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Determination of ARIES-CS Plasma & Device Parameters and Costing J. F. Lyon, ORNL ARIES-CS Review Oct. 5, 2006

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Topics Factors that Determine the ARIES-CS Device Parameters Optimization/Systems Code: device and plasma parameters, and costing Results for the Reference Case Sensitivity to Parameter Variations, Blanket & Shielding Models, and Different Magnetic Configurations

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Goal: Stellarator Reactors Similar in Size to Tokamak Reactors Need a factor of 2-4 reduction compact stellarators

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3 Plasma and Coil Configurations Studied NCSX ARE MHH2 only the quasi-axisymmetric type of compact stellarators were studied

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Magnetic Configuration Optimization Provides Basic Information (1) Basic configuration properties: – (r/a) and eff (r/a) -- needed for confinement calculations – stable Scaled plasma parameters: R / a pl & surface area/ R 2 ; then R determines – a pl, plasma volume – plasma surface area (for calculation of component volumes, costs) * for approx. fixed thicknesses, volumes of blanket, shield, structure, vacuum vessel ~ wall area ~ R 2 – volume of coils ~ L coil I coil /j coil ~ R 1.2 Minimum value for R (hence cost) depends on various constraints Using R = R axis for convenience

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R Depends on Available Plasma-Coil Space Need adequate space between plasma edge and coil center for blanket, shielding, vacuum vessel, coil, etc. – R / min = constant R = [ R / min ] NCSX-type plasmas close to coils only over small part of the wall area – allows a tapered blanket and shielding to reduce R – extent depends on R ; impacts the T breeding ratio Approach not possible for MHH2 configurations because coils are same distance from plasma everywhere R = 7.5 m

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Magnetic Configuration Optimization Provides Basic Information (2) Scaled coil parameters: coil-coil / R, L coil / R, area cws / R 2 ; for a given R determines – coil winding surface area (needed for coil structure calculations) – minimum coil-coil distance (for adequate spacing, avoid overlaps) – coil lengths (needed for calculating coil volume)

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Magnetic Configuration Optimization Provides Basic Information (3) Coil sets with a larger plasma- coil distance min – allow smaller R = [ R / min ] – but require more convoluted coils, resulting in larger B max / B axis smaller allowed B axis for a limit on B max (16 T) * B axis 16 T/ [B max / B axis ]

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Neutronics Calculations Constrain R min Allowable neutron wall power density: ~ P n (~ P e )/ R 2 – p n,wall,max / p n,wall = 2.02 p n,wall,max = 5.26 MW/m 2 – p n,wall,min / p n,wall = 0.12 (low neutron power density at divertor) Similar calculation gives radiation power density on the wall p rad,wall ~ P rad / R 2 – p rad,wall,max / p rad,wall = 1.39 p rad,wall,max = 0.68 MW/m 2 – occurs in a different place from p n,wall,max 20° apart toroidally) p n,wall (, ) U. Wisc.

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Factors Determining the Device Parameters Minimum size ( R ) determined by constraints on – required space for blanket, shield, vacuum vessel, coil, etc. – acceptable neutron wall loading – adequate tritium breed ratio Magnetic field depends on B max / B axis

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Topics Factors that Determine ARIES-CS Device Parameters Optimization/Systems Code: device and plasma parameters, and costing Results for the Reference Case Sensitivity to Parameter Variations, Blanket & Shielding Models, and Different Magnetic Configurations

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Systems Optimization Code Minimizes Cost of Electricity for a given plasma and coil geometry using a nonlinear constrained optimizer Iterates on a number of optimization variables – plasma: T i, n e, conf. multiplier; coils: coil width/depth, clearances – reactor variables: B axis, R Large number of constraints allowed (=, ) – P electric = I GW, and n limits, max. conf. multiplier, coil j vs B max 1.1, max. neutron wall power density, fraction of power radiated, -particle loss rate, etc. Large number of fixed parameters for – plasma and coil configuration, plasma profiles, – transport model, helium accumulation and impurity levels, – SC coil model (j,B max ), blanket/shield concepts, and – engineering parameters, cost component algorithms

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Cost Model Includes Full Geometry Min. distance for blanket & shielding R min from R / min Tritium breeding ratio vs R, shield thickness ~ ln(p n ), etc.

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Unit Costs Used to Determine Component Costs from Volumes Used ARIES-AT and ARIES-RS costing algorithms (based on a tenth-of-a kind power plant) Costs/kg used for each material in L. ElGuebaly's blanket and shielding models Inflation index used to keep costs on the same year basis Cost/kA-m vs j SC and B max from L. Bromberg Studied sensitivity to machining complexity cost factor for each major system (blankets, shielding, manifolds, vacuum vessel, coils) L.Waganer's analysis supports 85% availability assumption

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Determination of Modular Coil Parameters Maximizing toroidal width of the winding pack reduces radial depth –constrained by minimum coil-coil spacing R Use all space available between vacuum vessel and coil winding surface, which minimizes the coil cost –j coil and B max decrease; cost decreases faster than coil volume increases

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Plasma Models for Calculating Performance Plasma modeling assumptions – E = H x E ISS95 where E ISS95 = 0.079 a 2.21 R 0.65 P MW –0.59 n 19 0.51 B 0.83 0.4 – ISS-95 confinement multiplier H determined from power balance – Hollow n e (r) with center/peak = 0.8 (LHD, W 7-AS) – T(r) ~ parabolic 1.5 approx. same p(r) used in MHD calculations – He */ E = 6 for calculating helium accumulation Targeted various plasma metrics (optimization constraints) – ignited plasma -- no auxiliary power input – = 5% (no reliable instability limit, high equilibrium limit) – fraction of alpha-particle power lost 5% – fraction of alpha-particle power radiated 75% (determines %Fe impurity needed) – density 2 x Sudo value = 0.5(PB/Ra 2 ) 1/2 (3 in LHD) Test sensitivity to assumptions and constraints

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Constraints on Plasma n and T (some conflicting) = 5% n T / B axis 2 n < 2n Sudo B axis 0.5 Reduced -particle losses 5% higher nR/T 2 Acceptable n He (from He */ E = 6) for fuel dilution Maximum multiplier on E n 0.51 B 0.84 ; reduced saddle-point power P fus [P E = 1 GW] n 2 f 1 (T) ~ n 2 T 2 (approx.)~ rms 2 B axis 2 P radiation n 2 f 2 (T) ~ n 2 ; target 75% of P e,I ; choose n Z Operating point on stable branch of ignition curve T e,edge set by connection length and T e,divertor < 20 eV

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Magnetic Configuration Optimization Provides Basic Information (4) -particle loss rate depends on plasma n and T So need to determine R axis and B axis, also n and T

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Operating Point Moves to Higher T with Lower P startup as ISS95 Multiplier H Increases H = 2 H = 2.15 H = 2.5 H = 3 T (keV) n (10 20 m –3 ) x

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n e (r) Hollow in Stellarators at Low * Assume n e = n e0 [(1 – (r/a) 12 )(0.66 + 0.34(r/a) 2 ) + n edge /n e0 ], T e = T e0 [(1 – (r/a) 2 ) 1.5 + T edge /T e0 ] p(r/a) very close to that used for stability calculation P NBI = 1 MW, T i (0) = 1.3 keVECH, T e (0) = 1.5 keV P NBI = 6.5 MW, T i (0) = 1.9 keV LHD W 7-AS

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Density, Temperature & Pressure Profiles r/a central dip 1.7% 3.9% 9.7% 17% 25% 35% exper. 10% to 30% r/a Fe

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Treatment of Impurities n e = n DT + Zn Z, so impurities reduce P fusion through reduced n DT 2 and 2 (~ n e + n DT ) 2 ; P fusion ~ n DT 2 ~ 2 B 4 reduced T e (hence T i ) through radiative power loss requires higher B or H-ISS95 or larger R to compensate carbon (Z C = 6) for low Z & iron (Z Fe = 26) for high Z Standard corona model: line radiation and electron-ion recombination p radiation ~ n e n Z f(T e ) Choose n Z ~ n e

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Power Flow Fractions P fusion P neutron P P,loss Divertor First Wall P radiation P particle 80% 20% P rad, div. region 5% 75% 20% 75% 25% P rad, edge 50% P rad,sol 11% 89% 11% 89% Blankets, Shields P electric P pumps, BOP P elec,gross P thermal 116% 90%

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Topics Factors that Determine ARIES-CS Device Parameters Optimization/Systems Code: deice and plasma parameters, and costing Results for the Reference Case Sensitivity to Parameter Variations, Blanket & Shielding Models, Different Magnetic Configurations

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Summary for Reference ARE Case NCSX plasma with ARE coils; modified LiPb/FS/He; H 2 O-cooled internal vacuum vessel with SiC inserts and tapered blanket FINAL DESIGN major radius (m) 7.75 field on axis (T) 5.70 volume avg. density (10 20 m –3 ) 3.58 density averaged temp (keV) 5.73 coil dimensions (m x m) 0.19 x 0.74 FIGURE OF MERIT..................... Cost of Electricity (2004 $) 81.5 mills/kW-hr VARIABLES selected for iteration major radius 5.0 20.0 field on axis 3.0 10.0 ion density 1.0 10.0 ion temperature 1.0 50.0 coil width 0.01 5.0 confinement multiplier 0.10 9.0 n Fe /n e (%) 0 0.02 following CONSTRAINTS were selected: target final ignition = 1 target 1.00 1.00 electric power (GW) 1.0 1.00 tritium breeding ratio 1.1 1.115 R / R min 1 1.002 max. neutron wall load 5.3 5.26 max. volume averaged beta 5% 5% maximum density/n Sudo 2 1.88 max. confinement multiplier 2.0 1.48 min. port width (m)2.0 4.08 core radiated power fraction 75% 75% maximum -particle loss rate 5% 5% maximum field on coils (T)16 15.1 j coil /j max 1 1.00

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Typical Systems Code Results Plasma Parameters central ion temp (keV) 8.63 central ion density (10 20 m –3 ) 7.83 central elec. density (10 20 m –3 ) 8.09 fraction fuel to electrons 0.94 confinement time, taue (sec) 0.96 stored plasma energy (MJ) 430 volume averaged beta (%) 5.0 beta star (%) 8.2 fraction carbon impurity 0 fraction iron impurity 0.008 % fraction helium 2.93 % Z effective 1.11 Power Balance net electric power (MW) 1000 gross electric power (MW) 1167.5 fusion power (MW) 2365.9 thermal power (MW) 2659.5 heating power (MW) 472.3 power in neutrons (MW) 1893.6 radiated power (MW) 354.2 fuel bremsstrahlung (MW) 240.4 iron radiation (MW) 112.9 synchrotron radiation (MW) 0.9 conduction power (MW) 94.5 fusion power to plasma (MW) 472.3 fraction alpha power lost 5.0 % radiated power fraction 75.0 % max neut wall flux (MW/m 2 ) 5.26

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Cost Element Breakdown (2004 M$) Cost 20 (Land) 12.8 constant Cost 21 (Structure) 264.3 Cost 22 (Reactor Plant Equip.) 1642 Cost 23 (Turbine Plant) 294.2 ( th P th ) 0.83 + constant Cost 24 (Electric Plant) 133.8 ( th P th ) 0.49 Cost 25 (Misc. Plant Eq.) 67.7 ( th P th ) 0.59 Cost 26 (Spec. Matls.) 164.3 V LiPb Cost 27 (Heat Rejection) 53.3 P th – ( th P th ) Cost 90 (Total Direct Cost) 2633 Costs 91-98 = construction, home office, field office, owners costs, project contingency, construction interest, construction escalation Cost 99 (Total Capital Costs) 5080 = Costs 90 thru 98 = 1.93 x Cost 90

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CoE Breakdown (2004 mills/kW-hr) Capital return 65.9 O&M 10.0 Replacements 4.91 Decommissioning allowance 0.61 Fuel 0.04 Total CoE 81.5 Total CoE (1992 $) 66.4

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Stellarator Geometry-Dependent Components only Part of the Cost Fractions of reactor core cost modular coil 12.5% coil structure 19.9% blanket, first/back wall 8.7% shield and manifolds 26.5% cryostat 13.7% plasma heating 2.9% power supplies 6.8% Reactor core is 37.8% of total direct cost, which includes other reactor plant equipment and buildings Total direct cost is 51.8% of total capital cost Replaceable blanket components only contribute small % to COE a 30% increase in the cost of the complex components only results in a 8% increase in the total capital cost; 50% 13% increase

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Component Mass Summary (tonnes) total modular coil mass 4097 conductor mass 553 coil structure mass 3544 strongback 1443 inter-coil shell 2101 total blanket, first, back wall 1019 first wall mass 63.1 divertor mass 76.5 front full blanket mass 441 front blanket back wall 187 second blanket mass 130 tapered blanket mass 941 total vacuum vessel mass 1430 full blanket vac vessel mass 1123 tapered vac vessel mass 307 primary structure mass 2885 shield mass and back wall 2805 ferritic steel shield mass 1685 tapered FS shield mass 109 tapered back wall mass 71.0 tapered WC shield mass 941 penetration shield mass 266 mass of manifolds 1345 Total nuclear island 10,962 Cryostat mass 1333 Mass of LiPb in core 3221

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Component Cost Summary (2004 M$) total mod coil + str cost 323 mod coil SC cost 103 mod coil winding cost 22.1 coil structure cost 198 strongback 80.8 inter-coil shell 118 total blanket, first/back wall 102 first wall cost 6.5 divertor cost 7.9 front full blanket cost 38.3 front blanket back wall cost 31.5 second blanket cost 7.2 tapered blanket cost 10.6 total vacuum vessel cost 64.0 full blanket vac vessel cost 50.2 tapered vacuum vessel cost 13.8 primary structure cost 83.3 shield cost and back wall 135 ferritic steel shield cost 65.4 tapered FS shield cost 4.7 tapered back wall cost 30.5 tapered WC shield cost 34.5 penetration shield cost 20.7 cost of manifolds 108 total nuclear island cost 753 cryostat cost 59.8 cost of LiPb in core 65.7 nuclear island + core LiPb 849

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Comparing Masses with AT, RS & SPPS

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Comparison of General Plant Costs (1992 $) Only Reactor Plant Equip. contains stellarator costs

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Topics Factors that Determine ARIES-CS Device Parameters Optimization/Systems Code: device and plasma parameters, and costing Results for the Reference Case Sensitivity to Parameter Variations, Blanket & Shielding Models, and Different Magnetic Configurations

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Variations about the Reference Case Variations that affect the size and cost of the reactor – p n,wall limit – B max on modular coils – component complexity factor – full vs tapered blanket/shield – advanced blanket case – ARIES-AT, -RS assumptions – SNS configuration, R/a variation – MHH2 configuration Variations that affect the plasma parameters (base case) – limit – density limit n/n Sudo – -particle loss fraction – ISS-95 confinement multiplier – fraction of power radiated – fraction of SOL power radiated – density profile – temperature profile – edge T e

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p n,wall,max Has Impact on R min As the maximum allowed value for p n,wall increases, R decreases to the R min set by the available plasma- coil space The COE falls because the decreases due to the smaller R are more than the increased cost of coil and structure

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B max Has Modest Impact on R and Costs The decrease in the COE due to R falling with B max is partly offset by the increasing j and B max, which increases the cost of the coils and structure

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Impact of the Beta Limit Below = 5%, R = R min and p n,wall increases with until it hits the wall limit Above = 5%, R is fixed but the COE continues to fall because the decreasing B max reduces the cost of coils and structure

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Tapered/Full and Advanced Blanket Cases Tapered blanket/shield Advanced blanket case

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Magnetic Configurations and Blanket/Shield Options *for LiPb/FS/He case; LiPb/SiC will be lower because thermal higher (a) needed to limit neutron wall power density (b) requires better confinement

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Summary The ARIES-CS device parameters determined by plasma-coil space, neutron wall loading, TBR, B max / B on coils and j vs B max in coils Optimization/Systems code gives integrated optimization for device and plasma parameters, and costing Reference case comparable with previous reactor studies Parameters sensitive to NWL and blanket shield options

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Additional Material

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Cost Element Breakdown COST COMPONENTS in 2004 year M$ Cost 20 (Land) = 12.82 constant Cost 21.1 (site improvements) = 22.65 constant Cost 21.2 (reactor building) = 67.73 V reactor building 0.62 Cost 21.3 (turbine building) = 41.52 ( th P th ) 0.75 + constant Cost 21.4 (cooling system) = 10.01 ( th P th ) 0.3 Cost 21.5 (PS building) = 12.27 constant Cost 21.6 (misc. buildings) = 102.5 constant Cost 21.7 (vent. stack) = 2.42 constant Cost 21 (Structure) = 264.3 (incl. 2% spares) P th = P n x gloem + P

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Cost Element Breakdown (2004 M$) Cost 22.1.1.1 (FW) 6.49 Cost 22.1.1.3 (BL + BW) 80.35 Cost 22.1.1 (Bl/BW & 1st wl.) 86.85 8.72% Cost 22.1.2 (Sh/BW/man) 263.8 26.47% Cost 22.1.3 mod coils 124.4 Cost 22.1.3 VF coils 0.00 (to be added) Cost 22.1.3 divertor 7.89 Cost 22.1.3 mod coil struct 198.5 Cost 22.1.3 (coils + str) 322.9 32.40% Cost 22.1.4 (Heating) 28.60 constant 20 MW Cost 22.1.5 (Primary Str.) 83.27 core volume Cost 22.1.6 (Vac. Sys.) 136.3 cryostat Cost 22.1.7 (Power Sup.) 67.95 constant Cost 22.1.8 (Imp. Control) 6.79 Cost 22.1.9 (Dir. Ener. Conv. 0 Cost 22.1.10 (ECH) = 0 Cost 22.1 (Core) = 996.4

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Cost Element Breakdown (2004 M$) Cost 22.2.1 prim. coolant 298.9 P th 0.55 Cost 22.2.2 interm. coolant 0.00 Cost 22.2.3 sec. coolant 65.83 P th 0.55 Cost 22.2 (Heat transport) 448.0 Cost 22.3 aux. cooling 3.51 P th Cost 22.4 rad. waste 6.25 P th Cost 22.5.1 fuel injection 14.02 constant Cost 22.5.2 fuel processing 16.45 constant Cost 22.5.3 fuel storage 7.01 constant Cost 22.5.4 atm T recover. 3.33 constant Cost 22.5.5 H2O T recover. 7.01 constant Cost 22.5.6 BL T recover. 7.01 constant Cost 22.5 fuel handling 54.82 constant Cost 22.6 other plant equip 57.02 P th Cost 22.7 I&C 44.19 constant Cost 22 (Reactor Plant) 1642 (inc. 2% spare parts)

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Further Modeling of Impurities Is Possible Present approach – assumes n C = f C n e & n Fe = f Fe n e ; f Z is constant thruout plasma, so n Z (r) has the same (slightly hollow) profile as n e (r) Alternative: neoclassical model for impurity profiles – n Z (r) = n e (r) x f Z (n e /n e0 ) Z [T e /T e0 ] –Z/5 – ignore [T e /T e0 ] –Z/5 term -- probably is not applicable in stellarators n Z (r) more peaked near edge since n e (r) is hollow for regime of interest n Z (r) peaked at center if n e (r) peaked C Fe

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Even Flat n e (r) Produces Hollow Impurity Profiles W 7-AS results at high collisionality – Calculations show more extreme impurity edge peaking at lower collisionality

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