anis sects aV pee Ee p ege Tutorial Selly Stattin OPA 54 Berge xU Te RU AR Reb RUE TE 3 2 Restart Mode r 24d vetu A A V bp eae Gu WU dE Cue 3 35 Atitopliase Examplez sessi be mc EVI WR Ree bak es ue 3 4 Examplesor Beam Lines i aed ERU SAPE b SUUS Be a ee ESE 3 4 1 PSLXHEEE250 MeV Inje tor ae RORIS ee DRE 3 4 2 PSLInjector II Cyclotron
158. ple converts the value of the expression X 1 to a string and appends it to LEP giving the string LEP2 6 5 Logical Expressions Many commands in OPALrequire the setting of logical values flags to represent the on off state of an option A logical value is represented by one of the values TRUE or FALSE or by alogical expression A logical expression can occur in logical arrays see 6 14 1 A logical expression has the same format and operator precedence as a logical expression in C It is built from logical operators see Tab 6 3 and logical operands relation E rel operator and expr Di logical expr TRUE FALSE real expr rel operator real expr Ia c gt z z relation and expr amp amp relation and expr logical expr and expr Example OPTION ECHO TRUE output echo is desired When a logical attribute is not entered its default value is always false When only its name is entered the value is set to TRUE OPTION ECHO same as above Example of a logical expression 6 6 REAL EXPRESSIONS Table 6 3 Logical Operators in OPAL Operator Meaning result tvpe operand type X lt Y true if X is less than Y logical real real X Y true if X is not greater than Y logical real real A true if X is greater than Y logical real real X gt true if X is not less than
159. r see 86 2 3 Each attribute is entered in one of the forms attribute name attribute name attribute value attribute name attribute value and serves to define data for the command where 45 46 CHAPTER 6 COMMAND FORMAT e The attribute name selects the attribute it must be an identifier see 6 2 e The attribute value gives it a value see 56 3 When the attribute value is a constant or an expression preceded by the delimiter it is evaluated immediately and the result is assigned to the attribute as a constant When the attribute value is an expression preceded by the delimiter the expression is retained and re evaluated whenever one of its operands changes Each attribute has a fixed attribute type see 56 3 The attribute value can only be left out for logical attributes this implies a true value When a command has a 1 1 OPALkeeps the command in memory This allows repeated execution of the same command by entering its label only label or to re execute the command with modified attributes label attribute attribute If the label of such a command appears together with new attributes OPALmakes a copy of the stored command replaces the attributes entered and then executes the copy QF QUADRUPOLE L 1 Kl 0 01 first definition of QF QF L 2 xedefinition of QF MATCH LMD LMDIF CALLS 10 first execution of LMD LMD re execute LMD with the same attrib
160. r Prediction Proc of MULCOPIM 2005 2005 184 BIBLIOGRAPHV 60 S Anza and C Vicente and J Gil and V E Boria and B Gimeno and D Raboso Nonstationarv Statistical Theorv for Multipactor Phvs Plasmas 17 062110 2010 61 A Henderson Para View Guide A Parallel Visualization Application Kitware Inc 2007 62 L Serafini and J B Rosenzweig Phvs Rev E 55 1996 63 M Ferrario 7 E Clendenin D T Palmer J B Rosenzweig L Serafini HOMDYN Study for the LCLS RF Photo Injector SLAC PUB 8400 March 2000 64 arxiv
161. r the string describing the type of field map two integer numbers and a floating point number follow The first integer number describes the number of Enge coefficients to be used for the entry fringe field the second the equivalent for the exit fringe field The floating point number specifies the full gap height On the second line the first value describes the beginning of the entry fringe field in local coordinates corresponds to zbegin entry in Figure C 7 and Figure C 8 the second the origin of the Enge polynomial the third the end of the fringe field zend entry The last number of this line is only used in 1DProfile2 and specifies the number of grid points minus 1 of the field profile The third line looks identical to the sdcond but the last value on this line is not used yet The values on this line correspond to zbegin exit origin of Enge function and zend exit in Figure C 7 and Figure C 8 The following lines are the coefficients of the Enge function in the case of 1DProfilel and the actual field profile in 1DProfile2 see appendix C 1 Note that zbegin entry zend entry zbegin exit and zend exit have slightly different definitions when defining a rectangular bend as opposed to a sector bend Figure C 7 and Figure C 8 ELEMEDGE nd entr rigin of Enge function zbegin entry zend exit design path RBend Figure C 7 The profile of a rectangular bend and its corresponding design path 1
162. r with space charge or not either single bunch or multi bunches either serial or parallel environment either reading the initial distribution from a file or generating a typical distribution either running from the beginning or restarting from the last step of a former simulation Because this is the main mode as well as the key part of OPAL CYCL we will describe this in detail in Section 5 8 5 3 Variables in OPAL CYCL OPAL CyYCLuses the following canonical variables to describe the motion of particles X Horizontal position x of a particle in given global Cartesian coordinates m PX Horizontal canonical momentum eV c Y Longitudinal position y of a particle in global Cartesian coordinates m PY Longitudinal canonical momentum eV c Z Vertical position z of a particle in global Cartesian coordinates m PZ Vertical canonical momentum eV c The independent variable is t s 5 4 FIELD MAPS 37 NOTE unit conversion of momentum in OPAL T and OPAL CYCL Convert dimensionless to mrad P P By 5 5 1 0 P mrad 1000 x E 5 2 ref Convert from eV c to 6 dimensionless P eV e 8 7 il IED 12 1 5 3 This be deduced by analogy for the y and 2 directions 5 3 1 The initial distribution in the local reference frame To ensure compatibility with OPAL T the initial distribution of the bunch either read from file or generated by distributi
163. re empirical constants The functions v y and t y representing the image charge effects 52 as a function of the Fowler Nordheim parameter y with the following definition 54 3 795 x 107 16 2 4 e BE p p In our model we have chosen a simpler approximation originated bv J H Han 54 v y tly amp 1 These approximations are valid for a large range of y corresponding to typical applied electric field ranges in RF guns Whenever the normal components of an electric field are strong enough the field emission current density will be limited by space charge effect 52 To cover this situation we incorporated the 1D Child Langmuir law 3 2 J r t ja 7 4 22 2 s A m 16 3 into our field emission model J r t denotes space charge limited emission current density in position and time t the permittivity in vacuum the normal component of electric field on the surface and d the distance from the position where E is evaluated Currently we choose d to be equal to the distance traveled by emitted particles eEAt 2mo in one time step i e d where At is simulation time step 123 124 CHAPTER 16 FIELD EMISSION 16 1 Field Emission Command To perform field emission related simulation a triangulated surface geometrv defined bv G EOMETRY command see Chapter 14 should be specified and attached to the elements currently only RFCavity eleme
164. return smallest integer not less than X real array real array SIGN X return sign of X 1 for X positive 1 for X negative 0 for X zero real array real array SORT X return square root of X real array real array LOG X return natural logarithm of X real array real array EXP X return exponential to the base e of X real array real array SIN X return trigonometric sine of X real array real array COS X return trigonometric cosine of X real array real array ABS X return absolute value of X real array real array TAN X return trigonometric tangent of X real array real array ASIN X return inverse trigonometric sine of X real array real array ACOS X return inverse trigonometric cosine of X real array real array ATAN X return inverse trigonometric tangent of X real array real array TGAUSS X random number Gaussian distribution with c 1 truncated at X real array real array USERI X random number user defined distribution with one parameter real array real array EVAL X evaluate the argument immediately and transmit it as a constant real array real array 59 an array with 9 components evaluates to 1 4 7 10 13 table 5 9 2 3xtril equivalent to 0 0 0 0 16 0 22 0 28 ROW Generate a table row ROW table place implies all columns ROW table place column list This generates an array containing the named or all columns in the selected place COLUMN Generate a table column COLUMN ta
165. riable with the same name Its value depends on all quantities occurring in real expression see 86 6 Whenever an operand changes in real expression a new value is calculated The definition may be thought of as a mathematical equation However OPAL is not able to solve the equation for a quantity on the right hand side An assignment in the sense of the FORTRAN or C languages can be achieved by using the EVAL function see 87 4 4 A reserved variable is the value PO which is used as the global reference momentum for normalising all magnetic field coefficients Example REAL GEV 100 PO GEV Circular definitions are not allowed 1 X cannot be equal to 1 A B A and are equal but of unknown value However redefinitions by assignment are allowed X EVAL X41 66 CHAPTER 7 CONTROL STATEMENTS Real Vector Variables REAL VECTOR variable name vector expression The keyword REAL is optional This statement creates a new global variable variable name and discards any old variable with the same name Its value depends on all quantities occurring in vector expression see 6 14 on the right hand side Whenever an operand changes in vector expression a new value is calculated The definition may be thought of as a mathematical equation However OPAL is not able to solve the equation for a quantity on the right hand side Example REAL VECTOR A TABLE 10 f REAL VE
166. ringe field of an element The file provides field values at 1001 equidistant sampling points To calculate the field between the grid points a Enge function is fitted to these values To calculate the field the corresponding Enge coefficients 7 for the entrance fringe field and 8 for the exit fringe field polynomial order 6 and 7 respectively The element has a gap height of 3 0 cm The length of the entrance and the exit fringe field are determined by the field values and the total length 32 0 cm 6 0 cm 38 0 cm 176 C 8 2DElectroStatic APPENDIX C OPAL T FIELD MAPS 2D1 Doh f EA CO MEDE FNE eite otat eA 3 0 5SIL 0 4999 OF 129 00000 00 0 00000e 00 36222e 06 0 00000e 00 83270 06 0 00000e 00 99999248 32490 05 0 00000e 00 73710 05 0 00000e 00 18598 05 0 00000e 00 Figure C 11 2 field describing electrostatic field using 57000 grid points in longitudinal direction times 200 grid points in transvers direction The field between the grid points is calculated with a bilinear inter polation The field is non negligible from 3 0 cm to 51 0 cm relative to ELEMEDGE and the 200 grid points in transverse direction span a length of 2 0cm The field values are ordered in XZ orientation the index in longitudinal direction changes fastest on the first column the E values are stored on the second the E values C 9 2DMAGNETOSTATIC 177 C 9 2DMagnetostatic
167. s First we can specify the peak value of that field see the KO and KOS parameters below Second we can set the ANGLE parameter If the ANGLE is set then OPAL Twill attempt to calculate the required strength of the magnet to bend the beam through that angle using the average energy of the beam when it enters the magnet The ANGLE parameter overrides the field magnitude set by KO and or KOS The convention for a positive bend angle is to bend the beam to the right in the negative x direction If a negative bend angle is defined this is interpreted as a positive bend angle rotated by 180 about the z axis In the case where a negative bend angle is defined along with a magnet ROTATION see below this 180 rotation is added to the defined ROTATION KO Rather than set the bend angle we can also declare the field strength of the magnet via KO KO is the peak field in the vertical direction in Tesla A positive value of KO will bend a positive charge in the negative x direction positive bend angle KO in conjunction with KOS can also be used to rotate the magnet about the z axis See ROTATION parameter KOS KOS is analogous to KO but sets the peak field in the horizontal or x direction In conjunction with KO it can also be used to rotate the magnet about the z axis See ROTATION parameter KI KI defines the field gradient index of the magnet K B3 4 This introduces quadrupole focusing This gradient will alwavs be define
168. s led by Benedikt Oswald Parts of the envelope tracker was contributed by Colwyn Gulliford Misprints and obscurity are almost inevitable in a document of this size Comments and active contributions from readers are therefore most welcome They may be sent to andreas adelmann psi ch 1 7 Citation Please cite OPAL in the following way techreport Opal User Guide title The OPAL Object Oriented Parallel Accelerator Library Framework jJ author A Adelmann and Ch Kraus and Y Ineichen and S Russell and Yuanjie Bi and J Yang institution Paul Scherrer Institut number PSI PR 08 02 year 2008 18 CHAPTER 1 INTRODUCTION Chapter 2 Conventions 21 Physical Units Throughout the computations OPALuses international units see Tab 2 1 as defined bv SI Svst me Interna tional 20 Table 2 1 Phvsical Units CHAPTER 2 CONVENTIONS quantitv dimension Length m metres Angle rad radians Quadrupole coefficient Multipole coefficient 2n poles Electric voltage Electric field strength Frequency Phase angles Particle energy Particle mass Particle momentum Beam current Particle charge Impedances Emittances Emittances OPAL T RF power Higher mode loss factor m MV Megavolts MV m MHz Megahertz 27 GeV GeV c GeV c A Amperes e elementary charges Megohms m mrad m rad MW Megawatts V pc Chapter 3 Tutorial
169. sed The following three pictures show the longitudinal phase space after three gun simulations using different types of field maps In the first picture Figure C 2a we used a 1D field map which stores a sampling of the electric field in longitudinal direction E From these values E and off axis are calculated resulting in a smooth field field maps we used are made of the same solution file from a Poisson Superfish simulation In Figure C 2b we used the same on axis field map as in the first but we used the FAST switch which constructs a 2D field map from the on axis field maps Between the grid points the fields are calculated using a linear interpolation Here we see a structure which can be influence using more grid points in transverse direction In the last picture Figure C 2c we generated directely a 2D field map from the solution file of Poisson Superfish Here we could observe two different structures first the fine structure stemming from the linear interpolation and secondly a much stronger structure of unknown origin C 3 IDMAGNETOSTATIC 169 IDMagnetostatic 1DMagnetoStatic 40 60 0 9999 0 0 2 0 199 0 00000e 00 36222 06 83270 06 97994 lines 32490 05 73710 05 18598 05 Figure C 3 A ID field map describing a magnetostatic field using 10 000 grid points 97999 grid spacings in longitudinal direction If the FAST switch is set in the input deck 200
170. speed while E1 and BETA define the initial direction of the velocity in local coordinates From the path this particle travels a map between the path length s coordinate and the local z coordinate is constructed If the bend angle ANGLE is set DESIGNENERGY is automatically defined as the average energy of the beam when it enters the field and the element is re initialized at this time FINT The field integral default 0 HGAP The half gap of the magnet default 0 m The pole face rotation angles are referred to the magnet model for a RBEND see Fig and SBEND see Fig respectively The quantities FINT and HGAP specify the finite extent of the fringe fields as defined in SLAC 75 8 as follows Bo FINT T B 0 09 The default values of zero corresponds to the hard edge approximation i e rectangular field distribution For other approximations enter the correct value of the half gap and one of the following values for FINT Typical values for F INT Linear Field drop off 1 6 Clamped Rogowski fringing field 0 4 Unclamped Rogowski fringing field 0 7 Square edged non saturating magnet 0 45 A reasonable average value for F INT is 0 5 All these dipole examples have the same bend angle BR RBEND BR RBEND 0 001 Deflection to the right 0 0 001 5 5 Deflection to the right This magnet has a
171. ted To calculate the off axis field the 1 224 and 374 derivative have to be computed OPAL Tuses a Fourier transformation in conjunction with a low pass filter only a number of low frequency Fourier coefficients are kept In order to apply a Fast Fourier Transformation the data has to be equidistant To this end the sampling C 2 TYPES AND FORMAT 165 values of an ASTRA field map are resampled using a cubic spline interpolation The number of sampling points is preserved in this process From the resulting sampling the Fourier coefficients are calculated It is important to note that when a field map is read into OPAL T it is normalized so that the peak field value is equal to either 1 MV m in the case of electric field maps or 1 T in the case of magnetic field maps So when using a field map in an accelerating cell for instance the peak field in the simulation will be equal to the field scaling factor you specify in your input file At the beginning of the first line information of the kind of field map has to be provided in form of a string This can either be 1DElectroStatic 1D electrostatic field map 1D field maps are described by the on axis field Not implemented yet use a IDDvnamic field map with very low frequency instead 1DMagnetoStatic if the file describes a 1D magnetostatic field map AstraMagnetoStatic if the file describes a 1D magnetostatic field map with possibly non equidistant sampling This file type is compa
172. tens of magnitude larger within limited simulation time steps which may cause the exhaust of computing memory a re normalization of simulation particle number approach is also implemented In each elec tron impacting events instead of emitting the real number of simulation particles predicted by secondary emission models this re normalization approach emit only one particle and the current of newly emitted particle will be the current of incident particle multiplied by SEY value 128 CHAPTER 17 MULTIPACTING 17 1 Commands Related to Multipacting Simulation To perform multipacting simulation a triangulated surface geometrv defined in the command see Chapter 14 must be specified and attached to the elements currently only RFCavitv ParallelPlate and Drift elements are avaidable for multipacting simulation A distribution arrav containing SURFACEEMISSION and SURFACI ERANDCR fined in the DISTRIBUTION command must be attached to the GEOM in SURFACERANDCREAT within SURFAC ondary emission model in input file I EAT E type of distributions de A summary of multipacting simulation related parameters are given in Table 17 1 The following example shows the usage of the multipacting simulation related command ETRY Users can use commands contained E type of distribution to specify the position of initial seed electrons And commands
173. the current of a single initial particle An ASCII file named Part statistics dat containing the simulation time the number of impacts and associated total SEY value as well as the number of effective particles in each time step This makes the analysis of the time evolution of particle density feasible with tools like GNUPLOT 134 CHAPTER 17 MULTIPACTING Chapter 18 Phvsics Models Used in the Particle Matter Interaction Model 18 1 Energy Loss The loss is simulated using the Bethe Bloch equation KAZ 14 2 202 2 2 18 1 where Z is the aomic number of absorber is the atomic mass of absorber m is the electron mass 2 is the charge number of the incident particle K 47 ATr2mec Te is the classical electron radius Na is the Avogadro s number J is the mean excitation energy and y are kinematic variables is the maximum kinetic energy which can be imparted to a free electron in a single collision 2 E 202 2 18 2 1 2 2 dE dx Tmax where is the incident particle mass The stopping power is compared with PSTAR program of NIST in Fig 18 1 T T T T T T T T T 5l Model in PSTAR Stopping Power MeV 0 L 1 l L 50 0 150 200 250 300 350 400 450 500 50 100 E MeV Figure 18 1 The comparison of stopping power with PSTAR Energy straggling For rel
174. the derivative a standard second order stencil is used pa fi z2 8 fi 1 8 fiai l h This filter was designed by Pogorelov for the ImpactT implementation of the CSR 1D model The FFT based smoothers calculate the Fourier coefficients of the line density Then they set all coefficients corresponding to frequencies above a certain threshold to zero Finally the back transformation is calculate using this coefficients The two filters differ in the way they identify coefficients which should be set to zero FixedFFT LowPass uses the n lowest frequencies whereas RelativeFFTLowPass searches for the coefficient which has the biggest absolut value All coefficients which compared to this value are below a threshold measure in percents are set to zero For the derivative the coefficients are multiplied with the following function this is equivalent to a convolution JE lt 2 STi i gt where N is the total number of coefficients sampling points and L is the length of the bunch 116 CHAPTER 13 WAKEFIELDS Chapter 14 Geometrv At present the GEOMETRY command is still an experimental feature which is not to be used by the general user It can only be used to specify boundaries for the MG Solver The command can be used in two modes 1 specify a H5FED file holding the surface mesh of a complicated boundary geometry 2 specify a cylinder with an elliptic base area 14 1 Geometry Command Table 14 1 G
175. there is an ELSE the statement or group following the ELSE is executed 7 9 WHILE Repeated Execution Repeated execution can be requested by a WHILE statement It allows usages similar to the C language while statement WHILE logical statement WHILE logical statement group l Note that all statements must be terminated with semicolons but there is no semicolon after a closing brace The condition is re evaluated in each iteration The statement or group of statements following the WHILE is repeated as long as the condition is satisfied Of course some variable s must be changed within the WHILE group to allow the loop to terminate 7 10 MACRO Macro Statements Subroutines Subroutine like commands can be defined by a MACRO statement It allows usages similar to C language function call statements A macro is defined by one of the following statements name formals MACRO token list name MACRO token list A macro may have formal arguments which will be replaced by actual arguments at execution time An empty formals list is denoted by Otherwise the formals consist of one or more names separated by commas The token list consists of input tokens strings names numbers delimiters etc and is stored unchanged in the definition A macro is executed by one of the statements name actuals name Each actual consists of a set of tokens which repl
176. thode or in a plasma wake field accelerator can have a large energy spread In this case the static approximation using one Lorentz frame might not be sufficient Multiple Lorentz frames can be used so that within each Lorentz frame the energy spread is small and hence the electrostatic approximation is valid More details will be given in Version 1 1 9 4 6 WAKE FIELDS 33 4 6 Wake Fields Longitudinal and transverse short range wakefields wake fields are described in Chapter 13 4 7 Multiple Species In the present version only one particle species can be defined Chapter 10 however due to the underlying general structure the implementation of a true multi species version of OPAL is trivial 34 CHAPTER 4 OPAL T Chapter 5 OPAL CYCL 5 1 Introduction OPAL CYCL as one of the flavors of the OPAL framework is a fully three dimensional parallel beam dynamics simulation program dedicated to future high intensity cyclotrons and FFAG it tracks multiple particles which takes into account the space charge effects For the first time in the cyclotron community OPAL CYCL has the capability of tracking multiple bunches simultaneously and take into account the beam beam effects of the radially neighboring bunches we call it neighboring bunch effects for short by using a self consistent numerical simulation model Apart from the multiparticle simulation mode OPAL CYCL also has two other serial tracking modes for conventional cyclotron m
177. tible with ASTRA field maps with small changes 1DDynamic if the file describes a 1D dynamic electromagnetic field map AstraDynamic if the file descirbes a 1D dynamic electromagnetic field map with possibly non equidistant sampling This file type is compatible with ASTRA field maps with small changes IDProfilel if the file contains Enge coefficients see 441 which describe the fringe field of an element From these the correct field at any position is calculated This type of field map is special in the sense that the class processing these files doesn t return the actual field at a position but rather the on axis field profile and its first and second derivatives The classes elements supporting this kind of field map have to deal with this appropriately At the moment only the rectangular bend RBEND and the sector bend SBEND elements in OPAL t can use this type of field file 1DProfile2 if the file describes a mid plane on axis field profile which is processed to get the corresponding Enge coefficients Otherwise this type is the same as IDProfilel 2DElectroStatic if the file describes a 2D electrostatic field map 2D field maps are described by the electromagnetic field in one half plane 2DMagnetoStatic if the file describes a 2D magnetostatic field map 2DDynamic if the file describes a 2D dynamic electromagnetic field map 3DElectroStatic if the file describes a 3D electrostatic field map Not implemented yet 3DMa
178. tion method for gridpoints near the boundary CONSTANT LINEAR or QUADRATIC 12 11 Define Tolerance The tolerance for the iterative solver used by the MG solver 12 12 Define Maximal Iterations The maximal number of iterations the iterative solver performs 12 13 Define Preconditioner Behaviour The behaviour of the preconditioner can be STD HIERARCHY or REUSE This argument is only relevant when using the MG solver and should only be set if the consequences to simulation and solver are evident A short description is given in Table 12 2 Table 12 2 Preconditioner bahaviour command summary Value Behaviour STD The preconditioner is rebuilt in every timestep enabled by default HIERARCHY The hierarchy tentative prolongator is reused REUSE The preconditioner is reused 12 14 Define the number of Energy Bins to use Suppose dE the energy spread in the particle bunch is to large the electrostatic approximation is no longer valid One solution to that problem is to introduce k energy bins and perform k separate field solves in which d E is again small and hence the electrostatic approximation valid In case of a cyclotron Section 8 10 the number of energy bins must be at minimum the number of neighbouring bunches NNEIGHBB i e ENBINS lt NNEIGHBB 110 CHAPTER 12 FIELDSOLVER Chapter 13 Wakefields Basically there are two different kind of wakefields that can be used The first one is the wakefield of
179. to this give point using 5 4 After each time step 7 the code detects whether the particle crosses any one of the RF cavities during this step If it does the time point te of crossing is calculated and the particle return back to the start point of step 2 Then this step is divided into three substeps first the code tracks this particle for ti te t 1 then it calculates the voltage and adds momentum kick to the particle and refreshes its relativistic parameters f and y and then trackes it for t T t 5 7 Space Charge OPAL CYCL uses the same solvers as OPAL T to calculate the space charge effects see Section 4 5 The difference is that in a cyclotron both the origin and orientation of the local Cartesian frame are changed from time to time So the coordinates are transformed from the global frame to the local frame first then the space charge fields are calculated in the local frame After the space charge fields are solved both coordinates and self electric and magnetic field are transformed back to global frame Typically the space charge field is calculated once per time step This is no surprise for the second order Boris Buneman time integrator leapfrog like scheme which has per default only one force evaluation per step The fourth order Runge Kutta integrator keeps the space charge field constant for one step although there are 42 CHAPTER 5 OPAL CYCL four external field evaluations There is an experime
180. uded S M S 2 M From the marker M nested in the first occurrence of S to the marker M nested in the second occurrence of S S 1J S 2 Entrance of first occurrence of S through exit of second occurrence of 5 56 CHAPTER 6 COMMAND FORMAT 6 10 Constraints Please note this is not yet available in E 3 OPAL Tand OPAL CYCL In matching it is desired to specify equality constraints as well as lower and upper limits for a quantity OPALaccepts the following form of constraints constraint array expr constraint operator array expr ll mem gt constraint operator 6 11 Variable Names A variable name can have one of the formats variable name real variable object real attribute The first format refers to the value of the global variable see 7 4 1 the second format refers to a named attribute ofthe named object object can refer to an element or a command 6 12 Regular Expressions Some commands allow selection of items viaa regular expression Such a pattern string must be enclosed in single or double quotes and the case of letters is significant The meaning of special characters follows the standard UNIX usage utility Stands for a single arbitrary character letter letter Stands for a single character occurring in the bracketed string Example abc denotes the choice of one of a b c character character Stands for a single character from a range of ch
181. udinal direction times 76 grid points in transvers direction The field between the grid points is calculated with a bilinear interpolation The field is non negligible between 3 0 cm and 51 0 cm relative to ELEMEDGE and the 76 grid points in transvers direction span a distance of 1 0 cm The field values are ordered in XZ orientation the index in longitudinal direction changes fastest on the first column the E values are stored on the second the E values on the fourth the B values and the third column contains dummy values For the ZX orientation the first column would contain the values the second the E values the third dolumn the B values and the fourth column dummy values In addition the ordering of the values would be such that the index in transvers direction changes fastest and the second and fourth line of the file would be interchanged 11 3DDVNAMIC 11 3DDvnamic 3DDynamic XYZ 1498 953425154 TIS Jes 221 1 0 120 ial S0 90 41211 00e 00 0 00 00 0 00e 00 36e 06 0 00e 00 4 36e 06 83e 06 0 00 00 8 83e 06 142 852 026 lines 32e 05 0 00e 00 1 32e 05 736 05 9 598 900 1736 05 18e 05 0 00 00 2 18e 05 NS gt 9 ur oo qe xem 9 9 00 00 00 00 00 00 00 00 00 00 00 00 ES 00 00 5 359 308 5 51 3x95 18e 05 e 00 00 00 00 00 00 00 00 00 00 00 00 17
182. un sp1 sp2 sp3 examples OBLA Gun OBLA Gun in FMAPFN 1T3 T7 FMAPFN 1T3 T7 real real FMAPFN 1T2 T7 FMAPFN 1T1 T7 FREQ 1 0e 6 KS 0 0 KS 0 0 3 4 EXAMPLES OF BEAM LINES Distl DISTRIBUTION DISTRIBUTION gungauss sigmax 0 00030 sigmapx 0 0 corrx 0 0 sigmay 0 00030 sigmapv 0 0 corrv 0 0 sigmat 12 sigmapt 1 0 corrt 0 0 TEMISSION 3 9e 11 NBIN 39 DEBIN 1 MINSTEPFORREBIN 1000 Fsl FIELDSOLVER FSTYPE FFT MX 32 32 MT 32 PARFFTX true PARFFTY true PARFFTT false BCFFTX open BCFFTY open BCFFTT open BBOXINCR 1 GREENSF STANDARD beaml BEAM PARTICLE ELECTRON pc PO NPART 50000 BCURRENT 0 008993736 BFREQ rf CHARGE 1 Select Line 11 track line 11 beam beaml MAXSTEPS 2000 DT 1 0e 13 run method PARALLEL T beam beaml fieldsolver Fsl distribution Dist1 endtrack Stop 3 4 1 PSI XFEL 250 MeV Injector 24 CHAPTER 3 TUTORIAL examples diagnostic in Option ECHO FALSE Option TFS FALSE Option PSDUMPFREQ 10 Title string OPAL Diagnostics test Edes 0 0307 GeV gamma Edes EMASS EMASS beta sqrt 1 1 gamma 2 gambet gammaxbeta gammaxbetaxEMASS brho EMASS 1 0e9 gambet CLIGHT value gamma brho Edes beta gambet FINLBO2 MSLAC40 Solenoid L 0 001 KS 0 05 FMAPFN FINLBO2 MSLAC T7 ELEMEDGE 4 554 FIND1 010 Quadrupole L 0 1 Kl 2 788 ELEMEDGE 5 874 FIND1 020 Quadrupole L 0 1
183. ute operating system commands After execution of the system command successful or not control returns to OPAL At present this command is only available under UNIX or VM CMS It has two formats SYSTEM CMD string SYSTEM string shortcut The string see 86 4 string must be a valid operating system command 7 5 3 SYSTEM Command under UNIX Most UNIX commands can be issued directly Example SYSTEM 15 1 causes a listing of the current directory in long form on the terminal 7 6 TITLE STATEMENT 69 7 6 TITLE Statement The TITLE statement has three formats TITLE STRING page header define new page header TITLE page header shortcut for first format TITLE STRING clear page header page header is a string value see 56 4 It defines the page header which will be used as a title for subsequent output pages Before the first TITLE statement is encountered the page header is empty It can be redefined at any time 77 File Handling 7 7 1 CALL Statement The CALL command has two formats CALL FILE file name CALL file name file name is string see 86 4 The statement causes the input to switch to the named file Input continues on that file until a STOP or an end of file is encountered Example CALL FILE structure CALL structure 7 7 2 SAVE Statement The SAVE command has two formats SAVE FILE file name file name is a string see
184. utes LMD CALLS 100 TOLERANCE 1E 5 re execute LMD with new attributes ENDMATCH 6 2 Identifiers or Labels An identifier refers to a keyword an element a beam line a variable an array etc A label begins with a letter followed by an arbitrary number of letters digits periods underscores Other special characters can be used in a label but the label must then be enclosed in single or double quotes It makes no difference which type of quotes is used as long as the same are used at either end The preferred form is double quotes The use of non numeric characters is however strongly discouraged since it makes it difficult to subsequently process a OPALoutput with another program When a name is not quoted it is converted to upper case the resulting name must be unique An identifier can also be generated from a string expression see 6 4 6 3 Command Attribute Types An object attribute is referred to by the syntax object name attribute name If the attribute is an array see 6 14 one of its components is found by the syntax 6 4 STRING ATTRIBUTES 47 object name rattribute name index The following tvpes of command attributes are available in OPAL String see 56 4 Logical see 86 5 Real expression see 86 6 Deferred expression see 56 8 5 Place see 66 9 1 Range see 86 9 2 Constraint see 56 10 Variable Reference see 6 11 Regular expression see 86 12
185. y setting the length to zero KN A real vector see 86 14 containing the normal multipole coefficients A component is positive if B is positive on the positive x axis KS A real vector see 86 14 containing the skew multipole coefficients A component is negative if B is positive on the positive x axis The multipole coefficients are defined as K 1 22 default Om 7 The order n is unlimited but all components up to the maximum must be given even if zero The number of poles of each component is 2n 2 The most important error components of fully symmetric quadrupoles are KNORMAL 5 the 12 pole and KNORMAL 9 the twenty pole Superposition of many multipole components is permitted The reference system for a multipole is a Cartesian coordinate system see Fig Example M27 MULTIPOLE L 1 KNORMAL 3 0 0001 KSKEW 2 0 0001 A multipole with no dipole component has no effect on the reference orbit i e the reference system at its exit is the same as at its entrance If it includes a dipole component it has the same effect on the reference orbit as a SBEND with the same length and deflection angle KNORMAL 0 L 8 9 SOLENOID 83 8 9 Solenoid label SOLENOID TVPE string APERTURE real vector L real KS real A SOLENOID has two real attributes L The length of the solenoid default 0 m KS The solenoid strength X default 0 rad m For positive KS and positive particle charge t
186. ymmetric the field on median plain is periodic along azimuthal direction OPAL cvcrtake this advantage to only store 1 8 field data to save memory RF Cavity In the Ring all the cavities are typically single gap with some parallel displacement from its radial position OPAL CYCLhave an argument PDIS to manipulate this issue Figure 3 5 shows a single particle tracking result and tune calculation result in the PSI Ring cyclotron Limited by size of the user guide we don t plan to show too much details as in Injector II 3 4 EXAMPLES OF BEAM LINES m z gt 60 o 5 2 40 30 20 10 10 15 TIME s 95000 96000 97000 98000 99000 TrackStep Figure 3 3 Energv Vs time left and external B field Vs trackstep Right onlv show for about 2 turns 0 005 o 0 005 z m 0 0005 0 001 0 01 0 005 o 0 005 0 01 0005 0 0 005 z m z m Figure 3 4 Vertical phase at different energy from left to right 0 87 MeV 15 MeV and 35 MeV y mm 5000 4000 3000 2000 l 1000 0 1000 2000 3000 4000 5 Reference Particle Tracking 1 0 95 0 65 000 1 i 1 i 1 5000 4000 3000 2000 1000 0 1000 2000 3000 4000 5000 x mm 0 9 r 0 85 p 0 8 7 0 75 f 0 7 Fr FIXPO OPAL cycl mm nur 2nuz x 11 12 13 14 15 16 17 18 Figure 3 5 Reference orbit left and tune diagram right in Ring cyclotron
187. ything except newline anything except x la zA Z a zA 20 9 0 9 anything except single quote anything except double quote keyword attribute list label keyword attribute list identifier identifier empty attribute list attribute 153 154 APPENDIX B OPAL LANGUAGE SVNTAX attribute attribute name only for logical attribute attribute name attribute value expression evaluated attribute name attribute value expression retained attribute name identifier attribute value o String expression logical expression real expression array expression constraint variable reference place range token list token list array regular expression Real expressions real expression real term real factor real primarv real term real term real term real expression 4 real term real expression real term real factor real term x real factor real term real factor real primarv real factor 7 real primarv real literal svmbolic constant real name array index 1 object name gt real attribute object name gt array attribute index 1 table reference real function real function real expression real function real expression real expression function of array array expression real expression 155 156 real function RANF GAUSS USERO SI SC SO ABS TRUNC ROUND FLOOR SIG

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