Determination of ARIES-CS Plasma & Device

Parameters and Costing

J. F. Lyon, ORNL

ARIES-CS Review Oct. 5, 2006

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

Goal: Stellarator Reactors Similar in Size to Tokamak Reactors

• Need a factor of 2-4 reduction compact stellarators

0

2

4

6

8

10

12

14

0 4 8 12 16 20 24

Average Major Radius <R> (m)

Stellarator Reactors

HSR-5

HSR-4SPPS

CompactStellaratorReactorsARIES

AT ARIESRS

FFHR-1

MHR-S

Circle area ~ plasma areaTokamak Reactors

3 Plasma and Coil Configurations Studied

NCSX

ARE

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

MHH2

• only the quasi-axisymmetric type of compact stellarators were studied

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/apl & surface area/R2;

then R determines apl, plasma volume

– plasma surface area (for calculation of component volumes, costs)

*for approx. fixed thicknesses, volumes of blanket, shield, structure, vacuum vessel ~ wall area ~ R2

– volume of coils ~ LcoilIcoil/jcoil ~ R1.2

• Minimum value for R (hence cost) depends on various constraints

Using R = Raxis for convenience

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

Magnetic Configuration Optimization Provides Basic Information (2)

• Scaled coil parameters: coil-coil/R, Lcoil/R, areacws/R2; 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)

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 Bmax/Baxis

smaller allowed Baxis for a limit on Bmax (16 T)

Baxis ≤ 16 T/ [Bmax/Baxis] 1

2

3

4

5

6

7

8

0.2 0.3 0.4 0.5 0.6 0.7 0.8

d = (cross section)1/2

, m

MHH2-16

MHH2-8

square coil packcross section (k = 1)

NCSXcases

Neutronics Calculations Constrain

Rmin• Allowable neutron wall power density: ~ Pn (~ Pe)/R2

– pn,wall,max/pn,wall = 2.02 pn,wall,max = 5.26 MW/m2

– pn,wall,min/pn,wall = 0.12 (low neutron power density at divertor)

• Similar calculation gives radiation power density on the wall prad,wall ~ Prad/R2

– prad,wall,max/prad,wall = 1.39 prad,wall,max = 0.68 MW/m2

– occurs in a different place from pn,wall,max 20° apart toroidally)

pn,wall (,)

U. Wisc.

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 Bmax/Baxis

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

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: Ti, ne, conf. multiplier; coils: coil

width/depth, clearances

– reactor variables: Baxis, R

• Large number of constraints allowed (=, <, or >)

– Pelectric = I GW, and n limits, max. conf. multiplier, coil

j vs Bmax < 16 T, radial and coil-coil space, TBR > 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,Bmax), blanket/shield concepts, and

– engineering parameters, cost component algorithms

Cost Model Includes Full Geometry

• Min. distance for blanket & shielding Rmin from R/min

• Tritium breeding ratio vs R, shield thickness ~ ln(pn), etc.

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 jSC and Bmax 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

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

– jcoil and Bmax decrease; cost decreases faster than coil volume

increases

2

2.5

3

3.5

4

4.5

5

0.3 0.35 0.4 0.45 0.5 0.55 0.6

Coil Pack Depth d (m)

0

5

10

15

4 6 8 10 12 14 16 18

Conductor Cost($/kA-m)

Bmax

(T)

Current Density

(10-kA/mm2) Nb

3Sn

NbTiTa

Plasma Models for Calculating Performance

• Plasma modeling assumptions– E = H x EISS95 where EISS95 = 0.079 a2.21R0.65PMW

–0.59n190.51B0.830.4

– ISS-95 confinement multiplier H determined from power balance

– Hollow ne(r) with center/peak = 0.8 (LHD, W 7-AS)

– T(r) ~ parabolic1.5 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/Ra2)1/2 (3 in LHD)

• Test sensitivity to assumptions and constraints

Constraints on Plasma n and T(some conflicting)

= 5% nT/Baxis2

n < 2nSudo Baxis0.5

• Reduced -particle losses 5% higher nR/T2

• Acceptable nHe (from He*/E = 6) for fuel dilution

• Maximum multiplier on E n0.51B0.84; reduced saddle-point power

• Pfus [PE = 1 GW] n2f1(T) ~ n2T2 (approx.)~ rms2Baxis2

• Pradiation n2f2(T) ~ n2; target 75% of Pe,I; choose nZ

• Operating point on stable branch of ignition curve

• Te,edge set by connection length and Te,divertor < 20 eV

Magnetic Configuration Optimization Provides Basic Information (4)

-particle loss rate depends on plasma n and T

• So need to determine Raxis and Baxis, also n and T

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 0.2 0.4 0.6 0.8 1

nR/T2

Operating Point Moves to Higher T with Lower Pstartup as ISS95 Multiplier

H Increases

H = 2

H = 2.15

H = 2.5H = 3

T (keV)

n (1020 m–3)

xx

ne(r) Hollow in Stellarators at Low *

• Assume ne = ne0[(1 – (r/a)12)(0.66 + 0.34(r/a)2) + nedge/ne0],

• Te = Te0[(1 – (r/a)2)1.5 + Tedge/Te0]

• p(r/a) very close to that used for stability calculation

PNBI

= 1 MW, Ti(0) = 1.3 keV ECH, T

e(0)

= 1.5 keV

PNBI

= 6.5 MW, Ti(0) = 1.9 keV

LHD W 7-AS

Density, Temperature & Pressure Profiles

r/a

centra

l

dip

1.7%

3.9%

9.7%

17%

25%

35%

exper.

10%

to

30%

r/ar/a

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

pressure profiles

for Te ~ parabolic

1.5

Ku and Lyonpressureprofiles

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

ne = n

e0[(1 – (r/a)

12)(f

0 + (1 – f

0)(r/a)

2) + n

edge/n

e0]

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

1.52

1

Te profiles

parabolicn

10-7

10-6

10-5

0.0001

0.001

0.01

0.1

1

0 0.2 0.4 0.6 0.8 1r/a

nFe

~ ne26

Fe

Treatment of Impurities• ne = nDT + ZnZ, so impurities reduce Pfusion through

•reduced nDT2 and 2 (~ ne + nDT)2; Pfusion ~ nDT

2 ~2B4

•reduced Te (hence Ti) through radiative power loss

•requires higher B or H-ISS95 or larger R to compensate

• carbon (ZC = 6) for low Z & iron (ZFe = 26) for high Z

Standard corona

model: line radiation and electron-ion recombination

pradiation ~ nenZ f(Te)

Choose nZ ~ ne0.001

0.01

0.1

1

10

100

1000

0.1 1 10T

e (keV)

Fe

C

ImpurityBremsstrahlung

H Brems-strahlung

Power Flow Fractions

Pfusion

Pneutron

P

P,loss

Divertor

First

Wall

Pradiatio

n

Pparticle

80%

20%

Prad,

div.

region

5%

75%

20%75%

25%

Prad,

edge 50%

50%

50%

50%

Prad,sol

11%

89%

11%

89%

Blankets,

Shields

Pelectric

Ppumps, BOP

Pelec,gross

Pthermal

116%

90%

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

Summary for Reference ARE CaseNCSX plasma with ARE coils; modified LiPb/FS/He; H2O-cooled internal

vacuum vessel with SiC inserts and tapered blanket

FINAL DESIGNmajor radius (m) 7.75field on axis (T) 5.70

volume avg. density (1020 m–3) 3.58density averaged temp (keV) 5.73coil dimensions (m x m) 0.19 x 0.74

FIGURE OF MERIT ..................... Cost of Electricity (2004 $) 81.5 mills/kW-hr

VARIABLES selected for iterationmajor radius 5.0

20.0field on axis 3.0

10.0ion density 1.0

10.0ion temperature 1.0 50.0coil width 0.01

5.0confinement multiplier 0.10 9.0

nFe/ne (%) 0

0.02

following CONSTRAINTS were selected:

target finalignition = 1 target

1.00 1.00electric power (GW) 1.0

1.00tritium breeding ratio ≥ 1.1

1.115

R/Rmin ≥ 1 1.002

max. neutron wall load 5.3 5.26

max. volume averaged beta 5% 5%

maximum density/nSudo ≤ 2 1.88

max. confinement multiplier 2.0 1.48

min. port width (m) 2.0 4.08core radiated power fraction ≥ 75%

75%maximum -particle loss rate 5%

5%maximum field on coils (T) 16 15.1

jcoil/jmax

≤ 1 1.00

Typical Systems Code Results

Plasma Parameterscentral ion temp (keV)

8.63central ion density (1020 m–3)

7.83central elec. density (1020 m–3)

8.09fraction fuel to electrons

0.94confinement time, taue (sec)

0.96stored plasma energy (MJ)

430volume averaged beta (%)

5.0beta star (%)

8.2fraction carbon impurity

0fraction iron impurity

0.008 %fraction helium

2.93 %Z effective

1.11

Power Balancenet 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/m2) 5.26

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 (thPth)0.83 + constant

Cost 24 (Electric Plant) 133.8 (thPth)0.49

Cost 25 (Misc. Plant Eq.) 67.7 (thPth)0.59

Cost 26 (Spec. Matls.) 164.3 VLiPb

Cost 27 (Heat Rejection) 53.3 Pth – (thPth)

Cost 90 (Total Direct Cost) 2633

Costs 91-98 = construction, home office, field office, owner’s costs,

project contingency, construction interest, construction escalation

Cost 99 (Total Capital Costs) 5080 = Costs 90 thru 98

= 1.93 x Cost 90

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

Stellarator Geometry-Dependent Components only Part of the Cost

Fractions of reactor core costmodular 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

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 1333Mass of LiPb in core

3221

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

Comparing Masses with AT, RS & SPPS

Comparison of General Plant Costs (1992 $)

• Only Reactor Plant Equip. contains stellarator costs

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

Variations about the Reference Case

• Variations that affect the size and cost of the reactor– pn,wall limit – Bmax 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/nSudo

-particle loss fraction – ISS-95 confinement multiplier

– fraction of power radiated – fraction of SOL power radiated

– density profile – temperature profile– edge Te

pn,wall,max Has Impact on Rmin• As the maximum allowed value for pn,wall increases,

R decreases to the Rmin 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

5

5.5

6

6.5

7

7.5

8

8.5

9

4.2 4.4 4.6 4.8 5 5.2

pn,wall,max

(MW/m2)

Bmax

/2 (T)

Baxis

(T)

<R> (m)

0.1 COE (1992 mills/kWhe)

<R>min

(m)

Bmax Has Modest Impact on R and Costs

4

5

6

7

8

9

12 12.5 13 13.5 14 14.5 15 15.5

Bmax

(T)

Baxis

(T)

pn,wall

(MW/m2)

<R> = <R>min

, (m)

0.1 COE (1992 mills/kWhe)• The decrease in

the COE due to R falling with Bmax is partly

offset by the increasing j and Bmax, which

increases the cost of the coils and structure

Impact of the Beta Limit

• Below = 5%, R = Rmin and pn,wall increases

with until it hits the wall limit

• Above = 5%, R is fixed but the COE continues to fall because the decreasing Bmax reduces the

cost of coils and structure

4

5

6

7

8

9

4 5 6 7 8

<>%

Bmax

/2( )T

Baxis

( )T

p,n wall

( /MW m2)

< >R ( )m0.1 (1992 /COE mills kWh

e)

< >Rmin

( )m

Tapered/Full and Advanced Blanket Cases

• Tapered blanket/shield

• Advanced blanket case

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

Summary• The ARIES-CS device parameters determined by plasma-coil space, neutron wall loading, TBR, Bmax/B on coils and j vs Bmax 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

Additional Material

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 Vreactor building

0.62

Cost 21.3 (turbine building) = 41.52 (thPth)0.75 + constant

Cost 21.4 (cooling system) = 10.01 (thPth)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)

Pth = Pn x gloem + P

Cost Element Breakdown (2004 M$)

Cost 22.1.1.1 (FW) 6.49Cost 22.1.1.3 (BL + BW) 80.35Cost 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 124.4Cost 22.1.3 VF coils 0.00 (to be

added)Cost 22.1.3 divertor 7.89Cost 22.1.3 mod coil struct 198.5Cost 22.1.3 (coils + str) 322.9 32.40%Cost 22.1.4 (Heating) 28.60 constant

20 MWCost 22.1.5 (Primary Str.) 83.27 core

volumeCost 22.1.6 (Vac. Sys.) 136.3 cryostatCost 22.1.7 (Power Sup.) 67.95 constantCost 22.1.8 (Imp. Control) 6.79Cost 22.1.9 (Dir. Ener. Conv. 0Cost 22.1.10 (ECH) = 0

Cost 22.1 (Core) = 996.4

Cost Element Breakdown (2004 M$)

Cost 22.2.1 prim. coolant 298.9 Pth0.55

Cost 22.2.2 interm. coolant 0.00

Cost 22.2.3 sec. coolant 65.83 Pth0.55

Cost 22.2 (Heat transport) 448.0

Cost 22.3 aux. cooling 3.51 PthCost 22.4 rad. waste 6.25 PthCost 22.5.1 fuel injection 14.02 constantCost 22.5.2 fuel processing 16.45 constantCost 22.5.3 fuel storage 7.01 constantCost 22.5.4 atm T recover. 3.33 constantCost 22.5.5 H2O T recover. 7.01 constantCost 22.5.6 BL T recover. 7.01 constantCost 22.5 fuel handling 54.82 constant

Cost 22.6 other plant equip 57.02 PthCost 22.7 I&C 44.19

constant

Cost 22 (Reactor Plant) 1642 (inc. 2% spare parts)

Further Modeling of Impurities Is Possible

• Present approach

– assumes nC = fCne & nFe = fFene; fZ

is constant thruout plasma, so nZ(r) has the same (slightly

hollow) profile as ne(r)

• Alternative: neoclassical model for impurity profiles

– nZ(r) = ne(r) x fZ (ne/ne0)Z

[Te/Te0]–Z/5

– ignore [Te/Te0]–Z/5 term --

probably is not applicable in stellarators

nZ(r) more peaked near edge since

ne(r) is hollow for regime of

interest

nZ(r) peaked at center if ne(r)

peaked

C

Fe

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1

nC ~ n

e6

r/a

no T screening

0

0.5

1

1.5

2

0 0.2 0.4 0.6 0.8 1

nFe

~ ne

26

r/a

no T screening

Even Flat ne(r) Produces Hollow Impurity Profiles

• W 7-AS results at high collisionality– Calculations show more extreme impurity edge peaking at lower collisionality