Determination of ARIES-CS Plasma

1
Determination of ARIES-CS Plasma Device
Parameters and Costing

• J. F. Lyon, ORNL
• ARIES-CS Review Oct. 5, 2006

2
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

3
Goal Stellarator Reactors Similar in Size to
Tokamak Reactors

• Need a factor of 2-4 reduction compact
  stellarators

4
3 Plasma and Coil Configurations Studied
MHH2

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

NCSX ARE
5
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/?R?2
• 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 ?R?2
• volume of coils LcoilIcoil/jcoil ?R?1.2
• Minimum value for ?R? (hence cost) depends on
  various constraints

Using ?R? ?Raxis? for convenience
6
?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

7
Magnetic Configuration Optimization Provides
Basic Information (2)

• Scaled coil parameters ?coil-coil/?R?,
  Lcoil/?R?, areacws/?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)

8
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?

9
Neutronics Calculations Constrain ?R?min

• Allowable neutron wall power density Pn (
  Pe)/?R?2
• 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)

pn,wall (?,?)

• Similar calculation gives radiation power density
  on the wall prad,wall Prad/?R?2
• 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)

U. Wisc.
10
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?

11
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

12
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 (, lt, or gt)
• Pelectric I GW, b and n limits, max. conf.
  multiplier, coil j vs Bmax lt 16 T, radial and
  coil-coil space, TBR gt 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

13
Cost Model Includes Full Geometry

• Min. distance for blanket shielding ? ?R?min
  from ?R?/?min
• Tritium breeding ratio vs ?R?, shield thickness
  ln(pn), etc.

14
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

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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
• jcoil and Bmax decrease cost decreases faster
  than coil volume increases

17
Plasma Models for Calculating Performance

• Plasma modeling assumptions
• ?E H x ?EISS95 where ?EISS95 0.079
  a2.21R0.65PMW0.59n190.51B0.83i0.4
• 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

18
Constraints on Plasma ?n? and ?T?(some
conflicting)

• ??? 5 ? ?n??T?/?Baxis?2
• ?n? lt 2nSudo ? ?Baxis?0.5
• 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 ? ?n?2f1(T) ?n?2?T?2
  (approx.) ?rms2?Baxis?2
• Pradiation ? ?n?2f2(T) ?n?2 target 75 of
  P??e,I choose nZ
• Operating point on stable branch of ignition
  curve
• Te,edge set by connection length and Te,divertor
  lt 20 eV

19
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

20
Operating Point Moves to Higher ?T? with
Lower Pstartup as ISS95 Multiplier H Increases
21
ne(r) Hollow in Stellarators at Low n
LHD
W 7-AS
PNBI 1 MW, Ti(0) 1.3 keV ECH, Te(0) 1.5
keV PNBI 6.5 MW, Ti(0) 1.9 keV

• 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

22
Density, Temperature Pressure Profiles
r/a
23
Treatment of Impurities

• ne nDT S ZnZ, so impurities reduce Pfusion
  through
• reduced nDT2 and b2 ( ne nDT)2 Pfusion nDT2
  b2B4
• 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 ne
24
Power Flow Fractions
25
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

26
Summary for Reference ARE Case

• NCSX plasma with ARE coils modified LiPb/FS/He
  H2O-cooled internal
• vacuum vessel with SiC inserts and tapered blanket

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/nSudo 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 jcoil/jmax
1 1.00
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 nFe/ne () 0
0.02
FINAL DESIGN major radius (m)
7.75 field on axis (T)
5.70 volume avg. density (1020
m3) 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
27
Typical Systems Code Results

• Plasma Parameters
• central ion temp (keV) 8.63
• central ion density (1020 m3) 7.83
• central elec. density (1020 m3) 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 a 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
28
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
  (hthPth)0.83 constant
• Cost 24 (Electric Plant) 133.8
  (hthPth)0.49
• Cost 25 (Misc. Plant Eq.) 67.7
  (hthPth)0.59
• Cost 26 (Spec. Matls.) 164.3
  VLiPb
• Cost 27 (Heat Rejection) 53.3
  Pth (hthPth)
• 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

29
CoE Breakdown (2004 mills/kW-hr)

• Capital return 65.9
• OM 10.0
• Replacements 4.91
• Decommissioning allowance 0.61
• Fuel
  0.04
• Total CoE 81.5
• Total CoE (1992 ) 66.4

30
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

31
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
32
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

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
33
Comparing Masses with AT, RS SPPS
34
Comparison of General Plant Costs (1992 )

• Only Reactor Plant Equip. contains stellarator
  costs

35
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

36
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

37
pn,wall,max Has Impact on ?R?min

• As the maximum allowed value for pn,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

38
Bmax Has Modest Impact on ?R? and Costs

• 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

39
Impact of the Beta Limit

• Below ??? 5, ?R? ?R?min 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

40
Tapered/Full and Advanced Blanket Cases

• Tapered blanket/shield

• Advanced blanket case

41
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

42
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

43
Additional Material
44
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 building0.62
• Cost 21.3 (turbine building) 41.52
  (hthPth)0.75 constant
• Cost 21.4 (cooling system) 10.01
  (hthPth)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 Pa

45
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

46
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 Pth
• Cost 22.4 rad. waste 6.25 Pth
• 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 Pth
• Cost 22.7 IC 44.19
  constant
• Cost 22 (Reactor Plant) 1642 (inc.
  2 spare parts)

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49
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/Te0Z/5
• ignore Te/Te0Z/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
50
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