1. Progress on Systems Code and Revision of Previous Results J. F. Lyon, ORNL ARIES Meeting Sept. 16, 2004

2. What’s New Since June ARIES Meeting Progress on Systems/Optimization Code – changes required and progress to date – issues and next steps Revisions to 1-D POPCON calculations – corrected He calculation – edge T(r) and n(r) pedestals; profile and sensitivity studies Additional 0-D calculations – examined two A  cases for NCSX and extended scaling with for all cases Comments on LHD reactor systems study

3. Systems Code Purpose: integrate coil and plasma geometry, reactor constraints and costing Starting point -- last (mis)used in SPPS study – code written for tokamaks, revised for helical-coil stellarators (rotating ellipse, calculated B max interpolating from database) – has ~ 7400 lines of code, highly interconnected – written ~15 years ago and last used ~10 years ago on computer platforms using math routines that no longer exist Changes needed even for relative comparisons – incorporate modular coil geometry (main components) – update physics & engineering (scaling, profiles, limits) – consistent treatment of impurities and edge – new models for blankets, shields, coils, structure – new costing for main components (waiting for numbers) – updated costing of other cost accounts (need consultation) – incorporation of maintenance periods blue -- (partly) done, black -- in progress, red -- information needed

4. MHHOPT Reactor Optimization Code input: physics, coil, costing, geometry, reactor component parameters and constraints plasma/profile solver T e (r), T i (r), n e (r), n i (r), n Z (r), E r (r), , Z eff, P rad, P fusion, P ,loss, P wall, P divertor,  E, etc. masses of coil and structure, j, B max bl/sh volumes, TBR, access, radial build forces on coil and structure costs of all ARIES accounts, P electric evaluate all parameters & constraints output: all parameters and profiles nonlinear optimizer optimizes targets with constraints existing parts being updated waiting for information can update no plans to use

5. Systems Optimization Code Minimizes core cost or size or COE with constraints for a particular plasma and coil geometry using a nonlinear constrained optimizer Iterates on a number of optimization variables – plasma:,, H-ISS95; coils: width/depth of coils – reactor variables: B 0, Large number of constraints allowed (=, ) – P electric, ignition margin,  limit, ISS-95 multiplier, radial build, coil j and B max, plasma-coil distance, clearance between coils, blanket and shielding thicknesses, TBR, access for divertors and maintenance, etc. Large number of fixed parameters for plasma and coil configuration, plasma profiles, transport coefficients, cost component algorithms, and engineering model parameters Calculates a large number of parameters – plasma: , Z eff, power components (radiation,  i,  e),  losses, etc. – coils: components volumes and costs, j, B max, forces – reactor variables: blanket volumes, TBR, neutron wall loading, divertor area, access between coils, radial build, etc. – costs: equipment cost, annual operating cost, total project cost, CoE

6. Input Parameters Configuration geometry – plasma aspect ratio, surface area, coil aspect ratio, closest approach aspect ratio,  limit,  (r), ripple effective (r), etc. Reactor component parameters – inside & outside shield thickness; coil width and depth – blanket thickness inside & outside, under and between coils – coil case & vacuum vessel thickness, dimensions of modular coils and VF coils; scrapeoff thickness – first wall and reflector thickness; coil to vacuum vessel gap – allowable nuclear heating in coil; j max (B) – blanket energy multiplication Cost assumptions – modular and VF costs /kg – costs and multipliers for blanket and shield – duty factor, inflation, safety assurance

7. Four Configurations Now Studied NCSX MHH2 port or sectoraccess (end)through accessports both quasi-axisymmetric / constant for each case, can’t change separately

8. Cost Estimations

10. FOCI components: volume density frac. cost frac. thick. frac. density (1992) cost (kg/m^3) ($/kg) (m) SiC-comp 0.730 3200.000 0.950 405.771 1.000 PbLi 0.270 9400.000 0.000 15.771 0.000 Total FW 2219.200 405.771 0.014 0.014 breeding zone 0.336 SiC-comp 0.170 3200.000 0.950 405.771 1.000 PbLi 0.830 9400.000 0.000 15.771 0.000 reflector 0.000 Total BL(ib) 516.800 405.771 0.336 breeding zone 0.286 SiC-comp 0.170 3200.000 0.950 405.771 0.313 PbLi 0.830 9400.000 0.000 15.771 0.000 breeder 2 0.450 SiC-comp 0.193 3200.000 0.950 405.771 0.559 PbLi 0.773 9400.000 0.000 15.771 0.000 W 0.034 19300.000 1.000 82.919 0.128 reflector 0.000 Total BL(ob) 960.759 270.949 0.736 reflector 0.000 SiC-comp 0.150 3200.000 0.950 405.771 0.336 PbLi 0.100 9400.000 0.000 15.771 0.000 RAF 0.750 7800.000 1.000 62.438 0.664 Total BL(dv) 6306.000 87.265 0.000 reflector 0.000 SiC-comp 0.150 3200.000 0.950 405.771 0.336 PbLi 0.100 9400.000 0.000 15.771 0.000 RAF 0.750 7800.000 1.000 62.438 0.664 Total BL(bv) 6306.000 87.265 0.000 HT shield 0.240 SiC-comp 0.150 3200.000 0.950 405.771 0.307 PbLi 0.100 9400.000 0.000 15.771 0.000 W 0.047 19300.000 1.000 82.919 0.125 B-FS 0.703 7800.000 1.000 62.438 0.568 Total SH(ib) 6846.500 88.019 0.240 HT shield 0.150 SiC-comp 0.150 3200.000 0.950 405.771 0.336 PbLi 0.100 9400.000 0.000 15.771 0.000 B-FS 0.750 7800.000 1.000 62.438 0.663 LT shield ( 0.000) 0.000 Total SH(ob) 6306.000 87.265 0.150 HT shield 0.280 RAF 0.150 7800.000 1.000 62.438 0.037 Void 0.100 0.000 1.000 0.000 0.000 WC 0.750 15600.000 0.950 65.937 0.374 LT shield ( 0.400) 0.400 RAF 0.150 7800.000 1.000 62.438 0.053 Void 0.100 0.000 1.000 0.000 0.000 WC 0.750 15600.000 0.950 65.937 0.535 Total SH(BC) 12285.000 65.604 0.700 HT shield 0.150 SiC-comp 0.150 3200.000 0.950 405.771 0.112 PbLi 0.100 9400.000 0.000 15.771 0.000 RAF 0.750 7800.000 1.000 62.438 0.221 LT shield ( 0.300) 0.300 SiC-comp 0.150 3200.000 0.950 405.771 0.224 Void 0.100 0.000 0.000 0.000 0.000 B-FS 0.750 7800.000 1.000 62.438 0.443 Total SH(dv) 6306.000 87.265 0.470 HT shield 0.150 SiC-comp 0.150 3200.000 0.950 405.771 0.107 PbLi 0.100 9400.000 0.000 15.771 0.000 RAF 0.750 7800.000 1.000 62.438 0.212 LT shield ( 0.300) 0.300 SiC-comp 0.150 3200.000 0.950 405.771 0.215 Void 0.100 0.000 0.000 0.000 0.000 B-FS 0.750 7800.000 1.000 62.438 0.424 Total SH(bv) 6306.000 87.265 0.470 RAF 0.130 7800.000 1.000 62.438 0.091 Void 0.220 0.000 0.000 0.000 0.000 WC 0.650 15600.000 0.950 65.937 0.909 Inboard VV 10647.000 65.604 0.400 RAF 0.300 7800.000 1.000 62.438 1.000 Void 0.700 0.000 0.000 0.000 0.000 Outboard VV 2340.000 62.438 0.250 RAF 0.130 7800.000 1.000 62.438 0.167 Void 0.220 0.000 0.000 0.000 0.000 B-FS 0.650 7800.000 1.000 62.438 0.833 O/B (UC) VV 6084.000 62.438 0.200 RAF 0.130 7800.000 1.000 62.438 0.167 Void 0.220 0.000 1.000 0.000 0.000 B-FS 0.650 7800.000 1.000 62.438 0.833 Divertor VV 6084.000 62.438 0.400

11. Cost Estimations HT shield 0.280 RAF 0.150 7800.000 1.000 62.438 0.037 Void 0.100 0.000 1.000 0.000 0.000 WC 0.750 15600.000 0.950 65.937 0.374 LT shield ( 0.400) 0.400 RAF 0.150 7800.000 1.000 62.438 0.053 Void 0.100 0.000 1.000 0.000 0.000 WC 0.750 15600.000 0.950 65.937 0.535 Total SH(BC) 12285.000 65.604 0.700 HT shield 0.150 SiC-comp 0.150 3200.000 0.950 405.771 0.112 PbLi 0.100 9400.000 0.000 15.771 0.000 RAF 0.750 7800.000 1.000 62.438 0.221 LT shield ( 0.300) 0.300 SiC-comp 0.150 3200.000 0.950 405.771 0.224 Void 0.100 0.000 0.000 0.000 0.000 B-FS 0.750 7800.000 1.000 62.438 0.443 Total SH(dv) 6306.000 87.265 0.470 HT shield 0.150 SiC-comp 0.150 3200.000 0.950 405.771 0.107 PbLi 0.100 9400.000 0.000 15.771 0.000 RAF 0.750 7800.000 1.000 62.438 0.212 LT shield ( 0.300) 0.300 SiC-comp 0.150 3200.000 0.950 405.771 0.215 Void 0.100 0.000 0.000 0.000 0.000 B-FS 0.750 7800.000 1.000 62.438 0.424 Total SH(bv) 6306.000 87.265 0.470 RAF 0.130 7800.000 1.000 62.438 0.091 Void 0.220 0.000 0.000 0.000 0.000 WC 0.650 15600.000 0.950 65.937 0.909 Inboard VV 10647.000 65.604 0.400 RAF 0.300 7800.000 1.000 62.438 1.000 Void 0.700 0.000 0.000 0.000 0.000 Outboard VV 2340.000 62.438 0.250 RAF 0.130 7800.000 1.000 62.438 0.167 Void 0.220 0.000 0.000 0.000 0.000 B-FS 0.650 7800.000 1.000 62.438 0.833 O/B (UC) VV 6084.000 62.438 0.200 RAF 0.130 7800.000 1.000 62.438 0.167 Void 0.220 0.000 1.000 0.000 0.000 B-FS 0.650 7800.000 1.000 62.438 0.833 Divertor VV 6084.000 62.438 0.400 RAF 0.130 7800.000 1.000 62.438 0.167 Void 0.220 0.000 1.000 0.000 0.000 B-FS 0.650 7800.000 1.000 62.438 0.833 Bottom VV 6084.000 62.438 0.400 SS 0.180 7800.000 1.000 68.657 1.000 Void 0.820 0.000 0.000 0.000 0.000 Cryostat 1404.000 68.657 0.020 SiC-comp 0.460 3200.000 0.950 405.771 1.000 PbLi 0.540 9400.000 0.000 15.771 0.000

12. Output Plasma parameters and profiles –,, W plasma,  E, H factors,,  *, n Fe / n e, n O / n e, Z eff –, T i0, T i,edge, T e0, T e,edge,  0 / T e0,, n i0, n e0, / n Sudo, n DT / n e, – ignition margin, P fusion, P electric, P neutron, P charged, P divertor, components of P rad and P wall, P loss Coil parameters – modular & VF coil dimensions, currents, forces, inductance, stored energy, j, B max, case thickness Reactor parameters – blanket area accessible and blocked, inboard and outboard shield thickness, cryostat gap, access between coils

13. Output (cont.) Cost elements – land & structures; power supplies; impurity control; heat transport; power conversion; startup power – blankets & first wall; shields; modular & VF coils; structure; vacuum vessel – turbine plant equipment; electric plant equipment; misc. plant equipment; special materials; total direct cost – construction; home office; field office; owner’s costs; project contingency; construction interest; construction escalation; total capital cost – unit direct cost; unit base cost; total unit cost; capital return; O&M costs; blanket/first wall replacement; decommissioning allowance; fuel costs; cost of electricity Summary of all component masses & mass utilization Dimensions of each element in the radial build

14. Revision to 1-D (POPCON) Calculations Purpose of 1-D calculations: – test different profiles, physics models and assumptions for incorporation into systems code – examine effect of assumptions on operating point Corrected error in calculation of helium concentration – this affected n DT /n e, P fusion, etc. – removes earlier concern on  He /  E 6) Added edge pedestals to simulate edge cooling from enhanced (neoclassical impurity) edge radiation – small effect, but more consistent with large edge radiation Will later update confinement scaling ISS-95 --> ISS-04 – small effect, but dimensionally correct and fits data better  basis for assumed H-ISS values

15. Effect of Correction to n He Calculation Previously required  He */  E 6 OK Minimum H-ISS95 ==> 3.7 for a stable operating point

16. NCSX-1:  E /  E ISS-95 = 4.2, = 9.5 keV, = 3.5 10 20 m –3, = 6.1% operating point thermally stable branch 2-GW P fus 6% ignition contour (P in = 0) n Sudo 20100 20 P in = 10 MW 10 20  E ISS-95 = 0.26P heating –0.59 0.51 0.83 0.65 2.21  2/3 0.4 H-ISS95 =  E /  E ISS-95

17. Plasma Parameters from 1-D Power Balance ISS-95 of 3.75 to 4.2 is required; present stellarator experiments have up to 2.5 ISS-2004 scaling indicates  eff –0.4 improvement, so compact stellarators should have high H-ISS values

18. ISS-95 Confinement Scaling Is Being Updated  E ~  eff –0.4 should give large H-ISS for low  eff NCSX configuration Lays basis for higher H-ISS values ~  eff –0.4 ? H. Yamada, J. Harris et al. EPS 2004

19. H-ISS95 Is Sensitive to Some Assumptions Need to control alpha-particle power loss and helium recycling back into plasma -- both divertor issues

20. Parameters Insensitive to Profile Assumptions

21. 0-D (Volume-Average) Calculations PURPOSE Allows analytic treatment of – connection between different device parameters – effect of different assumptions and constraints Validates modules needed for systems code ADDITIONS NCSX case with different A  (2/25/03 case) Superconducting coil constraint Varied p wall from 1 to 3.3 MW/m 2 (assumed peak 1.5 times higher) to study variation in global parameters

22. Added 2/25/03 (NCSX-2) Case Smaller plasma-coil spacing leads to less convoluted coils and lower B max / Minimum coil-coil separation distance determined k max

23. Scaling Relations for Reactor Parameters Fusion power red indicates configuration-specific parameters – P fusion ~ 2 4 3 /A p – p n,wall /1.5 = = 0.8P fusion /[ 2 (A wall / 2 )] Coil-geometry related sh = sh 2 + c x ln( ) – = A  (so + fw + bl + sh + vv + gaps + 0.5dk 1/2 ) constraint – j coil = I coil /d 2 = [I coil / ]/d 2 – j SC (B max ) and d, k from B max / Cost-related (rationale for emphasis – blanket, shield, vacuum vessel, coil structure ~ wall area ~ P fusion /, but configuration constrained – fw/blanket replacement ~ frequency x cost ~ 1/ x P fusion / ~ P fusion independent of but actual cost depends on specifics – volume of coils ~ L coil I coil /j coil ~ C x P fusion 7/8 /( 5/8 1/2 j coil ) C = (L coil / )(I coil / )A p 1/2 /(A wall / 2 ) 5/8, C/j coil constant

24. NCSX-1 Values Determined by p n,max = 5 MW/m 2 = 6.22 m, = 6.48 T, B max = 12.65 T j coil approximately constant,, B max & d are constrained for other cases by radial build to lower (2.13–2.67 MW/m 2 )

25. Main Reactor Parameters from 0-D Study Wall (blanket, shield, structure, vacuum vessel) area smallest for NCSX-1  chose NCSX-1 (8/1/03 case) for more detailed study

26. LHD Reactor Study (T. Dolan) Based on LHD plasma and coil configuration Uses port maintainence scheme and three blanket + cooling models (RAFS + Flibe, Va + Li, SiC + PBLi) Based on Miller’s costing code with some new values H-ISS95 limited to 2, to 4%, B max = 13 T – consistent with LHD performance, higher  eff value Base case has R = 14.4 m, B axis ~ 5.5 T, H-ISS95 = 1.7, = 3%, P fusion = 4.5 GW (P electric = 1.94 GW), = 2.1 MW/m 2, j coil = 30 MA/m 2, k = 2, f loss = 0.1,  = 40% Studied CoE variation with T 0, n & T profiles,, k, plasma-wall dist, shield-coil gap, B max,, P electric

27. Summary Progress on Systems/Optimization Code – added modular coil geometry and updated physics models – treatment of impurities and edge and new models for blankets, shields, coils, structure in progress – information needed on new costing for main components and updated costing of other cost accounts Revised 1-D POPCON calculations – corrected He calculation – insensitive to profiles, edge n(r) & T(r) pedestals – more sensitive to alpha-particle losses and helium  p * 0-D -- added 2/25 NCSX case, superconducting coil constraint, and extended scaling with Examined LHD reactor systems study