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A User Guide to the PROCESS Systems Code

1. Pulsed Fusion Reactor Study AEA Fusion Report AEA FUS 205 1992 R L Reid and Y K M Peng Potential Minimum Cost of Electricity of Superconducting Coil Tokamak Power Reactors Proceedings of 13th IEEE Symposium on Fusion Engineering Knoxville Tennessee October 1989 p 258 J Sheffield et al Cost Assessment of a Generic Magnetic Fusion Reactor Fusion Technology 9 1986 199 Chapter 7 Acknowledgements amp Bibliography 70 37 S Thompson Systems Code Cost Accounting memo FEDC M 88 SE 004 1988 38 J D Galambos L J Perkins S W Haney and J Mandrekas Nuclear Fusion 35 1995 551 39 J P Holdren et al Report of the Senior Committee on Environmental Safety and Economic Aspects of Magnetic Fusion Energy Fusion Technology 13 1988 7 Appendix A Non optimisation Input File The following is a typical input file used to run PROCESS in non optimisation mode Comments in have been added to the right of each line Numerics information Comment NEQNS 14 Number of active constraint equations NVAR 14 Number of active iteration variables ICC 1 2 10 11 7 16 24 5 31 32 33 34 35 36 Constraint eqns ixc 5 10 12 3 7 6 36 9 48 49 50 51 53 54 Iteration variables IOPTIMZ 1 Turn off optimisation ISWEEP 0 No scans non optimisation mode F values and limits FBETATRY 1 0 Physics parameters ASPECT 3 5 BE
2. The code has the ability to perform calculations based on the physics and engineering of a stellarator which although being a toroidal device is radically different in a number of ways from a tokamak Chapter 3 Physics Engineering and Other Models 43 The model is derived from two main sources the physics is based on that assumed by the U S stellarator reactor study group 6 and the coil set is scaled from the proposed Wendelstein VII X design a modular advanced stellarator with a 5 period Helias configuration 7 To activate the stellarator coding it is necessary to create a file device dat containing the single character 1 in the first row in the working directory see Section 4 1 This has the effect of setting the internally used switch istell 1 If the file is absent or its first character is set to something other than 1 the stellarator model is not used and istell is set to 0 The stellarator model is largely contained within source file stellarator f90 The consistency equations relevant for tokamaks see Section 2 4 should be used without modification to ensure that the coil currents and the fields they produce are consistent with the plasma parameters An additional consistency equation 17 should be used to ensure that the radial build is correct see Section 3 5 2 1 3 5 1 Stellarator physics Much of the physics is identical to that for tokamaks including the plasma composition fusion power considerations
3. 3 10 Other Switches and Models 3 10 1 Output control Since the user may only be interested in a small proportion of the code s output a set of switches exists that controls whether a given section of the output file is produced Table 3 6 indicates how these switches affect the output switch relevant output section sect01 power plant costs sect02 detailed costings sect03 plasma sect04 current drive system sect05 divertor sect06 machine build sect07 TF coils sect08 PF coils sect09 volt second consumption sect10 support structure sect11 PF coil inductances sect12 shield blanket sect13 power conversion sect14 heat transport sect15 vacuum system sect16 plant buildings sect17 AC power sect18 neutral beams sect19 electron cyclotron heating sect20 Lower Hybrid heating sect21 times Table 3 6 Summary of the switches in PROCESS that control the format of the output file If a switch has a value 0 the relevant output section does not appear in the output file If its value is 1 the output section is included in the output file this is the default setting for all the switches 3 10 2 Code parameters affecting other models This chapter has summarised the methods by which several of the models in the code can be activated There are many others present however and it is suggested that the user refers to the variable descriptor file vardes html As
4. FWITH 0 035 Inboard first wall thickness SCRAPLI 0 14 Inboard scrape off layer thickness SCRAPLO 0 15 Outboard scrape off layer thickness FWOTH 0 035 Outboard first wall thickness BLNKOTH 0 235 Outboard blanket thickness SHLDOTH 1 05 Outboard shield thickness GAPOMIN 0 21 Outboard gap VGAPTF 0 Vertical gap First wall blanket shield parameters LBLNKT 0 Use old blanket model DENSTL 7800 Steel density TF coil parameters OACDCP 1 4e7 N B active iteration variable 12 ITFSUP 1 Use superconducting TF coils RIPMAX 5 Maximum TF ripple PF coil parameters NGRP 3 Three groups of PF coils IPFLOC 1 2 3 Locations for each group NCLS 2 2 2 1 Number of coils in each group COHEOF 1 85e7 OH coil current at End Of Flat top FCOHBOP 0 9 OH coil current at Begin Of Pulse COHEOF ROUTR 1 5 Radial position for group 3 ZREF 3 2 5 Z position for group 3 OHHGHF 71 Height ratio OH coil TF coil Vacuum system parameters NTYPE 1 Use cryopump Heat transport parameters ETATH 0 35 Thermal to electric conversion efficiency FMGDMW 0 Power to MGF units BASEEL 5 e6 Base plant electric load ISCENR 2 Energy store option Buildings FNDT 2 Foundation thickness EFLOOR 1 d5 Effective total floor space Appendix A Non optimisation Input File 73 Costs IREACTOR 1 IFUELTYP 0 UCHRS 87 9 UC
5. 2 6 ASPECT 3 5 BETA 0 042 BT 6 DENE 1 5e20 FVSBRNNI 1 0 DNBETA 3 5 HFACT 2 ICURR 4 ISC 6 IINVQD 1 IITER 1 ISHAPE 0 KAPPA 2 218 Q 3 0 RMAJOR 7 0 RNBEAM 0 0002 TBURN 227 9 Non inductive volt seconds fraction Troyon g coefficient N B active iteration variable 10 Use ITER current scaling Use ITER 89 P confinement time scaling law Use inverse quadrature Use ITER fusion power calculations Use input values for KAPPA and TRIANG Plasma elongation Edge safety factor N B active iteration variable 3 N B active iteration variable 7 Burn time 74 Appendix B Optimisation Input File 75 TE 15 N B active iteration variable 4 TRIANG 0 6 Plasma triangularity Current drive parameters IRFCD 1 Use current drive IEFRF 5 Use ITER neutral beam current drive FEFFCD 3 Artificially enhance efficiency Divertor parameters ANGINC 0 262 Angle of incidence of field lines on plate PRN1 0 285 Density ratio Machine build BORE 0 12 N B active iteration variable 29 OHCTH 0 1 N B active iteration variable 16 GAPOH 0 08 Inboard gap TFCTH 0 9 N B active iteration variable 13 DDWI 0 07 Vacuum vessel thickness SHLDITH 0 69 Inboard shield thickness BLNKITH 0 115 Inboard blanket thickness FWITH 0 035 Inboard first wall thickness SCRAPLI 0 14 Inboard scrape off layer t
6. A minimum burn time can be enforced via constraint equation no 13 and iteration variable no 21 ftburn 3 3 7 Thermal storage During every cycle there is a period when no fusion power is produced The net electric output from the plant must however be maintained and this is achieved using thermal storage There are three Chapter 3 Physics Engineering and Other Models 42 types of thermal storage available within PROCESS and the value of switch istore determines which is to be used If istore 1 the default option 1 of Ref 34 is assumed which utilises the thermal storage inherent in the machine s steam cycle equipment This should be used if the machine down time is less than 100 seconds If istore 2 option 2 of Ref 34 is assumed which uses the same method as before but augments it with an additional boiler This may be used for machine down times of up to 300 seconds Finally if istore 3 a large stainless steel block acts as the thermal storage medium 3 4 Hydrogen Production Facility Fusion power plants have been mooted as a means of producing hydrogen for use in fuel cells for cars for instance PROCESS includes options to enable the plant to produce hydrogen using a number of different processes To include the production of hydrogen by the power plant it is necessary to set the switch ihplant as follows l o ihplant 0 No hydrogen production default ihplant 1 Hydrogen production by low tem
7. Engineering and Other Models 28 isc scaling law reference 1 Neo Alcator ohmic 14 2 Mirnov H mode 14 3 Merezhkin Muhkovatov L mode 14 4 Shimomura H mode JAERI M 87 080 1987 5 Kaye Goldston L mode Nuclear Fusion 25 1985 p 65 6 ITER 89 P L mode Nuclear Fusion 30 1990 p 1999 7 ITER 89 O L mode 14 8 Rebut Lallia L mode Plasma Physics and Controlled Nuclear Fusion Research 2 1987 p 187 9 Goldston L mode Plas Phys Controlled Fusion 26 1984 p 87 10 T10 L mode 14 11 JAERI 88 L mode JAERI M 88 068 1988 12 Kaye Big Complex L mode Phys Fluids B 2 1990 p 2926 13 ITER H90 P H mode 14 ITER Mix minimum of 6 and 7 15 Riedel L mode 16 Christiansen et al L mode JET Report JET P 1991 03 17 Lackner Gottardi L mode Nuclear Fusion 30 1990 p 767 18 Neo Kaye L mode 14 19 Riedel H mode 20 ITER H90 P amended Nuclear Fusion 32 1992 p 318 21 Large Helical Device stellarator Nuclear Fusion 30 1990 p 11 22 Gyro reduced Bohm stellarator Bull Am Phys Society 34 1989 p 1964 23 Lackner Gottardi stellarator Nuclear Fusion 30 1990 p 767 24 ITER 93H H mode Plasma Physics and Controlled Nuclear Fusion Research Proc 15th Int Conf Seville 1994 IAEA CN 60 E P 3 25 TITAN RFP TITAN RFP Fusion Reactor Study Scoping Phase Report UCLA PPG 1100 page 5 9 Jan 1987 26 ITER H 97P ELM free H mode J G Cordey et al EPS
8. lt te sae e a ee ok aa eed a be 41 Hydrogen Production Facility 2 ee 42 Stellarator Models s 24 22 204 a aoe e Re Ee a wo eee be 42 3 5 1 Stellarator physics 2 2 a ana 2 hobs a eh og BH AG 43 3 5 2 Machine configuration 44 3 5 3 Limitations in the model e e 45 Reversed Field Pinch Model oaaae 48 3 0 REP PHYSICS dle o tsa A Stile Bot ae a Se a a ia 48 3 0 2 RH COIS sea a gear e SAD He a ein gies La Wd et Mean e 49 3 0 9 OH Cols a ok RARE RI he ae A 49 30 40 EE COUS a a otek ve So we ae ia gins amp A eal a e 49 3 0 9 DIVER geo Vee i aa ee ee Gd 49 3 6 6 Code modifications ee 50 3 7 Inertial Fusion Energy Model e 3 8 Safety and Environment Models ee 38l UNGUtrONICS at e A ey a a 3 8 2 Activation and inventory information e 3 9 Cost Models ius aan e Be o a a en oe Be ee ta aA 39 1 CostsOptions 4 4 aaa s Bache A A A A a ee ee Bs 3 10 Other Switches and Models ona aa ee 3 10 Output Controls 1 Mae Oe AA a E Pe ee a a 3 10 2 Code parameters affecting other models 2 204 Execution of the Code 4 1 The Input Bile 5 Pola say Bade a e God ea doth oy ee ee edo a 4 1 1 Tokamak stellarator RFP or IFE 0 AV 2 Pile StruGhire us li ds ed Bn e Ee ee de A S AS Format PUES snag o a a Pedal yee Go Eee eae dea AD The Output File ais ds doy we rd e id e Ri es 2 4 3 R
9. 3 6 1 3 Tz scaling law One confinement time scaling law relevant to RFPs is present within PROCESS The value of switch isc determines the scaling to be used in the plasma energy balance calculation Tr TITAN RFP 9 isc 25 0 05 a I MA 3 6 1 4 F plot Much of the RFP physics is derived from the characteristic F 0 plot where F Bg a Bg O Bo a Bg and Bg is the average value of the toroidal field over the plasma cross section Given a value of the pinch parameter O the corresponding value of the reversal parameter F may be read from the F O plot and from these the plasma current and the current in the TF coils may be obtained using Chapter 3 Physics Engineering and Other Models 49 Ho lTFC 27R Bla the second of these assumes that By a is approximately equal to the vacuum toroidal field at the plasma centre The pinch parameter O is set using iteration variable no 78 rfpth The corresponding value of the reversal parameter F rfpf is calculated using routine FTHETA F is constrained to be negative using constraint equation no 49 with f value frfpf iteration variable no 80 3 6 1 5 Current drive The RFP oscillating field current drive option is turned on by setting iefrf 9 with a fixed efficiency of 0 8 Amps per Watt of power injected into the plasma the coding for this model is therefore trivial The wall plug to injector efficiency is set using input parameter etaof which has a def
10. 45 fqval f value for energy multiplication limit equation 28 0 010DO 0 330D0 46 fpinj f value for injection power limit equation 30 0 001DO 1 000DO 47 fef cd current drive efficiency multiplier 0 001DO 1 000DO 48 fstrcase f value for TF coil case stress limit equation 31 0 001DO 1 000DO 49 fstrcond f value for TF coil conduit stress limit equation 32 0 001DO 1 000D0 50 fiooic f value for TF coil operational current limit equation 33 0 001DO 0 500D0 Table 2 2 Iteration variables 1 to 50 present in PROCESS The f values correspond to the given constraint equations see Table 2 1 The other iteration variables are shown in Table 2 3 Chapter 2 Program Overview The Fundamental Concepts 17 ixc icc lower upper no variable name description eqn bound bound 31 fvdump f value for TF coil dump voltage limit equation 34 0 001D0 1 000D0 52 vdalw allowable TF coil dump voltage 0 001D0 1 000D6 53 fjprot f value for TF coil current protection limit equation 35 0 001DO 1 000DO 54 ftmargtf f value for TF coil temperature margin limit equation 36 0 001D0 1 000DO 55 tmargmin minimum allowable TF coil temperature margin 0 001D0 100 0DO 56 tdmptf dump time for TF coil 10 00D0 1 000D6 57 thkcas TF coil external case thickness 0 050D0 1 000D0 58 thwcndut TF coil conduit case thickness 0 001D0 1 000D0 59 fcutfsu copper frac
11. Concepts 16 ixc icc lower upper no variable name description eqn bound bound 1 aspect plasma aspect ratio 1 100D0 10 00DO 2 bt toroidal field on axis 0 010D0 100 0DO 3 rmajor plasma major radius 0 100DO 10 00DO 4 te electron temperature 5 000DO 500 0DO 5 beta plasma beta 0 001DO 1 000DO 6 dene electron density 1 00D19 1 00D21 7 rnbeam hot beam density electron density 1 00D 6 1 000D0 8 fbeta f value for 3 limit equation 6 0 001DO 1 000DO 9 fdene f value for density limit equation 5 0 001D0 1 000DO 10 hfact confinement time H factor 0 100D0 3 000D0 11 pheat heating power not used for current drive 1 000D6 1 000D9 12 oacdcp overall current density in TF coil inboard leg 1 000D5 1 500D8 13 tfcth TF coil inboard leg thickness 0 100D0 5 000DO 14 fwalld f value for wall load limit equation 8 0 001DO 1 000DO 15 fvs f value for volt second limit equation 12 0 000DO 1 000DO 16 ohcth OH coil thickness 0 001D0 1 000D2 17 tdwell dwell time 0 100D0 1 000D8 18 la edge safety factor 2 000D0 100 0DO 19 enbeam neutral beam energy 1 000D0 1 000D6 20 tcpav average resistive TF coil temperature 40 00DO 1 000D3 21 ftburn f value for burn time limit equation 13 0 001DO 1 000DO 22 tbrnmn minimum burn time 0 001DO 1 000D6 23 fcoolcp coolant fraction of resistive TF coil 0 100D0 0 500D0 24 cdtfleg TF coil leg overall current density 1 000D4 1 000D8 25 fpnetel val
12. P J Knight PROCESS 3009 Incorporation of Inertial Fusion Energy Model Work File Note F MI PJK PROCESS CODE 032 Bourque et al Overview of the OSIRIS IFE Reactor Conceptual Design Fusion Technology 21 1992 1465 Meier and Bieri Economic Modeling and Parametric Studies for OSIRIS a HIB Driven IFE Power Plant Fusion Technology 21 1992 1547 Ghose et al BOP Designs for OSIRIS and SOMBRERO IFE Reactor Plants Fusion Technology 21 1992 1501 Sviatoslavsky et al A KrF Laser Driven Inertial Fusion Reactor SOMBRERO Fusion Technology 21 1992 1470 Meier and Bieri Economic Modeling and Parametric Studies for SOMBRERO a Laser Driven IFE Power Plant Fusion Technology 21 1992 1552 Moir et al HYLIFE I A Molten Salt Inertial Fusion Energy Power Plant Design Final Report Fusion Technology 25 1994 5 Moir HYLIFE IT Inertial Fusion Energy Power Plant Design Fusion Technology 21 1992 1475 Hoffman and Lee Performance and Cost of the HYLIFE II Balance of Plant Fusion Technology 21 1992 1475 P J Knight PROCESS IFE Build Details F MI PJK LOGBOOKI12 pp 52 53 56 57 Bieri and Meier Heavy Ion Driver Parametric Studies and Choice of a Base 5 MJ Driver Design Fusion Technology 21 1992 1557 P J Karditsas PROCESS Code Development simple blanket model neutron heat input Work File Note F RS CIRE5523 PWF 0142 November 1992
13. additional switches ifetyp 0 Generic device build ifetyp 1 OSIRIS type device build 23 24 25 ifetyp 2 SOMBRERO type device build 26 27 ifetyp 3 HYLIFE IEtype device build 28 29 30 Switch ifetyp defines the type of device that is assumed this varies widely between different conceptual designs The generic type assumes a cylindrically symmetric device while the other types are approximations to the builds of the given conceptual machines 31 In general the build from the centre of the device at the target ignition location is in the order chamber first wall gap blanket gap shield gap building wall The user specifies the thicknesses of these regions and also the materials that are present and in what proportions expand ifedrv 1 Driver efficiency and target gain are input as functions of driver energy ifedrv 0 Driver efficiency and target gain are input ifedrv 1 SOMBRERO laser drive efficiency and target gain assumed ifedrv 2 OSIRIS heavy ion beam driver efficiency and target gain are assumed 32 Switch ifedrv defines how the code calculates the driver efficiency and target gain these are the primary outputs required from the physics part of the model For the SOMBRERO and OSIRIS cases ifedrv 1 and ifedrv 2 respectively the driver efficiency and gain are calculated from curves of these parameters as functions of the driver energy For the ifedrv 1 case the user provides
14. and energy conversion and transport within the plasma However some physics topics do differ between stellarators and tokamaks as follows 3 5 1 1 Absense of plasma current Stellarators have zero plasma current so no current scalings are required 3 5 1 2 Beta limit The beta limit is assumed to be 5 based on 3 D MHD calculations 20 To apply the beta limit constraint equation no 24 should be turned on with iteration variable no 36 fbetatry 3 5 1 3 Density limit The density limit relevant to stellarators has been proposed to be 21 Mmax 0 25 PBo Ro a2 3 9 where n is the line averaged electron density in units of 10 m P is the absorbed heating power MW Bo is the on axis field T Ro is the major radius m and a is the plasma minor radius m To enforce the density limit turn on constraint equation no 5 with iteration variable no 9 fdene 3 5 1 4 Tg scaling laws Five confinement time scaling laws relevant to stellarators are present within PROCESS The value of switch isc determines which of these is used in the plasma energy balance calculation TE Large Helical Device isc 21 0 17 R9 as ABBA 3 10 Tr Gyro reduced Bohm isc 22 0 25 B98 n 8 p 06 ae Re 3 11 T Lackner Gottardi isc 23 0 17 Ro a ene PP 3 12 Here T is the rotational transform which is equal to the reciprocal of the tokamak safety factor q Chapter 3 Physics Engineering and Other Models 44 3 5 1 5 Hea
15. and ensures that operating limits are not violated An example of VMCON s application is to find the device providing the minimum cost of electricity which also satisfies the physics and engineering constraints There is in theory no upper limit to the number of variables that VMCON can use to optimise the machine so a very large region of parameter space can be searched A flow diagram of PROCESS in optimisation mode is shown in Figure 2 2 2 1 3 Scans It is often useful to be able to scan through a range of values of a given parameter to see what effect this has on the machine as a whole Sensitivity studies of this kind can be achieved very easily using PROCESS Scans are carried out in optimisation mode whereby the code performs initially a run using the parameters specified in the input file and then a series of runs using the parameters produced at the end of the previous iteration The value of the quantity being scanned is specified at every stage see Section 2 7 This method ensures that a smooth variation in the machine parameters is achieved 2 2 The Variable Descriptor File The variable descriptor file vardes html is an invaluable resource for the user of PROCESS It acts as a dictionary reference manual for the code s variables and contains the following information about each e name e dimensions of arrays e default value s of those variables that are not initially derived from a combination of other values The
16. arrowed labels adjacent to the axes are the total builds to that point The precise locations and sizes of the PF coils are calculated within the code see Section 3 1 8 Chapter 3 Physics Engineering and Other Models 24 ddwex clht hpfu gt tfcth ddwi vgap2 shldith shidoth 2 binkith binkoth y 2 fwith fwoth 2 7 2 scrapli scraplo hmax x J ohhghf rminor x kappa rminor x kappa vgap divfix shidtth vgap2 hmax ddwi 7 t cth elh1 ddwex PF coil ipfloc 1 PF coil ipfloc 1 bucking cylinder vacuum vessel shield blanket first wall external cryostat PF coil ipfloc 2 PF coil ipfloc 3 PF coil ipfloc 3 El PF coil ipfloc 2 Figure 3 2 Schematic diagram of the fusion power core of a typical tokamak power plant modelled by PROCESS showing the relative positions of the components A single null plasma is assumed snull 1 compare Figure 3 1 The radial build is the same as for a double null configuration shown along the vertical axis are the code variables used to define the vertical thicknesses of the components The arrowed labels adjacent to the axis are the total builds distance from the midplane Z 0 to that point The precise locations and sizes of the PF coils are calculated within the code see Section 3 1 8 Chapter 3 Physics Engineering and Other Models 25
17. by turning on constraint equation no 39 with iteration variable no 63 ftpeak 3 3 4 Start up power requirements The minimum auxiliary power required during the start up ignition phase is calculated on the basis of a POPCON analysis Ignition is accessed via the so called Cordey Pass the path in plasma density temperature space which minimises the power requirement and the code ensures that there is sufficient auxiliary power to accommodate this In fact this calculation is very CPU intensive so the relevant routine is not called at present In practice the auxiliary power tends to exceed the minimum allowable value anyway without any need to constrain it to do so The auxiliary power reaching the plasma can be forced to be more than the minimum allowable value auxmin by turning on constraint equation no 40 with iteration variable no 64 fauxmn The value of auxmin is determined by the code if the start up model is activated otherwise it may be initialised via the input file 3 3 5 OH coil swing time This calculation ensures that the plasma current ramp rate during start up is prevented from being too high as governed by the requirement to maintain plasma stability in l q space see Section 3 1 9 1 3 3 6 Burn time The length of the burn time is calculated from the surplus volt seconds available from the OH PF coil system during the plasma burn phase after the flux required during the plasma start up is taken into account
18. can be entered as if they were integers but NOT vice versa epsfcn 10 e 4 Ftol 1 D 4 The next line sets the first five elements of array icc Icc 2 10 11 24 31 The next line sets the first ten elements of array ixc ixc 10 12 3 36 48 1 2 6 13 16 IOPTIMZ 1 maxcal 200 NEQNS 5 NVAR 10 The following are invalid entries in the input file Q Why bound1 1 1 2 5 BOUNDU N 3 A line of random characters like this will clearly wreak havoc eps fcn 10 e 4 ftol 1 D 4 epsvmc 1 0 e 4 Icc 2 10 11 24 31 IOPTIMZ 1 0 4 2 The Output File The output from the code is sent to file OUT DAT in the working directory 4 3 Running the Code This section will attempt to guide the user through the actual running of the code in its various modes In most cases only minor changes to the input file are necessary to change the code s mode of operation usually the physics and engineering variables etc remain unchanged with the major differences occurring in the numerical input only 4 3 1 Non optimisation mode Non optimisation mode is used to perform benchmark comparisons whereby the machine size output power etc are known and one only wishes to find the calculated stresses beta values and fusion powers for example When starting to model a new machine PROCESS should always be run first in non optimisation mode before any attempt is made to optimise the mac
19. can extend over more than one line 7 One dimensional arrays can be explicitly subscripted or unscripted in which case the following element order is assumed A 1 A 2 A 3 8 At present multiple dimension arrays can only be handled without reference to explicit subscripts in which case the following element order is assumed B 1 1 B 2 1 B 3 1 The use of the input file to specify multiple dimension array elements is prone to error 9 Unscripted array elements must be separated by commas 10 Blank lines are allowed anywhere in the input file 11 Lines starting with a are assumed to be comments 12 Comment lines starting with five or more asterisks i e are reproduced verbatim in the output file These should be used copiously to give a great deal of information about the run being performed and should be updated before every single run of the code as it is very easy to lose track of what is being attempted It is useful to divide the input file into sections using suitable comment lines to help the user keep related variables together The following is a valid fragment of an input file the vertical lines are simply to help show the column alignment Chapter 4 Execution of the Code 56 This line is a comment that will not appear in the output k This line is a comment that will appear in the output boundl1 1 2 5 BOUNDU 10 3 BOUNDU 45 1 Another comment Note that real values
20. exp kx exp kx J POWER TO PLASMA RADIATION POWER SYNCHROTRON LINE RADIATION RADIATION FIRST WALL RECIRCULATING POWER SECONDARY HEAT etath 1 etath o TF COIL L G HEAT GROSS ELECTRIC A A PF COIL TRITIUM BASE A C WASTE INJ WALL PLUG INJECTION POWER 1 fgrosbop fgrosbop CRYO PLANT C P PUMP BASE ELECTRIC PULSED LOAD ELECTRIC Figure 3 5 Schematic diagram showing the power conversion mechanisms used in PROCESS 3 Note 0166 Many of the power conversion efficiencies shown in Figure 3 5 can be adjusted by the user Chapter 3 Physics Engineering and Other Models 39 3 1 13 Cryostat and vacuum system The internal vacuum vessel provides a toroidal evacuated chamber containing the plasma first wall blanket and shield and the space between this item and the external cylindrical cryostat encloses those components that need to operate at liquid helium temperatures These include any superconducting TF or PF coils the inter coil structure and the bucking cylinder PROCESS calculates the cryogenic power load and the resulting heat exchanger requirements The vacuum system is used for four different processes Firstly before plasma operations the chamber must be evacuated to remove outgassed impurities from the structure Secondly the chamber must be re evacuated between burn operations Thirdly helium ash
21. no OH coil is present in which case the thickness ohcth should be set to zero No PF coils should be located at positions defined by ipfloc j 1 if no OH coil is present 3 1 9 1 OH coil swing time In the steady state power plant scenario lpulse 4 1 see Section 3 3 the length of time taken for the OH coil current to reverse see Figure 3 4 is determined from the value of switch tohsin If tohsin 0 0DO then the swing time tohs in seconds is given by tohs 1p 0 5 where Ip is the plasma current in MA Furthermore the PF coil ramp time tramp and shutdown time tqnch are set equal to tohs If tohsin 0 0DO the swing time tohs tohsin and the ramp and shutdown times are input parameters If however a pulsed power plant is being modelled 1pulse 1 the OH coil swing time tohs is either an input parameter or it can be iterated by using iteration variable 65 The ramp and shutdown times in the pulsed case are always set equal to tohs To ensure that the plasma current ramp rate during start up is prevented from being too high as governed by the requirement to maintain plasma stability in 1 qy space constraint equation no 41 should be turned on with iteration variable no 66 ftohs 3 1 9 2 Current density limits The current density in the OH coil can be limited at the beginning of pulse BOP and at the end of flat top EOF see Figure 3 4 The limiting value is dependent on the maximum allowable stress in the coil as g
22. of the true cross sectional shape however the resulting coil set is a fair approximation to the true case see Figure 3 7 In order to use the existing routines for calculating the stresses in the coils it is necessary to describe the poloidal variation of the coil shape using four circular arcs For the purpose of these calculations the coil shape is assumed to be elliptical 3 5 2 3 Other systems Many of the fusion power core systems are assumed to have the same characteristics as for a tokamak device including the blanket divertor cryogenic and vacuum systems Of these only the calculations for the divertor are likely to be inaccurate as in a large stellarator device the divertor is expected to be helical rather than axisymmetric as is the case in tokamaks 3 5 3 Limitations in the model As may be already clear there are a number of simplifications in the stellarator model none of which should be too serious These may be summarised as follows 1 The plasma geometry calculations are not consistent with the stellarator situation in which the plasma cross sectional shape varies with toroidal angle This has knock on effects on parameters such as the first wall area and the poloidal field Bp Similarly the density and temperature profiles must be thought of as averages over toroidal angle in this representation Nevertheless the use of mean thicknesses etc is an acceptable approximation 2 The cross section of the coils in the p
23. resistive or superconducting This is determined from the value of ipfres If ipfres 0 the PF and OH coils are assumed to be superconducting If ipfres 1 they are assumed to be resistive with their resistivity given by the value of variable pfclres 3 1 8 4 Superconducting materials If ipfres 0 switch isumatpf specifies which superconducting material is to be used for the PF and OH coils isumatpf 1 binary Nb3Sn superconductor isumatpf 2 ternary Nb3Sn superconductor isumatpf 3 NbTi superconductor Chapter 3 Physics Engineering and Other Models 36 3 1 9 Ohmic heating coil The ohmic heating OH coil is a PF coil used primarily during start up but also during the burn phase to create and maintain the plasma current by inductive means Swinging changing the current through the OH coil causes a change in the flux linked to the plasma region inducing a current in it PROCESS calculates the amount of flux required to produce the plasma current and also the amount actually available The code measures the magnetic flux in units of Volt seconds Webers The OH coil is sometimes referred to as the central solenoid and can be either resistive or superconducting controlled via switches ipfres and isumatpf as for the other PF coils Switch iohcl controls whether an OH coil is present A value of 1 denotes that this coil is present and should be assigned a non zero thickness ohcth A value of iohcl 0 denotes that
24. sweep Runs involving scans of this kind can only be performed in optimisation mode The results from the previous scan point are used as the input to the next scan point Routine SCAN in source file scan 90 stores many of the output quantities in a separate output file PLOT DAT for use with a plotting program Scanning of derived quantities requires use of the appropriate constraint equations For instance if the net electric power is scanned constraint equation 16 should be employed For obvious reasons the active scanning variable must not also be an active iteration variable 2 8 Code Structure The structure of the majority of the code reflects to a certain extent the layout of the machine being modelled As stated above a large proportion of the code is simply a description of the underlying physics and engineering issues in terms of numerous expressions and relationships In effect these define the machine so that the numerical solver within the code can then get to work adjusting the parameters in its search for a self consistent solution It is essential for a program of the size and complexity of PROCESS to be modular to a high degree in order to simplify the tasks of understanding and maintaining the code The use of Fortran 90 95 modules provides a natural and convenient way for this to be done The following sections describe briefly the modules into which PROCESS is divided Chapter 2 Program Overview The Fundamental
25. the parameter ipnscnv in module scan_module in source file scan f90 to accommodate the new scanning variable 2 Add a short description of the new scanning variable to the nsweep entry in source file scan 90 3 Add a new assignment to the relevant part of routine SCAN in source file scan f90 following the examples already present including the inclusion of a short description of the new scanning variable in variable xlabel 4 Ensure that the scanning variable used in the assignment is contained in one of the modules specified via use statements present at the start of this routine Chapter 6 Code Management Utilities 6 1 Makefile 6 2 Automatic Documentation 66 Chapter 7 Acknowledgements z Bibliography The author would like to thank the following people for many useful and revealing discussions during his work on PROCESS John D Galambos Paul C Shipe and Y K Martin Peng of Oak Ridge National Laboratory USA Roger Hancox now retired Neill Taylor Robin Forrest and lan Cook of Fusion Physics Department UKAEA Fusion John Hicks of Engineering Department UKAEA Fusion Chris Gardner formerly of Microwave and Interpretation Department UKAEA Fusion Tim Hender of Microwave and Interpretation Department UKAEA Fusion and all the co authors of reference 15 This work was funded by the UK Department of Trade and Industry Euratom and by internal research funds of UKAEA 67 Bib
26. 3 1 2 Plasma physics models Arguably the most important component of the machine is the plasma itself By default this is assumed to have an up down symmetric double null configuration although this can be changed if desired see Section 3 1 4 with elongation and triangularity specified by the user A great number of physics models are coded within PROCESS to describe the behaviour of the plasma parameters such as its current temperature density pressure confinement etc and also the various limits that define the stable operating domain 3 1 2 1 Fusion reactions By default the code assumes that the deuterium tritium D T fusion reaction is utilised by the power plant being modelled D T tHe n 17 6 MeV 3 1 20 of the energy produced is given to the alpha particles He which remain within the plasma and thermalise slow down due to collisions thus heating the plasma The remaining 80 is carried away by the neutrons which deposit their energy within the blanket and shield The tritium fraction of the D T fuel is controlled using variable ftr PROCESS can also model D He power plants which utilise the following primary fusion reaction D He gt tHe p 18 3 MeV 3 2 The fusion reaction rate is significantly different from that for D T fusion and the power flow from the plasma is modified since charged particles are produced rather than neutrons Because only charged particles which remain in the plasma a
27. Berchtesgaden 1997 27 ITER H 97P ELMy H mode J G Cordey et al EPS Berchtesgaden 1997 28 ITER 96P L mode Nuclear Fusion 37 1997 p 1303 29 Valovic modified ELMy H mode 30 Kaye PPPL April 98 L mode 31 ITERH PB98P y H mode 32 IPB98 y H mode 33 IPB98 y 1 H mode 34 IPB98 y 2 H mode 35 IPB98 y 3 H mode 36 IPB98 y 4 H mode 37 ISS95 stellarator Nuclear Fusion 36 1996 p 1063 38 ISS04 stellarator Nuclear Fusion 45 2005 p 1684 Table 3 1 Summary of the energy confinement time scaling laws in PROCESS Chapter 3 Physics Engineering and Other Models 29 3 1 2 8 L H power threshold scalings Transitions from a standard confinement mode L mode to an improved confinement regime H mode called L H transitions are observed in most tokamaks A range of scaling laws are available that provide estimates of the auxiliary power required to initiate these transitions via extrapolations from present day devices PROCESS calculates these power threshold values for the scaling laws listed in Table 3 2 in routine PTHRESH name reference 1996 ITER scaling nominal ITER Physics Design Description Document 1996 ITER scaling upper bound D Boucher p 2 2 1996 ITER scaling lower bound 1997 ITER scaling excluding elongation J A Snipes ITER H mode Threshold Database 1997 ITER scaling including elongation Working Group Controlled Fusion and Plasma Physics 24th EPS C
28. CPCL1 250 UCCPCLB 150 Calculate cost of electricity Treat blanket first wall etc as capital cost Unit cost of heat rejection system Unit cost of high strength tapered copper Unit cost of TF outer leg plate coils Appendix B Optimisation Input File The following is a typical input file used to run PROCESS in optimisation mode Comments in have been added to the right of each line Numerics information bound1 1 2 5 BOUNDU 10 3 BOUNDU 60 4 d4 Comment Bound on iteration variable 1 aspect Bound on iteration variable 10 hfact Bound on iteration variable 60 cpttf NEQNS 15 Number of active constraint equations NVAR 25 Number of active iteration variables ICC 1 2 10 11 7 16 8 24 31 32 33 34 35 36 14 Constraint eqns ixc 5 10 12 3 7 36 48 49 50 51 53 54 19 Corresponding 1 2 4 6 13 16 29 56 57 58 59 60 IOPTIMZ 1 MINMAX 6 ISWEEP 7 NSWEEP 6 SWEEP 6 0 5 5 4 5 4 0 3 5 3 0 2 5 F values and limits FBETATRY 1 0 Physics parameters iteration variables Turn on optimisation Minimise cost of electricity Seven point scan Use WALALW as scanning variable Values of WALALW for each scan point N B active iteration variable 36 N B N B N B N B active active active active iteration iteration iteration iteration variable variable variable variable 11 5
29. ROCESS If the figure of merit is to be minimised minmaz should be positive and if a maximised figure of merit is desired minmaz should be negative 2 8 1 Numerics modules These modules contain the equation solvers their calling routines and other relevant procedures Various mathematical routines from a number of standard libraries are also incorporated into these files Table 2 6 summarises the numerics source file contents 2 8 2 Physics modules These modules contain the main physics routines that evaluate the plasma and fusion parameters Also included here are the routines describing the current drive and divertor systems Table 2 7 summarises the physics source file contents 2 8 3 Engineering modules These modules contain the description of the machine geometry and its major systems including the PF and TF coil sets the first wall blanket and shield and other items such as the buildings vacuum system power conversion and the structural components Table 2 8 summarises the engineering source file contents 2 8 4 Costing module The costing module costs f90 performs all the cost calculations including values in M for each machine system and the cost of electricity in m kWh Chapter 2 Program Overview The Fundamental Concepts 19 nsweep scan variable description 125002000 00nN NNNNNDNNDNNR PFP Ep OoPrwnNnr OO OND OK ON aspect hidivlim pnetelin hfact oacdcp walalw b
30. Ro is the plasma major radius rmajor For the sake of clarity the thicknesses are not drawn to scale and the space labelled as the divertor does not indicate in any way the actual shape of that component Most of the thicknesses shown in Figure 3 1 are input parameters so are not changed during the course of the simulation The rest are calculated by the code during execution In addition some of the component sizes can be used as iteration variables see Section 2 5 to help in the optimisation process 22 Chapter 3 Physics Engineering and Other Models 23 ddwex PF coil E bucking cylinder ii ipfloc 1 El PF coil ipfloc 2 MU vacuum vessel E shield blanket EE first wall E tfcth external cryostat hmax ddwi J hmax x m vgap2 ohhghf J shldtth divertor region divfix vgap PF coils ipfloc 3 rminor x kappa TT oO D Ex lt Z3NECE os cos o 5 gt 5 oz 3 3020 fe fe es 252 x 5 g o R o o o sD E 20 0 oo 83 B92 s 22 828 E 2 53 oa DDO Q 8 3 505 amp y 2 romax rsldi rmajor rsido rtot rdewex Figure 3 1 Schematic diagram of the fusion power core of a typical tokamak power plant modelled by PROCESS showing the relative positions of the components A double null plasma is assumed snull 0 compare Figure 3 2 Also shown are the code variables used to define the thicknesses of the components The
31. SS whether they are planning to modify or run the code or are simply trying to understand what the code aims to achieve 1 3 Layout of the User Guide The User Guide is divided into a small number of logically separate chapters each one of which provides specific information on a given topic It depends on the user s motive for referring to the manual as to which chapter will be the most useful although hopefully the style and structure adopted will allow one to browse through without difficulty Chapter 2 provides an overview of the program and outlines the numerical and programming concepts involved Chapter 3 describes the physics engineering and economic models that are used within the code and lists the switches available allowing the user to customise the models details to achieve the desired simulation Chapter 4 describes how to run the program from scratch and provides a number of hints and suggestions for the user to bear in mind to help the code find a feasible machine Chapter 5 shows how to modify the code in specific ways for example how to add extra constraints and variables to the code A useful set of code management utilities is introduced in Chapter 6 Finally the Appendices give example input files for PROCESS in non optimisation and optimisation modes and lists of references that provide information about the code status its location and other details relating to the implementation of PROCESS to date Chapter 2 P
32. T amp M PKNIGHT PROCESS MANUAL A User Guide to the PROCESS Systems Code P J Knight EURATOM CCFE Fusion Association Culham Science Centre Abingdon Oxon OX14 3DB UK Date 2013 04 16 15 58 27 0100 Tue 16 Apr 2013 Revision 163 1 Contents 1 Introduction LI Rationale strana eta a da e A ch ee ls ed A O RRA 1 3 Layout of the User Guide aaa aaa 2 Program Overview The Fundamental Concepts 21 Equation Solvers 1s ii A a ee ee eed eee a 2 1 1 Non optimisation mode aooaa a 2 1 2 Optimisation modes eu secas ra ee ee E DLL SCANS 2 2k fo Rw A a a Ao BR Pa e ee 2a 2 2 The Variable Descriptor File 0 0 0 00 a 2 3 Input Parameters nni 4 oc a0 we A Ward SS A do Se ee a Se Oe Aa 2 4 Constraint Equations cs oa ex a ee 2 4 1 Consistency equations ee 2 4 2 Limitsequationss 0s y o A A A A AAA AA 2 5 Iteration Variables ia i p std ea RD A Pea ke ee Shs 2 6 Figures of Merit oci adei pa fe Yawk eek Gare ER dee a ee ee ee 2 1 Scanning Variables cu soi na aer a eR ae a Paap a ea 2 8 Code Structure iia So Yawk eek a ESE Oa We es ee eee 2 8 1 Numerics Modules 22 4 62402 ee eee Re ee Pee eae ee 2 82 Physics Modes 22s isis ois a BR ee id be Reo ead da 2 8 3 Engineering modules e 284 Costing module laa a tan Boe ee BA adh i wm dra 28 0 Other modules ve s dois dedi gt ae Bid We BY Bees dad ow ad 3 Physics Engineering and Other Models 3 1 Tokamiak Power Pl
33. TA 0 042 BT 6 DENE 1 5e20 FVSBRNNI 1 0 DNBETA 3 5 HFACT 2 ICURR 4 ISC 6 TINVQD 1 TITER 1 ISHAPE 0 KAPPA 2 218 Q 3 0 RMAJOR 7 0 RNBEAM 0 0002 TBURN 227 9 TE 15 TRIANG 0 6 Current drive parameters IRFCD IEFRF FEFFCD 3 1 N B active iteration variable 36 Machine aspect ratio N B active iteration variable 5 Toroidal field on axis N B active iteration variable 6 Non inductive volt seconds fraction Troyon g coefficient N B active iteration variable 10 Use ITER current scaling Use ITER 89 P confinement time scaling law Use inverse quadrature Use ITER fusion power calculations Use input values for KAPPA and TRIANG Plasma elongation Edge safety factor N B active iteration variable 3 N B active iteration variable 7 Burn time Electron temperature Plasma triangularity Use current drive Use ITER neutral beam current drive Artificially enhance efficiency 71 Appendix A Non optimisation Input File 72 Divertor parameters ANGINC 0 262 Angle of incidence of field lines on plate PRN1 0 285 Density ratio Machine build BORE 0 12 Machine bore OHCTH 0 1 OH coil thickness GAPOH 0 08 Inboard gap TFCTH 0 9 Inboard TF coil leg thickness DDWI 0 07 Vacuum vessel thickness SHLDITH 0 69 Inboard shield thickness BLNKITH 0 115 Inboard blanket thickness
34. TF coil calculations vacuum system calculations Table 2 8 Summary of the engineering modules in PROCESS Chapter 2 Program Overview The Fundamental Concepts 21 2 8 5 Other modules These modules perform miscellaneous tasks such as initialisation of variables and file input output File process f90 contains the main program and includes the overall controlling loop Table 2 9 summarises these modules source file description global _variables f90 defines and initialises most shared variables initial f90 checks self consistency of input variables and switches input f90 reads in user defined settings from input file output f90 utility routines to format output to file process f90 main program and top level calling routines Table 2 9 Summary of the remaining modules in PROCESS Chapter 3 Physics Engineering and Other Models There are a great number of individual models within PROCESS characterising many different aspects of a fusion power plant Several of these will always be used by the code and so require no input by the user to activate them However in many cases there is a choice of model available and each of these has its own user controlled switches or flags This chapter summarises these models and indicates their location and interaction within the code together with the relevant switch settings and required parameter values The concepts used iteration variables
35. a scanning variable 11 is to be performed A useful practice in optimisation mode is to perform stationary scans whereby the same value is given to the scanning variable on successive iterations This provides a check as to how well converged the solution has become If scans of a given variable are to be made over a large range of values it is often a good idea to start the scan in the middle of the desired range and to split the scan in two one going downwards from the initial value and the other upwards This ensures that the whole range of the scan produces well converged machines assuming a good initial point without sharp changes in gradient in the parameter values It should be remembered that the value of the scan variable is set in the array sweep and this overrules any value set for the variable elsewhere in the input file For instance in the example above the values of dnbeta set in the sweep array would overrule any value for dnbeta set elsewhere in the file The output from an optimisation run contains an indication as to which iteration variables lie at their limiting values On the whole there is a greater chance of unfeasible solutions being found whilst in optimisation mode and Section 4 4 will hopefully be of some use in this situation A typical input file for use with PROCESS in optimisation mode is contained in Appendix B 4 4 Problem Solving Experience has shown that the first few attempts at run
36. actor with no safety credit 3 9 1 3 Replaceable components The first wall blanket divertor centrepost if present and current drive system have relatively short lifetimes because of their hostile environment after which they must be replaced Because of this frequent renewal they can be regarded as though they are fuel items and can be costed accordingly Switch ifueltyp is used to control whether this option is used in the code If ifueltyp 1 the costs of the first wall blanket divertor and a fraction fcdfuel of the cost of the current drive system are treated as fuel costs If ifueltyp 0 these are treated as capital costs 3 9 1 4 Cost of electricity calculations Switch ireactor determines the type of cost of electricity calculation that is performed If ireactor 0 no cost of electricity calculation is performed If ireactor 1 then the cost of electricity is evaluated with the value quoted in units of m kWh 3 9 1 5 Net electric power calculation Related to the cost of electricity is the net electric power calculation performed in routine POWER It is possible that the net electric power can become negative due to a high recirculating power Switch ipnet determines whether the net electric power is scaled to always remain positive ipnet 0 or whether it is allowed to become negative ipnet 1 in which case no cost of electricity calculation is performed Chapter 3 Physics Engineering and Other Models 53
37. alue as it requires and the program will fail 5 3 Other Global Variables This type of variable embraces all those present in the modules in global variables f90 and some others elsewhere which do not need to be given initial values or to be input as they are calculated within the code These should be added to the code in the following way 1 Choose the most relevant module usually one of those in source file global_variables f90 Keeping everything in alphabetical order add a declaration statement for the new variable specifying the initial value 0 0DO and a correctly formatted comment line to describe the variable copying the examples already present 2 Ensure that all the modules that use the new variable reference the relevant module via the Fortran use statement 5 4 Constraint Equations Constraint equations see Section 2 4 are added to PROCESS in the following way 1 Increment the parameter ipeqns in module numerics in source file numerics f90 to accommodate the new constraint 2 Add an additional line to the initialisation of the array icc in module numerics in source file numerics f90 3 Assign a description of the new constraint to the relevant element of array lablcc in module numerics in source file numerics f90 4 Add the constraint equation to routine CONSTRAINTS in source file constraint equations f90 ensuring that all the variables used in the formula are contained in the modules specified via use s
38. anges i e if the machine jumps from leaning on the beta limit to leaning on the density limit the output parameters may well become discontinuous in gradient and trends may suddenly change direction 4 4 3 Unfeasible results In the numerics section of the output file the code indicates whether the run produced a feasible or unfeasible result The former implies a successful outcome although it is always worth checking that the estimate of the constraints sqsumsq is small 107 or less the code will issue a warning if the run seems feasible but the value of sqsumsq exceeds 107 If this occurs reducing the value of the HYBRID tolerance ftol or VMCON tolerance epsvmc as appropriate should indicate whether the result is valid or not the output can usually be trusted if 1 the constraint residues fall as the tolerance is reduced to about 1078 and 2 the code indicates that a feasible solution is still found An unfeasible result occurs if PROCESS cannot find a set of values for the iteration variables which satisfies all the given constraints In this case the values of the constraint residues shown in the output The constraint residues are the final values of c in the constraint equations see Section 2 4 The value sqsumsq is the square root of the sum of the squares of these residuals Chapter 4 Execution of the Code 61 give some indication of which constraint equations are not being satisfied those with the h
39. ant osa th eee er a kk dd Sang Oh ee ek eee a 3 1 1 Radial and vertical build 00000000000 000 4 IN DO o o o 00 10 10 12 12 12 12 13 15 15 15 18 18 18 18 21 3 2 3 3 3 4 3 5 3 6 3 1 2 Plasma physics models ee 25 Sia First wall secsi is e a A a A A 30 SA DIVECOO Laa a Ra a o 30 30 Blanket occa sates Sis iS A A e Se Se at 30 SUELOS Shield 2 124 5 Al eke nd Oa BO be le es eee ie i 31 3 1 7 Voroidal field coils st aie mica a a a a ca a a 32 3 1 8 Poloidal field coils o e 34 3 1 9 Ohmic heating COll e 36 3 1 10 Auxiliary power systems heating and current drive 36 3 1 11 Structural components 37 3 1 12 Power conversion and heat dissipation systems 204 38 3 1 13 Cryostat and vacuum system ooa ee 39 3 14 Buildings tra 8 cata Bigeye ah Se ae he A Ss ae a Es 39 Tight Aspect Ratio Tokamak Model 02 e 39 3 2 1 Tight aspect ratio tokamak switches 2 ee 40 Pulsed Plant Operation 40 3 3 1 Thermal cycling package e ee 40 3 3 2 First wall coolant temperature rise limit o 41 3 3 3 First wall peak temperature liMib o e o 41 3 3 4 Start up power requirements 2 0 ee 41 3 3 0 OH coil swing times bus hera e a a ad he e 41 3900 Burm time 2 A aa a a e A ee Ss Se Gh es ped 41 33 7 Thermal storage lt
40. asma reaching the scrape off layer and heavy ions that are ejected from the first wall By default two divertors are assumed in the PROCESS tokamak placed symmetrically above and below the plasma The principal outputs from the code are the divertor heat load used to determine its lifetime and its peak temperature The divertor is cooled either by gaseous helium or by pressurised water Switch snull controls the overall plasma configuration Setting snull O corresponds to an up down symmetric double null configuration the default while snul1 1 assumes a single null plasma with the divertor at the bottom of the machine The vertical build see Figure 3 2 and PF coil current scaling algorithms take the value of this switch into account although not the plasma geometry at present The Harrison Kukushkin Hotston divertor model 14 developed for ITER is used except for the case of tight aspect ratio tokamaks see later This is appropriate for conventional aspect ratio machines but care should be taken in inputting the divertor magnetics for this model and projections far from the ITER CDA machine parameters are likely to be unreliable The divertor calculations are carried out in routines DIVCALL and DIVERT 3 1 5 Blanket The blanket performs a number of tasks An incoming neutron from a deuterium tritium D T fusion reaction in the plasma loses energy in the blanket This energy is removed by the blanket coolant and used to prod
41. ault value of 0 5 and the unit cost is set using input parameter ucof The default value for ucof is 3 3 per Watt of injected power The bootstrap fraction is assumed to be zero Plasma ignition and additional plasma heating using auxiliary power are treated as for tokamaks 3 6 2 TF coils The TF coils for the RFP option are derived from the TITAN II coil set which uses circular copper coils The radial thickness is set using tfcth as usual but the toroidal thickness may also be set using iteration variable no 77 tftort This is constrained to be no larger than is geometrically possible using constraint equation no 47 with iteration variable no 76 frfptf 3 6 3 OH coils The TITAN I OH coil locations currents etc are assumed These comprise 14 copper coils with currents swinging from positive to negative during the plasma start up period and then decaying back to zero To account for different plasma geometries and currents the OH coil locations relative to the plasma centre scale with the TF coil radius and with the plasma major radius and the current per turn scales linearly with the plasma current 3 6 4 EF coils The Equilibrium Field coils are based on the TITAN I EF coils which are two superconducting NbTi coils that provide the correct vertical field at the plasma centre The coil locations scale with the plasma major radius and TF coil radius along with the OH coils 3 6 5 Divertor The TITAN divertor conce
42. be fblbe LiPb pa fbllipb lithium fb11i coolant v blkt v blkt v blkt Table 3 3 Summary of the materials comprising the blanket in the various scenarios available The fractions given are all available to be modified and should of course add up to 1 0 for any given model The type of coolant used is given by the value of switch costr 3 1 6 Shield The stainless steel shield reduces the neutron flux reaching the TF coils and beyond This minimises the radiological impact of the neutrons and their heating of the TF coils which if superconducting need to remain at liquid helium temperatures The shield is cooled either by gaseous helium or by pressurised water as chosen using switch costr see Section 3 1 5 1 and as with the blanket the Chapter 3 Physics Engineering and Other Models 32 energy deposited in the coolant is used to produce electricity The shield coolant fraction is stored in input parameter vfshld 3 1 7 Toroidal field coils The toroidal field TF coils can be either resistive or superconducting Switch itfsup should be set to 1 for superconducting coils or 0 for purely copper coils In the superconductor model the CICC Conductor In Cable Conduit structure shown in Figure 3 3 is assumed and the coils are cooled using a liquid helium cryogenic system Among the TF coil parameters calculated by the code are the maximum allowable current density the stresses on the structure the energy
43. c corresponding no description type ixc variables 1 plasma beta consistency C 5 2 global power balance C 10 1 2 3 4 6 11 3 ion power balance C 10 1 2 3 4 6 11 4 electron power balance C 10 1 2 3 4 6 11 5 density limit L 9 1 2 3 4 5 6 6 epsilon beta poloidal limit L 8 1 2 3 4 6 7 beam ion density NBI C 7 8 neutron wall load limit L 14 1 2 3 4 6 9 fusion power limit L 26 1 2 3 4 6 10 toroidal field 1 R consistency C 12 1 2 3 13 11 radial build consistency C 3 1 13 16 29 42 61 12 volt second limit L 15 1 2 3 13 burn time limit PULSE L 21 1 16 17 22 29 42 44 61 14 beam energy NBI C 19 1 2 3 6 15 burn time PULSE N B not usually necessary C 41 44 16 net electric power limit L 25 1 2 3 17 stellarator radial build STELLARATOR C 61 18 divertor heat load limit L 27 19 MVA limit L 30 20 port size limit L 33 31 3 13 21 minor radius limit L 32 22 divertor collisionality limit L 34 43 23 TF coil current density limit L 28 12 24 20 23 24 Troyon beta limit also beta limit in stellarators L 36 1 2 3 4 6 18 25 peak toroidal field limit L 35 3 13 29 26 OH coil current density at End of Flat top limit L 38 37 41 12 27 OH coil current density at Beginning of Pulse limit L 39 37 41 12 28 energy multiplication Q limit L 45 47 40 29 inboard radial build specified value C 3 1 13 16 29 42 61 30 injection power limit L 46 47 11 31 TF coil case stress limit SCTF L 48 56 57 58 59 60 24 32 TF coil cond
44. cally above and below the midplane and each group j has an element ipfloc j assigned to it Input parameter ngrp should be set to the number of groups and ncls j should be assigned the number of coils in each group which should be 2 in each case In the following all variables are defined in the variable descriptor file vardes html The values for rpf1 rpf2 zref j and routr should be adjusted by the user to locate the PF coils accurately The three possible values of ipfloc j correspond to the following PF coil positions ipfloc j 1 PF coils are placed above the OH coil one group only R rohc rpfi Z hmax ohhghf 0 1 0 5 hmax x 1 0D0 ohhghf tfcth 0 1 ipfloc j 2 PF coils are placed above the TF coils one group only R rmajor rpf2 triang rminor Z hmax tfcth 0 86 ipfloc j 3 PF coils are placed radially outside the TF coils any number of groups R rtot tfthko 2 0D0 routr Z rminor zref j Chapter 3 Physics Engineering and Other Models 35 3 1 8 2 PF coil currents The PF coil currents are calculated in routine EFC and vary as a function of time during the tokamak operation as indicated in Figure 3 4 current time OH swing heat dwell beginning of pulse Figure 3 4 Plot showing schematically the current waveforms for the plasma a typical PF coil and the OH coil 3 1 8 3 PF coil resistance The PF coils can be either
45. cling package This performs calculations on the first wall of the machine Evaluation of the mechanical and thermal stresses on this component lead to a measure of the maximum number of cycles to which the first wall can be subjected and hence to the minimum allowable length of each reactor cycle for a specified first wall lifetime The cycle time can be constrained to be at least the minimum value by turning on constraint equation no 42 with iteration variable no 67 ftcyc1 Chapter 3 Physics Engineering and Other Models 41 The thickness of the first wall is constrained to lie within lower and upper bounds which ensures that it can withstand the internal coolant pressure and the peak temperature and neutron fluence Switch itcycl activates the desired model for the first wall axial stress calculations If itcycl 1 the default the wall is fully constrained axially and no bending can occur If itcycl 2 there is no constraint on the axial motion but no bending can occur Finally if itcycl 3 again there is no axial constraint and bending is allowed to occur 3 3 2 First wall coolant temperature rise limit The rise in temperature of the first wall coolant can be limited to be no more than the value of dtmpmx by turning on constraint equation no 38 with iteration variable no 62 fdtmp 3 3 3 First wall peak temperature limit The maximum first wall temperature can be limited to be no more than the value of variable tpkmax
46. constraint equations etc and instructions on how to set switches etc are explained fully in Chapter 2 3 1 Tokamak Power Plant The default and most detailed power plant model in PROCESS is based on the tokamak magnetic confinement fusion concept This section describes the models relevant to such a plant in some detail starting with the plasma at the centre of the fusion power core and moving outwards to the external components power subsystems and buildings However many of these models are also partly or wholly relevant for the other available machine types especially outside the fusion power core The specific details for these alternative models are introduced later in the Chapter 3 1 1 Radial and vertical build Figure 3 1 shows schematically the layout of a typical tokamak as modelled by PROCESS This is the so called build of the machine the relative locations of the major components Their positions are referenced to the R Z coordinate system where R is the radial distance from the vertical centreline axis of the torus and Z is the vertical distance from the equatorial midplane about which the machine is assumed to be up down symmetrical by default the vertical build is slightly different for single null plasma devices see Figure 3 2 Components are often referred to as being inboard or outboard which simply means that they lie at a radius R less than or greater than Ro respectively where
47. critsc and the critical temperature at zero field and strain is set using input parameter tcritsc 3 1 7 2 Stress model Switch itfmod controls whether a simple stress model itfmod 0 or more complex stress model itfmod 1 should be used To enforce the stress limits calculated using either of these models constraint equation no 31 case stress and or constraint equation no 32 conduit stress should be turned on with iteration variables no 48 fstrcase and or no 49 fstrcond respectively The stress limit can be adjusted using input parameters csutf and csytf Chapter 3 Physics Engineering and Other Models 33 View from above Winding wwp1 wwp2 Pack inter turn void ar thkcas gt fraction wpvf thkwp Single turn thicndut thwendut Figure 3 3 Schematic diagram of the cross section of the inboard leg of a superconducting TF coil showing the CICC Conductor In Cable Conduit construction The winding pack contains many turns of cable conduit The cable space contains the superconducting filaments and circulating liquid helium coolant The variables shown in red may be changed by the user and those in italics may be chosen as iteration variables Chapter 3 Physics Engineering and Other Models 34 3 1 7 3 Current density limits The current in the TF coils must be sufficient to produce the required toroidal field at the centre of the plasma The field falls off at a rate 1 R with th
48. default values are mostly set in the modules contained within source file global_variables f90 e description including physical units if relevant e for switches flags the meanings of all allowed values e iteration variable number if relevant e corresponding constraint equation if relevant In addition global code parameters are labelled FIX These can only be changed by editing the relevant source file but this should not be carried out unless it is absolutely necessary All the variables that are shown with a default value are available to be changed by the user using the input file Section 4 1 except for those which are labelled FIX Variables not shown with a default value are calculated by the code from a combination of other parameters and so it would be meaningless to initialise them Obviously these variables cannot be changed using the input file The file is generated from specially formatted comment lines within the source code see Section 6 2 for more details Therefore it is exceedingly important to keep these comment lines relevant and in sync with the variables they describe Chapter 2 Program Overview The Fundamental Concepts 11 define rules define performance requirements define figure of merit evaluate physics engineering and cost functions apply consistency equations and limit equations iterate free parameters self consistent F o M minimised ye
49. e between the values 101 m and 107 m Of course it can also be constrained to lie below the calculated density limit if constraint equation 5 is activated and the f value fdene iteration variable no 9 is bounded by the values 0 and 1 It is important to remember that iteration variables must never be initialised to zero The code will not be able to adjust the variable s value if this is done and it will stop with an error message 2 6 Figures of Merit In optimisation mode PROCESS finds the self consistent set of iteration variable values that maximises or minimises a certain function of them known as the figure of merit Several possible figures of merit are available all of which are formulated in routine FUNFOM in source file evaluators f90 Switch minmax is used to control which figure of merit is to be used as summarised in Table 2 4 If the figure of merit is to be minimised minmax should be positive and if a maximised figure of merit is desired minmax should be negative 2 7 Scanning Variables One of a number of variables can be scanned during the course of a PROCESS run This option provides a method of determining the sensitivity of the results to different input assumptions The user specifies which variable is to be scanned see Table 2 5 and its required value at each point in the scan The scanned variable to use is defined by the value of nsweep and the chosen variable s values during the scan are set in array
50. e constraints being imposed no matter how many degrees of freedom i e iteration variables are available In this case and many others the user has to relax the constraints slowly until a feasible result is found Chapter 5 Inclusion of Additional Variables and Equations It is often useful to add extra features to the code in order to model new situations This chapter provides instructions on how to add various numerics related items to PROCESS Please remember to modify the relevant Table s in this User Guide if changes are made to the source code 5 1 Input Parameters Input parameters see Section 2 3 are added to the code in the following way 1 5 2 Choose the most relevant module usually one of those in source file global_variables f90 Keeping everything in alphabetical order add a declaration statement for the new variable specifying a sensible default value and a correctly formatted comment line to describe the variable copying the examples already present Ensure that all the modules that use the new variable reference the relevant module via the Fortran use statement Add the parameter to routine PARSE_INPUT_FILE in source file input 90 in a suitable place keep to alphabetical order The existing examples provide guidance on how to do this Note that real i e double precision and integer variables are treated differently as are scalar quantities and arrays Iteration Variabl
51. e is defined by the value of switch iefrf iefrf 1 Fenstermacher Lower Hybrid model iefrf 2 Ion cyclotron model 14 iefrf 3 Fenstermacher electron cyclotron resonance model iefrf 4 Ehst Lower Hybrid model iefrf 5 ITER neutral beam model 14 15 iefrf 6 Culham Lower Hybrid model 15 iefrf 7 Culham electron cyclotron model 15 iefrf 8 Culham neutral beam model 15 iefrf 9 Oscillating Field current drive RFPs only see Section 3 6 1 5 It is sometimes useful to adjust artificially the current drive efficiency values produced by these routines This can be achieved by setting the scaling coefficient feffcd The wall plug to plasma efficiencies can also be adjusted by changing the relevant variable etaech etalh etanbi or etaof 3 1 10 2 Plasma heating In addition to current drive some auxiliary power can be used purely to heat the plasma The value of input parameter pheat determines the amount of auxiliary heating power in Watts to be applied to the plasma This variable may be used as an iteration variable no 11 3 1 10 3 Ignited plasma Switch ignite can be used to denote whether the plasma is ignited i e fully self sustaining without the need for any injected auxiliary power during the burn If ignite 1 the calculated injected power does not contribute to the plasma power balance although the cost of the auxiliary power system is taken into account the system is then assumed to be r
52. e iteration variables that determines whether the code will be successful at producing a useful result It can be a somewhat laborious process to arrive at a working case and unfortunately perhaps experience is often of great value in this situation It should be remembered that sufficient iteration variables should be used to solve each constraint equation For instance a particular limit equation may be A lt B i e A fB where the f value f must lie between zero and one for the relation to be satisfied However if none of the iteration variables have any effect on the values of A and B and A happens to be greater than B then PROCESS will clearly not be able to solve the constraint The lower and upper bounds of the iteration variables are all available to be changed in the input file Constraints can be relaxed in a controlled manner by moving these bounds although in some cases care should be taken to ensure that unphysical values cannot occur The code indicates which iteration variables lie at the edge of their range It is suggested that constraint equations should be added one at a time with sufficient new iteration variables activated at each step If the situation becomes unfeasible it can be helpful to reset the initial iteration variable values to those shown in the output from a previous feasible case and rerun the code Finally it should be borne in mind that the machine that is envisaged may not be a valid solution to th
53. e peak value occurring at the outer edge of the inboard portion of the TF coil Rmax Tr rbmax The maximum TF coil current depends on the field it produces and the allowable current density Two limits can be applied to the current density J in the superconducting TF coils To ensure that J does not exceed the critical value constraint equation no 33 should be turned on with iteration variable no 50 fiooic To ensure that J does not exceed the current density protection limit constraint equation no 35 should be turned on with iteration variable no 53 fjprot A similar constraint on the TF coil current density exists if resistive coils are being used itfsup 0 In this case constraint equation no 23 should be turned on with iteration variable no 28 f jtfc 3 1 8 Poloidal field coils The poloidal field PF coils are used initially to cancel the vertical field produced at the centre of the plasma by the OH coil Section 3 1 9 during start up and then to maintain the plasma position and shape during the flat top period 3 1 8 1 PF coil positions The positions and sizes of the PF coils are partly input and partly calculated after consideration of the required currents and allowable current density The PF coil locations are controlled using a set of switches stored in array ipfloc see Figure 3 1 and are calculated in routine PFCOIL The coils are usually organised into groups containing two PF coils placed symmetri
54. eamfus0 fqval te boundu 15 dnbeta bscfmax boundu 10 fiooic fjprot rmajor bmxlim gammax bound 16 tbrnmn sigpfalw cfactr boundu 72 powfmax kappa triang plasma aspect ratio maximum divertor heat load required net electric power confinement time H factor overall current density in TF coil inboard leg allowable wall load beam background fusion multiplier f value for energy multiplication limit eqn electron temperature upper bound on f value fvs Troyon g coefficient bootstrap current fraction use negative values upper bound on confinement time H factor hfact f value for TF coil operational current limit eqn f value for TF coil current protection limit eqn plasma major radius maximum toroidal field maximum current drive gamma lower bound on OH coil thickness ohcth minimum burn time pulsed operation machine allowable stress in the PF coils plant availability factor upper bound on f value fipir maximum fusion power plasma elongation plasma triangularity Table 2 5 Summary of the scanning variables available in PROCESS source file description caller f90 evaluators f90 maths_library f90 numerics f90 scan f90 constraint_equations f90 iteration variables f90 calls physics and engineering routines defines the constraint equations function evaluators for HYBRID and VMCON packages adjusts values of iteration variables miscellaneous black box
55. ed Field Pinch model Note 009 e Test cases Note 019 TT
56. eir initial values whether they are set in the input file or in the relevant module However some of the calculated parameters may be wrong the most common of which are as follows e Plasma current this can be adjusted using the edge safety factor q Ip x 1 q e Fusion power this scales roughly with the density profile factor alphan e Build parameters it may be necessary to change non critical thicknesses to achieve the correct machine build It may still be difficult if not impossible to reconcile the fusion power and the net electric power with the required values This may well be due to the power conversion efficiency values being used refer to Figure 3 5 With luck a few iterations of this process will produce an adequate benchmark case A typical input file for use with PROCESS in non optimisation mode is contained in Appendix A 4 3 2 Optimisation mode Running PROCESS in optimisation mode requires few changes to be made to the input file from the non optimisation case The main differences between optimisation mode and non optimisation mode are 1 Optimisation mode applies lower and upper bounds to all active iteration variables 2 There is no upper limit to the number of active iteration variables in optimisation mode 3 A figure of merit must be specified in optimisation mode 4 Scans can be performed in optimisation mode Switch ioptimz must be set to 0 or 1 for optimisation mode If ioptimz 0 a non optimisatio
57. equired to provide heating etc during the plasma start up phase only use pheat to indicate the power requirement If ignite 0 the plasma is not ignited and the auxiliary power is taken into account in the plasma power balance during the burn phase 3 1 11 Structural components Structural components are required to provide support for the fusion power core systems against gravity and the magnetic forces that will be encountered during operation The required structural masses and their costs are calculated Chapter 3 Physics Engineering and Other Models 38 3 1 11 1 Bucking cylinder The bucking cylinder provides some strength to the inboard TF coil structure If the TF coils are superconducting the bucking cylinder is cooled by the cryogenic system 3 1 12 Power conversion and heat dissipation systems The PROCESS power plant takes into account all the systems required to perform the necessary conversion of fusion power to electricity from the coolant systems in the plant components to the heat exchangers and turbines Figure 3 5 shows schematically the overall power transfer mechanisms used by the code N B FUSION WALL PLUG INJECTION POWER CORE FUSION 0 8 20 gt 08 0 2 L efficiency Dee INJECTION POWER emult fhole 1 exp kx MULTIPLIED n POWER etaech L HYBRID a TEtpion fpion ELECTRONS
58. es New iteration variables see Section 2 5 are added in the same way as input parameters with the following additions Increment the parameter ipnvars in module numerics in source file numerics f90 to accommodate the new iteration variable Add an additional line to the initialisation of the array ixc in module numerics in source file numerics f90 63 Chapter 5 Inclusion of Additional Variables and Equations 64 3 Assign sensible values for the variable s bounds to the relevant elements in arrays boundl and boundu in module numerics in source file numerics f90 4 Assign the relevant element of character array lablxc to the name of the variable in module numerics in source file numerics f90 5 Add the variable to routines LOADXC and CONVXC in source file iteration_variables f90 mimicking the way that the existing iteration variables are coded Don t forget to add suitable correctly formatted comment lines to numerics f90 to document the above changes If an existing input parameter is now required to be an iteration variable then simply carry out the tasks mentioned here It should be noted that iteration variables must not be reset elsewhere in the code That is they may only be assigned new values when originally initialised in the relevant module or in the input file if required and in routine CONVXC where the iteration process itself is performed Otherwise the numerical procedure cannot adjust the v
59. es is used Chapter 3 Physics Engineering and Other Models 26 3 1 2 2 Plasma profiles All the plasma profiles are assumed to be parabolic i e they are of the form Density n r no y hi 3 5 To y 3 6 Current J r Jo 7 3 7 a Temperature T r where r varies from 0 to a the plasma minor radius This gives volume averaged values n no 1 an and line averaged values n no 1 Qn etc These volume and line averages are used throughout the code along with the profile indices a in the various physics models many of which are fits to theory based or empirical scalings Thus the plasma model in PROCESS may be described as 3 D The relevant profile index variables are alphan alphat and alphaj respectively 3 1 2 3 Beta limits The Troyon beta limit 14 15 is given by 8 lt g atm B T 3 8 where Bo is the axial vacuum toroidal field and 8 is defined with respect to the total equilibrium B field 15 The Troyon coefficient g is set using input parameter dnbeta To apply the beta limit constraint equation no 24 should be turned on with iteration variable no 36 fbetatry The limit can be applied to either the total plasma beta in which case switch iculbl should be set to 0 to only the thermal component of the plasma beta in which case iculbl should be set to 1 or to the thermal plus neutral beam components in which case iculbl should be set to 2 Aspect ratio
60. f the machine The centrepost is constructed from copper as are the outboard TF coil sections and is tapered lengthways so that it is narrowest at the midplane of the device Routine CNTRPST calculates various parameters relevant to the centrepost including the pump pressure maximum temperature and pipe radius and these may be limited using constraint equations 43 to 46 if required e Equation 43 is a consistency equation for the average centrepost temperature e Equation 44 can be used to limit the peak centrepost temperature to a maximum value ptempalw using iteration variable no 68 fptemp e Equation 45 can be used to force a lower limit to the edge safety factor using iteration variable no 71 fq e Equation 46 can be used to apply an upper limit to the ratio of plasma current to TF coil rod current using iteration variable no 72 fipir Chapter 3 Physics Engineering and Other Models 40 3 A gaseous divertor model is used and a simple divertor heat load calculation is employed rather than the ITER CDA like divertor assumed for conventional aspect ratio tokamaks 4 A simple PF coil current scaling algorithm is available for use with the TART option 5 The plasma shaping terms elongation and triangularity can be calculated directly given the aspect ratio Switch ishape controls whether the input values for the plasma elongation kappa and triangularity triang should be used ishape 0 or whether they
61. ges produced by the code attempt to provide diagnostic information telling the user where the problem occurs and also suggest a possible solution These messages are out of necessity brief and so cannot promise to lead to a more successful outcome 4 4 2 Optimisation problems On reflection it is perhaps surprising that PROCESS ever does manage to find the global minimum figure of merit value since if there are nvar iteration variables active the search is over nvar dimensional parameter space in which there may be many shallow minima of approximately equal depth Remember that nvar is usually of the order of twenty The machine found by PROCESS may not therefore be the absolutely optimal device It is quite easy to have two or more solutions with results only a few per cent different but a long way apart in parameter space The technique of stationary scans described in Section 4 3 2 above can often help in this situation which is why this method is recommended at all times Scans should be started in the middle of a range of values to try to keep the scan within the same family of machines The optimum machine found may otherwise suddenly jump to a new region of parameter space causing the output variables to seem to vary unpredictably with the scanning variable It should be noted that in general the machine produced by PROCESS will always sit against one or more operation limits If during a scan the limit being leant upon ch
62. gion is not confined and is removed by the divertor PROCESS treats the scrape off layer merely as a gap Switch iscrp determines whether the scrape off widths should be calculated as 10 of the plasma minor radius iscrp 0 or set equal to the input values scrapli and scraplo iscrp 1 High Z impurities The assumed high Z impurity affecting the plasma composition and radiation power calculations can be switched between argon zfear 1 and iron zfear 0 the latter is the default option Add section on radiation power etc Chapter 3 Physics Engineering and Other Models 30 3 1 3 First wall The first wall acts as a physical barrier protecting the rest of the machine from the hot plasma Due to its hostile environment the first wall has only a short lifetime and therefore needs to be replaced regularly Its stainless steel structure is cooled either by gaseous helium or by pressurised water as chosen using switch costr see Section 3 1 5 1 The first wall coolant fraction is given by the value of fwclfr which is calculated if a pulsed power plant is being modelled lpulse 1 see Section 3 3 and assumed to be the input value otherwise Wall load calculation Switch iwalld determines whether the neutron wall load power per unit area should be calculated using the plasma surface area iwalld 1 or the first wall area iwalld 2 as the denominator 3 1 4 Divertor The divertor provides a means of removing pl
63. her laboratories in the USA In addition many of the mathematical routines have been taken from a number of different well established source libraries Since the code is descended from such a wide range of sources its structure was initially not ideal from the programmer s viewpoint Non standard practices and inconsistent layout within the code led to difficulties in modifying interpreting and indeed running the code A great deal of effort was therefore expended at Culham on the code s arrival from ORNL in the early 1990s to improve this situation with the code being given a complete but careful upgrade routine by routine For many years this Fortran 77 code was used for systems code studies of various power plant scenarios and was modified from time to time by the addition of new and or improved models including machines based on the stellerator reversed field pinch and inertial confinement concepts In 2012 the code structure was revised again to allow it to benefit from modern software practices and the whole program was upgraded to Fortran 90 95 At the same time a number of useful code management utilities were added As with all active research codes PROCESS will continue to be developed into the future This User Guide is updated in parallel with the Fortran source code itself to ensure that the documentation remains consistent with the latest version of the code It is to be hoped that it will be of assistance to all users of PROCE
64. hickness SCRAPLO 0 15 Outboard scrape off layer thickness FWOTH 0 035 Outboard first wall thickness BLNKOTH 0 235 Outboard blanket thickness SHLDOTH 1 05 Outboard shield thickness GAPOMIN 0 21 Outboard gap VGAPTF 0 Vertical gap First wall blanket shield parameters LBLNKT 0 Use old blanket model DENSTL 7800 Steel density TF coil parameters DACDCP 1 4e7 N B active iteration variable 12 ITFSUP 1 Use superconducting TF coils RIPMAX 5 Maximum TF ripple PF coil parameters NGRP 3 Three groups of PF coils IPFLOC 1 2 3 Locations for each group NCLS 2 2 2 1 Number of coils in each group COHEOF 1 85e7 OH coil current at End Of Flat top FCOHBOP 0 9 OH coil current at Begin Of Pulse COHEOF ROUTR 1 5 Radial position for group 3 ZREF 3 2 5 Z position for group 3 OHHGHF 71 Height ratio OH coil TF coil Vacuum system parameters NTYPE 1 Use cryopump Heat transport parameters ETATH 0 35 Thermal to electric conversion efficiency FMGDMW 0 Power to MGF units Appendix B Optimisation Input File 76 BASEEL 5 e6 ISCENR 2 Buildings FNDT 2 EFLOOR 1 d5 Costs IREACTOR 1 IFUELTYP 0 UCHRS 87 9 UCCPCL1 250 UCCPCLB 150 Base plant electric load Energy store option Foundation thickness Effective total floor space Calculate cost of electricity Treat blanket first wall etc a
65. hine s parameters The first thing to do is to add to the input file all the known details about the machine to be modelled This may include some or all of the following Chapter 4 Execution of the Code 57 e machine build e plasma aspect ratio e PF coil locations e type of current drive to be used e net electric power e various physics parameters e g toroidal field on axis electron density electron temperature elongation triangularity Troyon g coefficient edge safety factor In addition some of the switch values summarised in Chapter 3 may have to be altered from their default values Next the relevant numerics information must be entered Switch ioptimz must be set to 1 for non optimisation mode Then the user must decide which constraint equations and iteration variables to activate this choice is dictated partly by the information required by the user and partly by the machine being modelled itself As stated earlier all the relevant consistency equations must be activated together with the corresponding iteration variables A number of limit equations can also be activated to investigate how the calculated values compare with the physics or engineering limits The following is part of an example non optimisation input file IOPTIMZ 1 NEQNS 8 NVAR 8 Icc 1 2 10 11 7 16 5 24 IXC 5 10 12 29 7 9 36 4 FPNETEL 1 0 PNETELIN 1200 0 Consistenc
66. ighest residues should be examined further In optimisation mode the code also indicates which iteration variables lie at the edge of their allowed range Unfeasible runs are caused either by ill defining the problem to be solved or by starting the problem in an unfavourable region of parameter space The latter can be checked simply by changing the initial values of the active iteration variables in the input file but the former requires some extra work This situation arises if there are insufficient iteration variables for the given constraint equations It is important to choose the right number of useful iteration variables for the problem to be solved it is possible to activate too many iteration variables as well as too few some of which may be redundant Both optimisation and non optimisation runs can fail with an error message suggesting that the iteration process is not making good progress This is likely to be due to the code finding itself unable to escape a region of the parameter space where the minimum in the residuals is significantly above zero In this situation there is either no solution possible the residuals can therefore never approach zero or the topology of the local minimum makes it difficult for the code to escape to the global minimum Again a helpful technique is to either change the list of iteration variables in use or to simply modify their initial values to try to help the code avoid such regions A techniq
67. is a systems code that calculates in a self consistent manner the parameters of a fusion power plant with a specified performance ensuring that its operating limits are not violated and with the option to optimise a given function of these parameters It would not be fair to call PROCESS a fusion power plant design code as this implies that a great deal of complexity would need to be present in each and every model describing one of the component systems Such complexity is however incompatible with the code s iterative approach to solving the optimisation problem since this requires repeated evaluation of the same large number of expressions This is not to say that the models employed by the code are oversimplified in general they represent good numerical estimates of present theoretical understanding or are fits to experimental data PROCESS provides a useful overall description of how a conceptual and feasible power plant may look Chapter 1 Introduction 7 1 2 History PROCESS is derived from several earlier systems codes but is largely based on the TETRA Tokamak Engineering Test Reactor Analysis code 1 and its descendant STORAC Spherical TOrus Reactor Analysis Code 2 which includes routines relevant to the tight aspect ratio class of tokamaks These codes and much of the original version of PROCESS itself were written by personnel at Oak Ridge National Laboratory in Tennessee USA with contributions from a number of ot
68. iven by the value of sigpfalw To limit the current density at the BOP constraint equation no 27 should be turned on with iteration variable no 39 f fjohc0 To limit the current density at the EOF constraint equation no 26 should be turned on with iteration variable no 38 fjohc 3 1 10 Auxiliary power systems heating and current drive 3 1 10 1 Current Drive The use of purely inductive current drive leads to pulsed plant operation because of the limited flux swing that can be achieved using the OH coil This poses problems due to the fact that fatigue failures may result and there would also be a need for thermal storage to maintain a level supply between pulses However the plasma current can also be produced and maintained partially or wholly using non inductive means which in principle removes this restriction PROCESS contains a number of auxiliary current drive schemes including various RF methods Lower Hybrid Electron Cyclotron Chapter 3 Physics Engineering and Other Models 37 and Ion Cyclotron Fast Wave current drives and also Neutral Beam current drive systems The code calculates the efficiency and the resulting power requirements of the chosen system The fraction of the required flux swing Volt seconds to be produced by non inductive means fvsbrnni should be set and flag irfcd should be set to O for purely inductive scenarios or 1 otherwise The current drive efficiency model to be used in this latter cas
69. k TF coils so some modification has been necessary Firstly the inboard legs do not form a continuous ring of material on the midplane adjacent coil cases do not touch This causes the calculation of the inboard coil conductor area to change and also the shape of the winding pack cross section This is assumed to be rectangular for the stellarator coils rather than the complicated two step cross section assumed for tokamaks see Figure 3 6 The radial thickness is set using tfcth as usual but the toroidal thickness may also be set using iteration variable no 77 tftort This is constrained to be no larger than is geometrically possible using constraint equation no 47 with iteration variable no 76 frfptf Secondly the shape of the coils in the poloidal plane is not D shaped and varies from coil to coil This has a number of implications not least on the length and hence total mass and cost of the coil set In order to model a set of realistically shaped stellarator coils geometry 6 data were taken from the Wendelstein VII X coil set design 7 and these are fitted onto the surface of a helically modulated torus whose radii scale with the machine s desired radial build The total length of the coils is then calculated For simplicity the poloidal cross section of the torus onto which the coils are mapped is assumed to be elliptical with the major axis of the ellipse rotating with toroidal angle This is only a rough estimate
70. larator is inherently non axisymmetric the build of the PROCESS stellarator is defined in terms of the mean thicknesses of components This allows the code to use the existing algorithms for the surface areas volumes and masses of the plasma and the machine s structural materials without introducing unacceptably large errors in the calculated values It is important that the relative size of the plasma and coils within the stellarator being modelled remains correct For the Helias configuration used in PROCESS the average coil minor radius is 2 6 times the average plasma minor radius This is enforced in the code by using constraint equation no 17 Furthermore the plasma aspect ratio and elongation should not be modified from their default values 12 5 and 2 0 respectively The whole machine can however be scaled in size The recommended build related iteration variables are as follows 3 rmajor 13 tfcth 29 bore 31 gapomin 61 gapds All items external to the fusion power core buildings turbines power conversion systems etc remain unchanged Chapter 3 Physics Engineering and Other Models 45 3 5 2 2 Modelling of stellarator coils The stellarator coils are assumed to be superconducting no resistive coil calculations are performed The overall calculations on the coils are largely unchanged as the present superconducting routines still apply However the geometry of the coils is different from that for tokama
71. liography 10 11 12 13 14 15 R L Reid et al ETR ITER Systems Code Oak Ridge Report ORNL FEDC 87 7 1988 J D Galambos STAR Code Spherical Tokamak Analysis and Reactor Code Unpublished internal Oak Ridge document A copy exists in the PROCESS Project Work File 3 N P Taylor holder and P J Knight PROCESS Reactor Systems Code AEA Fusion Project Work File F RS CIRE5523 PWF 1992 L Bottura J B T e Parameterizations for the ITER Nb3Sn Production ITER Document 2MMF7J 2008 https user iter org uid 2MMF7J action get_document Y K M Peng and J B Hicks Engineering Feasibility of Tight Aspect Ratio Tokamak Spherical Torus Reactors AEA Fusion Report AEA FUS 64 1990 J F Lyon K Gulec R L Miller and L El Guebaly Status of the U S Stellarator Reactor Study report communicated privately to T Hender Wendelstein Project Group Wendelstein VII X Application for Preferential Support IPP Euratom Association August 1990 G Grieger et al Fusion Technology 21 1992 1767 The TITAN Reversed Field Pinch Fusion Reactor Study Scoping Phase Report UCLA Report UCLA PPG 1100 January 1987 The TITAN Reversed Field Pinch Fusion Reactor Study Final Report UCLA Report UCLA PPG 1200 1990 J J More B S Garbow and E Hillstrom User Guide for MINPAC 1 Argonne National Laboratory Report ANL 80 74 1980 M J D P
72. lue of the quantity h Sometimes the limit equation and f value are used to ensure that quantity his larger than its minimum value Amin In this case 0 lt f lt 1 as before but the equation takes the form h hmin c 1 f By fixing the f value i e not including it in the ixc array the limit equations can be used as equality constraints For example to set the net electric power to a certain value the following should be carried out 1 Activate constraint equation 16 by including it in the first neqns elements of array icc 2 Set fpnetel 1 0DO 3 Ensure that fpnetel iteration variable no 25 DOES NOT appear in array ixc 4 Set pnetelin to the required net electric power Limit equations are not restricted to optimisation mode In non optimisation mode the iteration variables are not bounded but the f values can still be used to provide information about how calculated values compare with limiting values without having to change the characteristics of the device being benchmarked to find a solution It is for this reason that all the constraint equations used in PROCESS are formulated as equalities despite the fact that equation solver VMCON can solve for inequalities as well The use of f values precludes this need and allows the non optimising equation solver HYBRID to use the same constraint equations 2 5 Iteration Variables It is necessary to calculate numerical derivatives during the solution of the const
73. maths routines including HYBRID and VMCON numerics array definitions and calling routines for HYBRID and VMCON packages performs a parameter scan Table 2 6 Summary of the numerics modules in PROCESS Chapter 2 Program Overview The Fundamental Concepts 20 source file description current_drive f90 divertor f90 fispact f90 ife f90 physics f90 plasma geometry f90 rfp f90 startup f90 stellarator f90 current drive efficiency calculations divertor model calculations nuclide inventory activation calculations inertial fusion energy physics engineering tokamak plasma and fusion calculations plasma geometry algorithms reversed field pinch physics engineering plasma start up auxiliary power requirements stellarator relevant physics engineering Table 2 7 Summary of the physics modules in PROCESS source file description availability f90 buildings f90 fwbs f90 machine build f90 p coil f90 plant _power f90 pulse f90 safety f90 sctfcoil f90 structure f90 tfcoil f90 vacuum f90 plant component lifetimes and overall availability buildings calculations first wall blanket and shield calculations machine build calculations PF coil calculations heat transport and power balance calculations pulsed power plant calculations steady state temperatures after a LOCA event superconducting TF coil calculations support structure calculations resistive
74. modified from the axisymmetric tokamak case 3 6 Reversed Field Pinch Model In addition to the tokamak and stellarator magnetic confinement devices the code has the ability to perform calculations based on the physics and engineering of a reversed field pinch RFP device This third type of toroidal magnetic device is superficially similar in design to a tokamak so therefore shares many of the same components but the magnetic field configuration differs The model used in PROCESS is largely based on the TITAN fusion power plant 9 10 The following sections summarise its main features where they differ from those for tokamaks To activate the RFP coding it is necessary to create a file device dat containing the single character 2 in the first row in the working directory see Section 4 1 This has the effect of setting the internally used switch irfp 1 If the file is absent or its first character is set to something other than 2 the RFP model is not used and irfp is set to 0 3 6 1 REP physics The plasma in RFPs is circular in cross section and is axisymmetric 3 6 1 1 Beta limit The poloidal beta is limited to a maximum value given by input parameter betpmx default 0 19 using constraint equation 48 and iteration variable 79 fbetap 3 6 1 2 Density limit No density limit is explicitly coded for RFPs other than by simply constraining the upper bound of the electron density variable dene iteration variable 6
75. must be removed to prevent it from diluting the fuel Finally deuterium and tritium is removed on a steady state basis PROCESS calculates the parameters of a vacuum system that satisfy all four requirements with the option of either turbo pumps or cryo pumps being used Switch ntype controls whether a turbopump ntype 0 or a cryopump ntype 1 is used in the vacuum system 3 1 14 Buildings The volume and ground area of all the various buildings on a power plant site are included in the PROCESS calculations for the benefit of the costing algorithms 3 2 Tight Aspect Ratio Tokamak Model PROCESS has the ability to perform studies on tokamaks in the low aspect ratio regime major radius lt 2x minor radius The physics and engineering issues 5 associated with these machines are somewhat different from those of conventional aspect ratio and this is reflected by the following special models 2 in PROCESS 1 The inboard build of a tight aspect ratio tokamak TART is very different from that in a conventional tokamak There is no inboard blanket and possibly no inboard shield and the inboard TF coil legs are replaced by a single centrepost The radial build is altered so that starting from the centreline R 0 the component order is bucking cylinder TF coil gap OH coil cryostat and then continuing as in Figure 3 1 2 Tight aspect ratio tokamaks have resistive TF coils that combine into a single centrepost at the centre o
76. n pass is performed first to provide a hopefully feasible set of initial conditions if ioptimz 1 this is skipped and the code runs in optimisation mode from the start It is usually recommended to use ioptimiz 0 for optimisation runs As before the user must decide which constraint equations and iteration variables to activate Again the choice depends largely on the information required by the user and the extent of the freedom that the code may have with the machine s parameters The following is part of an example optimisation input file IOPTIMZ 1 NEQNS 16 NVAR 19 Icc 1 2 10 11 7 16 5 24 14 8 31 32 33 34 35 36 Chapter 4 Execution of the Code 59 IXC 5 10 12 29 7 9 36 19 14 48 49 50 51 53 54 4 6 1 18 BOUNDL 1 2 5 BOUNDU 10 2 0 MINMAX 6 FPNETEL 1 0 PNETELIN 1200 0 WALALW 4 4 ISWEEP 3 NSWEEP 11 SWEEP 3 5 3 7 3 9 The figure of merit in this example is the minimum cost of electricity minmax 6 Note that additional limit equations are now active along with a second consistency equation related to the neutral beam current drive the number of decay lengths to the plasma centre is constrained to be equal to the input value tbeamin which is not shown here Furthermore there are now more iteration variables than constraint equations to aid the minimisation process Finally note that a three point scan in the Troyon g coefficient dnbet
77. ning PROCESS with a new input file tends to produce unfeasible results that is the code will not find a consistent set of machine parameters The highly non linear nature of the numerics of PROCESS is the reason for this difficulty and it often requires a great deal of painstaking adjustment of the input file to overcome 4 4 1 General problems A code of the size and complexity of PROCESS contains myriads of equations and variables Virtually everything depends indirectly on everything else because of the nature of the code structure so perhaps it is not surprising that it is often difficult to achieve a successful outcome Chapter 4 Execution of the Code 60 Naturally problems will occur if some of the parameters become unphysical For example if the aspect ratio becomes less than or equal to one then we must expect problems to appear For this reason the default bounds on the iteration variables and the allowed ranges of all the input variables have been selected with great care The code contains a large though probably not exhaustive number of error traps to try and prevent problems from propagating These include tests for unphysical values and checks to prevent divisions by zero and non sensible arguments for logarithms and square roots etc However occasionally arithmetic NaN errors still occur although their incidence is low They now usually only occur due to unfeasibility problems see later The error messa
78. of the costed items have a unit cost associated with them These values scale with for example power output volume component mass etc and many are available to be changed via the input file All costs and their algorithms correspond to 1990 dollars Chapter 3 Physics Engineering and Other Models 52 3 9 1 Cost options 3 9 1 1 N of a kind costs The unit costs of the components of the fusion power core are relevant to first of a kind items That is to say the items are assumed to be relatively expensive to build as they are effectively prototypes and specialised tools and machines have perhaps been made specially to create them However if a production line has been set up and R amp D progress has allowed more experience to be gained in constructing the power core components the costs will be reduced as a result Variable fkind may be used to multiply the raw unit costs of the fusion power core items by a factor less than one to simulate this cost reduction for an N of a kind device In other systems studies of fusion power plants 38 values for this multiplier have ranged from 0 5 to 0 8 3 9 1 2 Level of safety assurance Many of the unit costs have four possible choices relating to the level of safety assurance 39 flag 1sa A value 1sa 1 corresponds to a plant with a full safety credit i e is truly passively safe Levels 2 and 3 lie between the two extremes and level 4 corresponds to a present day fission re
79. oloidal plane is rather inaccurately modelled using ellipses This has implications on the calculation of the coil masses and on the stresses on the coils The calculated stresses are especially likely to be inaccurate as the stellarator coils are non planar so extra torque components will be present Chapter 3 Physics Engineering and Other Models 46 lt machine axis gt plasma Winding Pack inter turn void tftort fraction wpvf Ground wall thkcas insulation layer steel external case AH tteth gt Single turn steel conduit case thicndut gt thwendut Figure 3 6 Schematic diagram of the cross section of the inboard leg of a superconducting stellarator coil showing the CICC Conductor In Cable Conduit construction The winding pack contains many turns of cable conduit The cable space contains the superconducting filaments and circulating liquid helium coolant The variables shown in red may be changed by the user and those in italics may be chosen as iteration variables Chapter 3 Physics Engineering and Other Models 47 GA s ya NED dl H iH ce a T r EA r El ee tn P fa a3 Figure 3 7 Comparison between a the Wendelstein VII X coil set and b the PROCESS stellarator coil set The inboard sections of the PROCESS coils are plotted with circular symbols for clarity Chapter 3 Physics Engineering and Other Models 48 3 The divertor model has not been
80. onference Berchtesgaden June 1997 vol 21A part III p 961 6 2008 Martin scaling nominal Martin et al 11th IAEA Tech Meeting on H mode 7 2008 Martin scaling 95 upper bound Physics and Transport Barriers Journal of Physics 8 2008 Martin scaling 95 lower bound Conference Series 123 2008 012033 oR O N e S_E NE OL OS Table 3 2 Summary of the L H power threshold scalings implemented in PROCESS 3 1 2 9 Other plasma physics options Neo classical correction effects Switch ires controls whether neo classical correction effects 19 are included in the calculation of the plasma resistance and ohmic heating power in routine POHM which is called by routine PHYSICS If ires 1 these effects are included Note that the scaling used is only valid for aspect ratios between 2 5 and 4 and it is possible for the plasma resistance to be wrongly calculated as negative if ires 1 and the aspect ratio is too high Inverse quadrature in Tz scaling laws Switch iinvgd determines whether the energy confinement time scaling laws due to Kaye Goldston isc 5 and Goldston isc 9 should include an inverse quadrature scaling with the Neo Alcator result isc 1 A value iinvgd 1 includes this scaling Scrape off layer The region directly outside the last closed flux surface of the core plasma is known as the scrape off layer and contains no structural material Plasma entering this re
81. ouble null divertor scaling TART icurr 3 Simple ITER scaling icurr 4 Revised ITER scaling icurr 5 Todd empirical scaling I icurr 6 Todd empirical scaling II icurr 7 Connor Hastie model 3 1 2 6 Confinement time scaling laws Many energy confinement time scaling laws are present within PROCESS for tokamaks RFPs or stellarators These are calculated in routine PCOND The value of isc determines which of the scalings is used in the plasma energy balance calculation Table 3 1 summarises the available scaling laws 3 1 2 7 Bootstrap current scalings The fraction of the plasma current provided by the so called bootstrap effect can be either input into the code directly or calculated using one of three methods as summarised here e Direct input To input the bootstrap current fraction directly set bscfmax to 1 times the required value e ITER scaling 14 To use the ITER scaling method for the bootstrap current fraction set ibss 1 and bscfmax to the maximum required bootstrap current fraction lt 1 This method is valid at high aspect ratio only e General scaling 16 To use a more general scaling method set ibss 2 and bscfmax to the maximum required bootstrap current fraction lt 1 e Numerically fitted scaling 17 To use a numerically fitted scaling method valid for all aspect ratios set ibss 3 and bscfmax to the maximum required bootstrap current fraction lt 1 Chapter 3 Physics
82. owell A Hybrid Method for Non linear Algebraic Equations Numerical Methods for Non linear Algebraic Equations ed P Rabinowitz Prentice Hall R L Crane K E Hillstrom and M Minkoff Solution of the General Nonlinear Programming Problem with Subroutine VMCON Argonne National Laboratory Report ANL 80 64 1980 N A Uckan and ITER Physics Group ITER Physics Design Guidelines 1989 ITER Documentation Series No 10 IAEA ITER DS 10 1990 T C Hender M K Bevir M Cox R J Hastie P J Knight C N Lashmore Davies B Lloyd G P Maddison A W Morris M R O Brien M F Turner and H R Wilson Physics Assessment for the European Reactor Study AEA Fusion Report AEA FUS 172 1992 68 Chapter 7 Acknowledgements amp Bibliography 69 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 W M Nevins et al Summary Report ITER Specialists Meeting on Heating and Current Drive ITER TN PH 8 4 13 17 June 1988 Garching FRG H R Wilson Nuclear Fusion 32 1992 257 N P Taylor R A Forrest P J Knight and L J Baker Safety and Environmental Modelling in the PROCESS Code Strategic Studies Note 94 14 1994 N A Uckan et al Fusion Technology 13 1988 411 J Nithrenberg et al Plasma Physics and Controlled Fusion 35 1993 B115 S Sudo Y Takeiri H Zushi et al Nuclear Fusion 30 1990 11
83. parameters is found This is useful for performing benchmark comparisons when the device size is kept fixed and one only wishes to find calculated stresses beta values fusion powers etc A flow diagram of PROCESS in non optimisation mode is shown in Figure 2 1 2 1 2 Optimisation mode The HYBRID equation solver will naturally find only one of perhaps several possible machines that may satisfy the prescribed problem To choose one machine in preference to the others it is necessary to define a figure of merit and the selection process then simply involves finding the machine parameters that maximise or minimise this figure of merit The second equation solver within PROCESS VMCON 13 performs this optimisation and therefore finds the best machine that satisfies all the Chapter 2 Program Overview The Fundamental Concepts initialise variables input from file define free parameters define rules to be obeyed evaluate physics engineering and cost functions apply consistency equations iterate free parameters self consistent yes write output Figure 2 1 Flow diagram of PROCESS in non optimisation mode Chapter 2 Program Overview The Fundamental Concepts 10 given constraints An important advantage that VMCON has over HYBRID is its ability to limit the ranges of the variables it uses This prevents the code from attempting to find machines that are physically unattainable
84. perature electrolysis ihplant 2 Hydrogen production by endothermic high temperature electrolysis ihplant 3 Hydrogen production by exothermic high temperature electrolysis ihplant 4 Hydrogen production by thermo chemical processes Table 3 5 describes the additional options available for each of the types of hydrogen production given above The different processes use either electrical power or thermal power directly so the required inputs differ Variable helecmw iteration variable no 87 is the electrical power in MW required for hydrogen production while hthermmw iteration variable no 88 is the thermal power required Note that hthermmw must not be used as an iteration variable if ihplant 4 as it will be calculated from the required electrical power instead Similarly helecmw must not be used as an iteration variable if ihplant 4 The efficiency variables given in Table 3 5 are all input parameters and are the factors hydrogen plant option helecmw hthermmw efficiency variable ihplant 1 input Zero etahlte ihplant 2 input calculated etahten ihplant 3 input calculated etahtex ihplant 4 Zero input etahth Table 3 5 Summary of the variables in PROCESS that relate to the different hydrogen plant processes to be used to convert the value of helecmw to the amount of hydrogen produced in MW equivalent these can be greater than unity in all cases except ihplant 4 3 5 Stellarator Model
85. pt uses three poloidal divertors which bear little resemblance to the typical tokamak toroidal divertor systems The code uses the TITAN divertor lifetime of one year to enable the divertor costs to be reasonable although the divertor surface area and therefore the cost per divertor is likely to be inaccurate Chapter 3 Physics Engineering and Other Models 50 3 6 6 Code modifications As with the stellarator model the RFP model has been incorporated in such a way as to allow its simple removal again if required in the future All new routines are confined to the dedicated source file rfp f90 The tokamak relevant consistency equations in PROCESS see Section 2 4 are used without modification to ensure that the coil currents and the fields they produce are consistent with the plasma parameters 3 7 Inertial Fusion Energy Model As well as magnetic confinement devices PROCESS has the ability to model inertial fusion plants in which a laser or ion beam is used to ignite a target pellet containing the fusion fuel To activate the inertial fusion energy IFE coding it is necessary to create a file device dat containing the single character 3 in the first row in the working directory see Section 4 1 This has the effect of setting the internally used switch ife 1 If the file is absent or its first character is set to something other than 3 the IFE model is not used and ife is set to 0 The IFE model 22 is controlled using two
86. raint equations The iteration variables are the parameters that the equation solvers use for this purpose all the other code variables input parameters see above remain fixed at their initial value Successive calls are made to the physics and engineering routines with slightly different values for the iteration variables on each call and the equation solver determines the effect on the output due to these small changes to the input see Figures 2 1 and 2 2 The nvar iteration variables that the user chooses for a given run are activated by including the variable numbers in the first nvar elements of array ixc Tables 2 2 and 2 3 list the iteration variables available in PROCESS Clearly the equation solvers need at least as many variables to iterate as there are equations to solve i e nvar gt negns If the run is a non optimising case then neqns variables are iterated the values of the remaining nvar neqns variables are left alone If the run is an optimising case then all the active iteration variables are adjusted so as to find the minimum or maximum value of a parameter the figure of merit in the nvar dimensional space of the problem All the iteration variables are constrained to lie between lower and upper bounds stored in arrays bound1 and boundu respectively For instance the plasma electron density is by default confined to Chapter 2 Program Overview The Fundamental Concepts 14 ic
87. rd first wall and blanket components The spectra are based on a simplified tokamak device that has a fixed ratio 1 5825 between the outboard blanket thickness and the inboard blanket thickness and are scaled according to the actual thickness of the outboard blanket This relatively limited single parameter approach is expected to be replaced by a more general method which should allow a more accurate portrayal of the device being modelled by PROCESS 3 8 2 Activation and inventory information The code evaluates the consequences of exposing the power plant s materials to the calculated neutron fluxes subject to the limitations imposed by the neutronics module A library of neutron cross sections and decay data is used to calculate the total activity gamma ray dose rate and decay heat output due to the materials exposure to neutrons both at the end of the plant s life and at a time 100 years later These values are relevant to decommissioning and disposal studies and additional parameters that can be obtained from the nuclide inventory will also be included as the need arises 3 9 Cost Models The cost accounting used by PROCESS combines methods 35 used in the TETRA code 1 and the Generomak 36 scheme The costs are split into the standard accounting categories 37 generally used in the reporting of power plant costs The best references for the algorithms used are 2 and source file costs f90 in the code itself The majority
88. re produced by this reaction the whole of the fusion power is used to heat the plasma Useful energy is extracted from the plasma since the radiation power produced is very high and this can be converted to electricity in a number of ways Since the temperature required to ignite the D He reaction is considerably higher than that for D T 1t is necessary to take into account the following D D reactions which have significant reaction rates at such temperatures D D gt He n 3 27MeV 3 3 D D T p 4 03MeV 3 4 Also as tritium is produced by the latter reaction D T fusion is also possible As a result there is still a small amount of neutron power extracted from the plasma D He tokamak power plants do not include blankets because of the near absence of neutrons leaving the plasma and the fact that no tritium needs to be produced for fuel The use of the D He coding within PROCESS is controlled using the switch idhe3 If idhe3 1 then the D He fusion reaction is assumed otherwise the D T reaction is assumed The ratio of the fuel ions D He and T may be modified if idhe3 1 using the three variables fdeut fhe3 and ftrit respectively Fusion power calculations For the case of D T fusion reactions idhe3 0 switch iiter controls which of two numerical models for the fusion power calculations should be used If iiter 1 the 1989 ITER model 14 is used otherwise an integration method over the plasma profil
89. rmines whether the cooling channels lie in the radial direction estr 1 or in the poloidal direction estr 2 The former case is the default e Coolant type The value of switch costr determines the type of coolant used in the first wall blanket and shield If costr 1 the coolant is assumed to be gaseous helium If costr 2 the coolant is assumed to be pressurised water steam which is the default This switch is used whether or not the full blanket model is used i e is independent of the setting of switch 1b1nkt e Boundary condition The value of switch bstr determines whether the coolant output temperature is to be fixed bstr 1 or whether the maximum blanket temperature is to be fixed bstr 2 The former case is the default The desired coolant output temperature for bstr 1 is set using input parameter xtfo and the required maximum blanket temperature is set using input parameter xtb 3 1 5 2 Blanket materials Table 3 3 summarises the possible options for the blanket materials Switch smstr determines whether a solid blanket of LigO Be smstr 1 or a liquid blanket of LiPb Li smstr 2 is used The former is the default and is the type assumed if lblnkt H 1 material lblnkt 1 lblnkt 1 full thermodynamic model simple model smstr 1 solid blanket smstr 2 liquid blanket stainless steel fblss fblss fblss vanadium fblvd fblvd fblvd LigO fblli2o fblli2o beryllium fbl
90. rogram Overview The Fundamental Concepts Fusion power plants are complex systems consisting of many non linear interactions One method that can be used to model this kind of system is to iterate a number of free parameters the so called iteration variables see Section 2 5 in a controlled way so as to find a self consistent set of device parameters that satisfy all of the system s constraint equations see Section 2 4 PROCESS is organised in a standard equation solver format to enable this task to be performed efficiently The physics and engineering routines together serve as a function evaluator providing the information used in the solution of the constraints The numerical modules present in PROCESS perform the iteration required and also incorporate the option to maximise or minimise a given figure of merit see Section 2 6 2 1 Equation Solvers PROCESS contains two non linear equation solver packages which reflect the two major modes of operation available Each of these has its own uses as is now discussed 2 1 1 Non optimisation mode The first of the two equation solvers present in PROCESS is the non optimisation package HYBRID 11 12 Formally HYBRID finds a zero of a system of N non linear functions in N variables This means simply that N variables power plant parameters are iterated by PROCESS in such a way as to solve a set of N equations physics or engineering laws i e a set of self consistent power plant
91. s write output Figure 2 2 Flow diagram of PROCESS in optimisation mode Chapter 2 Program Overview The Fundamental Concepts 12 2 3 Input Parameters Input parameters make up a large proportion of the variables listed in the variable descriptor file They comprise all those variables that once set in the initialisation routine or redefined in the input file do not change throughout a PROCESS run In fact only those variables defined as iteration variables Section 2 5 can change during the course of a run 2 4 Constraint Equations Any computer program naturally contains myriads of equations The built in equation solvers within PROCESS act on a special class known as constraint equations all of which are formulated in routine CONSTRAINTS in source file constraint_equations f90 Table 2 1 summarises the constraint equations available in PROCESS These can be split into two types 1 consistency equations that enforce consistency between the physics and engineering parameters and 2 limit equations that enforce various parameters to lie within their allowed limits The neqns constraint equations that the user chooses for a given run are activated by including the equation numbers in the first neqns elements of array icc 2 4 1 Consistency equations Consistency equations are usually equalities that ensure that the machine produced by PROCESS is self consistent This means therefore that many of these constraint equation
92. s capital cost Unit cost of heat rejection system Unit cost of high strength tapered copper Unit cost of TF outer leg plate coils Appendix C Source Code Documentation The development of the PROCESS code since its shipment from Oak Ridge National Laboratory in April 1992 has been fully documented in the Project Work File 3 Presented here is a list of Project Work File Notes as of April 16 2013 that address various issues related to the source code e Documentation of each individual source routine is an ongoing task A Work File Note will be produced as each routine is processed with the eventual aim of bringing all these together into a single document i e a future edition of this manual e Summary of work performed since April 1992 Note 0160 e Code status routine SCCS version numbers Note 0165 e SCCS Source Code Control System implementation for PROCESS Note 0003 e Present code standard Note 0160 e Future code standard to be adhered to Note 0167 e Directory structure and location of all relevant files Note 0168 e Proposed future work Note 0160 e Pulsed power plant coding Note 0189 e Nuclide inventory and activation FISPACT module Notes 0195 and 0231 e New cost algorithms Note 0224 e Stellarator model Note 0246 e D He tokamak model Note 0265 Reference 3 has recently been superseded by a new Project Work File F MI PJK PROCESS e Tight Aspect Ratio Tokamak model Note 001 e Revers
93. s should always be used namely equations 1 2 10 and 11 see Table 2 1 Equation 7 should also be activated if neutral beam injection is used and equation 15 should be used if a pulsed machine 1pulse 1 is being modelled The other consistency equations can be activated if required A typical consistency equation ensures that two functions g and h are equal AB eye Rd G gt b 2 i h The equation solvers VMCON and HYBRID need the constraint equations c to be given in the form shown since they adjust the iteration variables so as to obtain c 0 thereby ensuring that g h 2 4 2 Limit equations The limit equations are usually inequalities that ensure that various physics or engineering limits are not exceeded Each of these equations has an associated f value which allow them to be coded as equalities The f values are used as follows In optimisation mode all iteration variables have prescribed lower and upper bounds In general limit equations have the form calculated quantity f x maximum allowable value where f is the f value If f has a lower bound of zero and an upper bound of one then the limit equation does indeed constrain the calculated quantity to lie between zero and its maximum allowable value as required Chapter 2 Program Overview The Fundamental Concepts 13 As with the consistency equations the general form of the limit equations is Ci 1 de a where hmax is the maximum allowed va
94. scaling of Troyon g coefficient Switch gtscale determines whether the Troyon g coefficient dnbeta should scale with aspect ratio gtscale 0 or be fixed at the input value gtscale 0 Limiting e 5 To apply a limit to the value of 3 where e a R is the inverse aspect ratio constraint equation no 6 should be turned on with iteration variable no 8 fbeta The limiting value of 3 should be set using input parameter epbetmax 3 1 2 4 Density limits Several density limit models 15 are available in PROCESS These are calculated in routine CULDLM which is called by PHYSICS To enforce any of these limits turn on constraint equation no 5 with iteration variable no 9 fdene In addition switch idensl must be set to the relevant value as follows idensl 1 ASDEX model idensl 2 Borrass model for ITER I Chapter 3 Physics Engineering and Other Models 27 idensl 3 Borrass model for ITER II idensl 4 JET edge radiation model idensl 5 JET simplified model idensl 6 Hugill Murakami M q model idensl 7 Greenwald model 3 1 2 5 Plasma current scaling laws A number of plasma current scaling laws exploiting the inverse relationship between plasma current and edge safety factor qy 15 are available in PROCESS These are calculated in routine CULCUR which is called by PHYSICS Flag icurr must be set to the relevant value as follows Il pa icurr Peng analytic fit icurr 2 Peng d
95. should be scaled with the plasma aspect ratio ishape 1 The latter case should only be used with a TART machine 6 Among the physics models that differ from those relevant to conventional aspect ratio machines are i the bootstrap current fraction ii the Troyon beta limit and iii the neutron heating of the centrepost 3 2 1 Tight aspect ratio tokamak switches Switch itart provides overall control of the TART switches within the code and subroutine CHECK ensures that no conflicting values are inadvertently set by the user in the input file Table 3 4 summarises the switch values relevant to each aspect ratio regime conventional aspect ratio tight aspect ratio switch itart 0 itart 1 ishape 0 0 1 ibss Section 3 1 2 7 123 2 3 icurr Section 3 1 2 5 1 3 4 5 6 7 2 itfsup Section 3 1 7 0 1 0 Table 3 4 Summary of the switch values in PROCESS that relate to conventional aspect ratio and tight aspect ratio machines 3 3 Pulsed Plant Operation If the plasma current is not to be driven by purely non inductive means it is necessary to operate the plant in a pulsed manner as the current swing in the OH PF coils cannot be continued indefinitely PROCESS can perform a number of calculations relevant to a pulsed power plant as detailed below Switch 1pulse determines whether the power plant is assumed to be based on steady state 1pulse 0 or pulsed 1pulse 1 operation 3 3 1 Thermal cy
96. stated earlier this contains details of all the parameters within the code that can be changed by the user in order to customise the machine modelled by PROCESS Chapter 4 Execution of the Code The intention of this chapter is to provide a comprehensive prescription for setting up and performing runs with the code Firstly the input file s structure and format is described The user is then taken through the process of setting up the code to model a new machine and finally an attempt is made to indicate and solve the problems that the user will face whilst trying to achieve a feasible solution 4 1 The Input File The input file IN DAT is used to change the values of the physics engineering and other code parameters from their default values and to set up the numerics constraint equations iteration variables etc required to define the problem to be solved 4 1 1 Tokamak stellarator RFP or IFE In addition to the main input file IN DAT a second input file device dat is used to signal to the code whether a tokamak stellarator reversed field pinch or inertial fusion enery plant is to be modelled If the file does not exist in the working directory the standard tokamak model is used File device dat should contain a single character in the first line which is interpreted as follows use tokamak model use stellarator model use reversed field pinch model use inertial fusion energy model WN Fr Oo 4 1 2 File s
97. stored and the magnetic field produced by the coils Each TF coil is defined in the R Z plane by four circular arcs of different radius which create a D shaped profile Because of the finite number of TF coils used in a tokamak typically around 20 the toroidal field has a ripple introduced into it the amplitude of which can be limited to a few percent by the code by adjusting the outboard gap thickness labelled gapsto in Figure 3 1 Ports are often necessary for auxiliary power systems etc and the gaps between adjacent TF coils can be made large enough to accommodate such equipment using constraint equation no 20 with iteration variable no 33 fportsz The following options are available within the superconducting TF coil model itfsup 1 3 1 7 1 Superconducting materials Switch isumattf specifies which superconducting material is to be used isumattf 1 Nb3Sn superconductor ITER critical surface parameterization 4 standard critical values isumattf 2 not used isumattf 3 NbTi superconductor isumattf 4 Nb3Sn superconductor ITER critical surface parameterization 4 user defined critical parameters The fraction of copper present in the superconducting filaments is given by the value of variable fcutfsu iteration variable no 59 For isumattf 4 important superconductor properties may be input by the user as follows the upper critical field at zero temperature and strain is set using input parameter b
98. tatements present at the start of this routine Use a similar formulation to that used for the existing constraint equations remembering that the code will try to force cc i to be zero Chapter 5 Inclusion of Additional Variables and Equations 65 Don t forget to add suitable correctly formatted comment lines to numerics f90 to document the above changes Remember that if a limit equation is being added a new f value iteration variable may also need to be added to the code 5 5 Figures of Merit New figures of merit see Section 2 6 are added to PROCESS in the following way 1 Increment the parameter ipnfoms in module numerics in source file numerics f90 to accommodate the new figure of merit 2 Assign a description of the new figure of merit to the relevant element of array lablmm in module numerics in source file numerics f90 3 Add the new figure of merit equation to routine FUNFOM in source file evaluators f90 following the method used in the existing examples The value of fc should be of order unity so select a reasonable scaling factor if necessary Ensure that all the variables used in the new equation are contained in the modules specified via use statements present at the start of this file Don t forget to add suitable correctly formatted comment lines to numerics f90 to document the above changes 5 6 Scanning Variables Scanning variables see Section 2 7 are added to PROCESS in the following way 1 Increment
99. th one another Which machine of a given size and shape produces the cheapest electricity What is the effect of a more optimistic limit on the maximum plasma density on the amount of auxiliary power required Questions such as these are extremely difficult to answer since the large number of parameters involved are highly dependent on one another Fortunately computer programs have been written to address these issues and PROCESS is one of them Suppose that an outline power plant design calls for a machine with a given size and shape which will produce a certain net electric power There may be a vast number of different conceptual machines that satisfy the problem as stated so far and PROCESS can be used in non optimisation mode to find one of these whose physics and engineering parameters are self consistent However the machine found by PROCESS in this manner may not be possible to build in practice the coils may be overstressed for instance or the plasma pressure may exceed the maximum possible value PROCESS contains a large number of constraints to prevent the code from finding a machine with such problems and running the code in so called optimisation mode forces these constraints to be met The number of possible conceptual machines is thus considerably reduced and optimisation of the parameters with respect to say the cost of electricity will reduce this number to a minimum possibly one Formally then PROCESS
100. the driver efficiency and target gain versus driver energy via the two arrays etave 1 10 and gainve 1 10 respectively the element number corresponds to the driver energy in MJ and outside the range 1 10 MJ the curves are extrapolated linearly Finally for the ifedrv 0 case the user inputs single values for the driver efficiency drveff and target gain tgain Chapter 3 Physics Engineering and Other Models 51 Constraint equation no 50 can be turned on to enable the ignition repetition rate to remain below a user specified upper limit rrmax iteration variable no 86 frrmax is the associated f value see Section 2 4 The other iteration variables relevant for the IFE model are nos 81 85 edrive drveff tgain chrad and pdrive see Table 2 3 3 8 Safety and Environment Models At present the neutronics activation and inventory calculations comprise the safety and environment models in the code The models comprising the safety and environmental calculations 18 within the code are all called from routine FISPAC They are only performed once at the end of each run as they take a relatively long time to evaluate and the results are only used for diagnostic purposes no constraints are imposed at present to minimise doses for instance N B These models are currently not available in the present version of the code 3 8 1 Neutronics The neutronics module predicts the neutron flux spectra in the inboard and outboa
101. ting power options Stellarators require no current drive although provision for auxiliary heating does need to be present The method by which auxiliary heating power is supplied is determined by the switch isthtr isthtr 1 electron cyclotron resonance heating isthtr 2 lower hybrid heating isthtr 3 neutral beam injection The value of variable pheat determines the actual amount of auxiliary heating power in Watts to be applied to the plasma This variable may be used as an iteration variable no 11 Switch ignite may be used if necessary see Section 3 1 10 3 3 5 2 Machine configuration There are a large number of possible stellarator configurations The one chosen for the PROCESS model is based on the HELIcal Advanced Stellarator Helias concept in which all the coils resemble distorted non planar TF coils no helical coils or tokamak like PF coils are present This approach was chosen because at the time the model was introduced into the code the Helias was the most promising stellarator concept for a power plant with a modular engineering design and optimised plasma MHD and magnetic field properties 8 Furthermore this choice also enabled the coil engineering issues to be coded easily by simply modifying the existing PROCESS superconducting TF coil model The coil geometry is scaled from the Wendelstein VII X device which is based on a five field period Helias configuration 3 5 2 1 Machine build Since a stel
102. tion of cable conductor 0 001DO 1 000DO 60 cpttf current per turn in the TF coils 0 001D0 4 000D4 61 gapds gap between vacuum vessel and inboard shield 0 000D0 10 00D0 62 fdtmp value for 1st wall coolant temperature rise limit equation 38 0 001DO 1 000DO 63 ftpeak value for 1st wall peak temperature limit equation 39 0 001DO 1 000DO 64 fauxmn value for minimum auxiliary power limit equation 40 0 001DO 1 000DO 65 tohs OH coil swing time 0 100D0 1 000D3 66 ftohs value for OH coil swing time limit equation 41 0 001D0 1 000DO 67 ftcycl value for minimum cycle time limit equation 42 0 001D0 1 000D0 68 fptemp value for maximum centrepost temperature limit equation 44 0 001D0 1 000DO 69 rcool average radius of centrepost coolant channel 0 001D0 0 010D0 70 vcool maximum centrepost coolant flow speed at midplane 1 000D0 1 000D2 71 fq value for minimum edge safety factor limit equation 45 0 001D0 1 000DO 72 fipir value for maximum lp L 0g limit equation 46 0 001DO 1 000DO 73 scrapli inboard scrape off layer thickness 0 000D0 10 00DO 74 scraplo outboard scrape off layer thickness 0 000D0 10 00DO 75 tfootfi ratio of TF coil outboard inboard leg thickness 0 200D0 5 000D0 76 frfptf f value for TF coil toroidal thickness limit equation 47 0 001D0 1 000DO 77 t tort TF coil toroidal thickness 0 050D0 2 000D0 78 rfpth RFP pinch parameter O 0 010DO 1 800DO 79 fbetap f
103. tructure The input file comprises a number of lines reminiscent of the Fortran NAMELIST format used by some programs to read in data Except for comment lines that start with a character each line is of the form variable value where variable is the name of one of the input parameters or iteration variables listed in the variable descriptor file and value is the usually numerical initial value required for that variable Arrays 54 Chapter 4 Execution of the Code 55 as opposed to scalar quantities are treated differently see below Variables can be specified in any order in the input file The routines that read in and parse the data from the input file are in source file input 90 They allow a great deal of error trapping to be carried out at the input stage All input data are screened for non sensible values directly this is a useful feature of the code since without such intervention modern computers are notorious at not terminating programs when an arithmetically impossible or undefined operation NaN error is encountered 4 1 3 Format rules The following rules must be obeyed when writing an input file 1 Each variable must be on a separate line 2 Variable names can be upper case lower case or a mixture of both 3 Spaces may not appear within a variable name or data value 4 Other spaces within a line and trailing spaces are ignored 5 Commas are not necessary between variables 6 Data
104. uce electricity The neutron may also react with a lithium nucleus present in the blanket to produce a tritium nucleus which can be re used as fuel The competing requirements of heating and tritium synthesis mean that a neutron multiplier must be present to ensure balance between tritium destruction and creation The blanket therefore contains beryllium to fulfil this purpose As with the first wall the blanket has a relatively short lifetime because of the high neutron fluence Steel and vanadium may be used as structural materials within the blanket which is cooled either by gaseous helium or by pressurised water 3 1 5 1 Full thermodynamic blanket model Switch lblnkt determines whether the blanket is to be simulated using a full thermodynamic model 33 lblnkt 1 or simply assumed to be made up of relevant materials see Section 3 1 5 2 in Chapter 3 Physics Engineering and Other Models 31 user defined proportions The former model also performs a self consistent calculation of the thermal to electric conversion efficiency whereas the latter simply uses the input value etath The following switches control the details of the full thermodynamic model of the blanket e Cooling channel geometry The value of switch astr determines whether the cooling channels have a circular cross section astr 1 or an annular cross section astr 2 The latter case is the default e Cooling channel orientation The value of switch estr dete
105. ue for net electric power limit equation 16 1 000DO 1 000DO 26 ffuspow value for fusion power limit equation 9 0 001DO 1 000DO 27 fhldiv value for divertor heat load limit equation 18 0 001DO 1 000DO 28 fjtfc value for T F coil current density limit equation 23 0 100DO 1 000DO 29 bore machine bore 0 100D0 10 00DO 30 fmva value for MVA limit equation 19 0 010DO 1 000DO 31 gapomin minimum gap between outboard shield and vacuum vessel 0 001D0 10 00DO 32 frminor value for minor radius limit equation 21 0 001DO 1 000DO 33 fportsz value for port size limit equation 20 0 010D0 1 000DO 34 fdivcol value for divertor collisionality limit equation 22 0 001D0 1 000D0 35 fpeakb value for peak toroidal field limit equation 25 0 001DO 1 000DO 36 fbetatry value for Troyon beta limit equation 24 0 001DO 1 000D0 37 coheof OH coil current density at end of flat top 1 000D5 1 000D8 38 fjohc value for OH coil current at EOF limit equation 26 0 010D0 1 000DO 39 fjohcO value for OH coil current at BOP limit equation 27 0 001D0 1 000DO 40 fgamcd value for current drive gamma limit equation 37 0 001D0 1 000DO 41 fcohbop OH coil current density ratio BOP EOF 0 001DO 1 000DO 42 gapoh gap between OH coil and bucking cylinder 0 000DO 10 00DO 43 cfe0 seeded high Z impurity fraction 1 00D 6 3 00D 3 44 fvsbrnni fraction of volt seconds from non inductive means 0 001DO 1 000DO
106. ue that occasionally removes problems due to unfeasible results particularly if an error code ifail 3 is encountered during an optimisation run is to adjust slightly one of the limits imposed on the iteration variables even if the limit in question has not been reached This subtly alters the gradients computed by the code during the iteration process and may tip the balance so that the code decides that the device produced is feasible after all For instance a certain component s temperature might be 400 K and its maximum allowable temperature is 1000 K Adjusting this limit to 900 K which will make no difference to the actual temperature may be enough to persuade the code that it has found a feasible solution Similarly the order in which the constraint equations and iteration variables are stored in the icc and ixc arrays can make the difference between a feasible and unfeasible result This seemingly illogical behaviour is sadly typical of the way in which the code works Note added 17 01 2013 It has been found that during optimisation runs the iteration variable indicated by the final specified element in array ixc i e ixc nvar does not finish the run with consistent values in the output file its value is roughly 0 1 less than the correct value The reason is partly understood but difficult to correct in the source code A quick fix is to increment nvar by one and add another iteration variable to the end of ixc which will ha
107. uit stress limit SCTF L 49 56 57 58 59 60 24 33 TF coil Toperational Lcritical limit SCTF L 50 56 57 58 59 60 24 34 TF coil dump voltage limit SCTF L 51 52 56 57 58 59 60 24 35 TF coil Jwinding pack protection limit SCTF L 53 56 57 58 59 60 24 36 TF coil temperature margin limit SCTF L 54 55 56 57 58 59 60 24 37 current drive gamma limit L 40 47 38 first wall coolant temperature rise limit PULSE L 62 39 first wall peak temperature limit PULSE L 63 40 minimum injection power for ignition limit PULSE L 64 41 OH coil swing time limit PULSE L 66 65 42 cycle time limit PULSE L 67 65 17 43 average centrepost temperature TART C 69 70 13 44 peak centrepost temperature limit TART L 68 69 70 45 edge safety factor limit TART L 71 1 2 3 46 Ip Irod limit TART L 72 2 60 47 TF coil toroidal thickness RFP STELLARATOR L 76 77 13 3 48 poloidal beta limit L 79 2 3 18 49 reversal parameter lt 0 RFP L 80 78 3 1 50 IFE repetition rate limit IFE L 86 51 Startup volt seconds consistency PULSE C 16 29 3 1 Table 2 1 Summary of the constraint equations present in PROCESS Consistency equations are marked C limit equations are marked L Some non exhaustive iteration variable numbers see Tables 2 2 and 2 3 that directly affect the associated constraint equations are given the one listed first being the most relevant Chapter 2 Program Overview The Fundamental Concepts 15 li
108. unninethesGodes pias pia Sok cog aw a de a ek Ee ee A 4 3 1 Non optimisation mode 0 a 432 Optimisation modes 4 25 core gk i ee Re RM Pd eee ee a TAA E Aa 4 45 Problem Solving ti ds doy BOR Ree Be ee Ee Bee he ee ee Be S AAA General problems cio dl dvd i Bh ea be He a ek Sa es ae 4 4 2 Optimisation problems 0 0 e LA Unteasible results a 4 25 a a HR ee ee Sib eS Ed AAA Hints sl bday we haben SE OA Gk BS bh ody ee a ee eS Inclusion of Additional Variables and Equations oul Input Parameters iis sh hae eet ite oop Oe we AS ah ee oe ee SS E 52 Iteration Variables ADA eee hes en es EE 5 3 Other Global Variables cc A ee a a Be FA Constraint Equations gt bits ais ave PR LR ae oe es ee a Jos Hipuresvob Merits ariki As eth Be a ele ek Me UA at Soe EA SE ee BA at 5 6 Scanning Varia bles yz a aes gale LR Ae ae a Es ee a Ra Code Management Utilities 6 1 Makefile A ee ee ee a oe ee es 6 2 Automatic Documentation 54 54 54 54 55 56 56 56 58 59 59 60 60 62 63 63 63 64 64 65 65 7 Acknowledgements amp Bibliography A Non optimisation Input File B Optimisation Input File C Source Code Documentation 67 71 74 77 Chapter 1 Introduction 1 1 Rationale During the course of studies into a proposed fusion power plant there may be times when questions of the following type arise Are the machine s physics and engineering parameters consistent wi
109. value for poloidal beta limit equation 48 0 001DO 1 000DO 80 frfpf f value for RFP reversal parameter limit equation 49 0 001DO 1 000DO 81 edrive IFE driver energy 1 000D5 5 000D7 82 drveff IFE driver wall plug to target efficiency 0 010D0 1 000DO 83 tgain IFE target gain 1 000D0 500 0DO 84 chrad radius of IFE chamber 0 100D0 20 00D0 85 pdrive IFE driver power reaching target 1 000D6 2 000D8 86 frrmax f value for maximum IFE repetition rate equation 50 0 001DO 1 000DO 87 helecmw electrical power required for hydrogen production 1 000D0 4 000D3 88 hthermmw thermal power required for hydrogen production 1 000D0 4 000D3 Table 2 3 Iteration variables 51 to 88 present in PROCESS The f values correspond to the given constraint equations see Table 2 1 The other iteration variables are shown in Table 2 2 Chapter 2 Program Overview The Fundamental Concepts 18 minmax description 1 plasma major radius 2 ratio of fusion power to input power 3 neutron wall load 4 total TF coil PF coil power 5 ratio of fusion power to injection power 6 cost of electricity 47 direct cost if ireactor 0 Hi constructed cost otherwise 8 aspect ratio 9 divertor heat load 10 toroidal field on axis 11 injection power 12 hydrogen plant capital cost 13 hydrogen production rate 14 pulse length Table 2 4 Summary of the available figures of merit in P
110. ve no effect on the convergence for instance use an f value for a constraint equation which has not been turned on Then it will be this redundant variable which will have an inconsistency but this is of no consequence Unfeasible cases often produce unrealistic machines so one should not believe the output values from these runs Unfortunately the stationary scan method sometimes though not always fails to help these cases since it will tend to keep starting the run at the same point Ill defined problems sometimes produce arithmetic errors for obscure reasons Though a great deal of work has been performed on the code to improve its standard there can be no guarantee that PROCESS is entirely bug free simply because of its large size Rarely then it may be that an unfeasible result indicates that the code has encountered a programming error although its precise location will be almost impossible to find by simply examining the output file It may be the case that the act of satisfying all the required constraints is impossible No machine can exist if the allowed operating regime is too restrictive or if two constraint equations require conflicting parameter spaces In this case some relaxation of the requirements is needed for the code to produce a successful machine design Chapter 4 Execution of the Code 62 4 4 4 Hints The above sections should indicate that it is the complex interplay between the constraint equations and th
111. y equations 1 2 10 11 and 7 are activated together with limit equations 16 5 and 24 refer to Table 2 1 This example assumes that neutral beam current drive is present equation 7 with variable 7 and that the net electric power is to be fixed at 1200 MW Note the optional but beneficial practice of vertically aligning corresponding equations and variables constraint equation 16 has no corresponding iteration variable which would normally be no 25 fpnetel as we want the net electric power to be fixed at the value given by pnetelin Since in non optimisation mode the number of variables must be equal to the number of equations we have scope to add a free iteration variable refer to Tables 2 2 and 2 3 in this case no 4 electron temperature to help raise the fusion power sufficiently to obtain the required net electric power Finally note the Chapter 4 Execution of the Code 58 use of the density and Troyon beta limit equations 5 and 24 respectively the final values of the corresponding f values will indicate if the limits are exceeded and by how much On running PROCESS and hopefully achieving a feasible result examination of the output may well show up discrepancies between some of the parameter values produced and their known values if available Remember that of all the variables shown in the variable descriptor file with a default value only those declared as active iteration variables can change from th

A User Guide to the PROCESS Systems Code

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