# Presentation: 822911

## Determination of ARIES-CS  Plasma & Device Parameters and Costing

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

**Notes:**
The design is being done as a collaboration

## 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

## 3 Plasma and Coil Configurations Studied

**NCSX**
**ARE**

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

**MHH2**

##  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

## Factors Determining the Device Parameters

- Component cost depends on plasma surface area (~ *R*2)
- for approx. fixed thicknesses, volumes of blanket, shield, coil structure, vacuum vessel ~ wall area ~ *R*2
- volume of coils ~ LcoilIcoil/*j*coil ~ *R*1.2
- Minimum *R* is determined by constraints on
- acceptable power flux at wall (~ 1/*R*2) for radiation (wall limit) and neutrons (lifetime issue -- could modify wall where flux too high)

- space  needed between plasma edge and coil center for blanket, shielding, vacuum vessel, coil, etc. and tritium breeding ratio > 1.1
- Coil sets with a larger plasma-coil space min allow smaller *R* = [*R*/min], but require more convoluted coils, resulting in larger *B*max/*B*axis, hence lower *B*axis

## 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

##  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 (=, <, or >)
*P*electric = I GW, ** and *n* limits, max. conf. multiplier, coil* j* vs *B*max < 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*,*B*max), blanket/shield concepts, and
- engineering parameters, cost component algorithms

## 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.

## 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

## Slide 11

## 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

## Plasma Models for Calculating Performance

- Plasma modeling assumptions
-  E = H x EISS95 where EISS95 =  0.079 *a*2.21*R*0.65*P*MW–0.59*n*190.51*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*) ~ 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*/*Ra*2)1/2             (3 in LHD)
- Test sensitivity to assumptions and constraints

## Constraints on Plasma n and T(some conflicting)

- ** = 5%  *n**T*/*B*axis2
- *n* < 2*n*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*2f1(*T*) ~ *n*2*T*2 (approx.)~ ***rms*2*B*axis2
*P*radiation  *n*2f2(*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

## 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*

- ~ collisionality

## Operating  Point  Moves  to  Higher  T  with Lower Pstartup as  ISS95  Multiplier  H  Increases

**Operating  Point  Moves  to  Higher  *********T*********  with Lower *****P*****startup**** as  ISS95  Multiplier  H  Increases**

- illustrative,
- a different
- reactor
- example

## ne(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 keV****	****	****	****ECH, T****e****(0) = 1.5 keV **
**P****NBI**** = 6.5 MW,  T****i****(0) = 1.9 keV**

**LHD**

**W 7-AS**

## Density, Temperature & Pressure  Profiles

- r/a

**central**
**dip**
**1.7%**
**3.9%**
**9.7%**
**17%**
**25%**
**35%**
**exper.**
**10%**
**to**
**30%**

- r/a

- r/a

- Fe

## Treatment of Impurities

-  *n*e = *n*DT + Z*n*Z, so impurities reduce *P*fusion through
- reduced *n*DT2 and **2 (~ *n*e + *n*DT)2; *P*fusion ~ *n*DT2 ~**2B4
- reduced *T*e (hence *T*i) 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
*p*radiation ~ *n*e*n*Z f(*T*e)
- Choose *n*Z ~ *n*e

## Power Flow Fractions

## 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, different magnetic configurations

## Summary for Reference ARE Case

- NCSX plasma with ARE coils; modified LiPb/FS/He with SiC inserts (tapered blanket/shield) ; H2O-cooled internal vacuum vessel

**  **

**FINAL DESIGN**
- major radius (m)                              7.75
- field on axis (T)                                5.70
- volume avg. density (1020 m–3)       3.58
- density averaged temp (keV)          5.73
- coil dimensions (m x m)          0.19 x 0.74

**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

**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. neut. wall load (MW/m2)  5-6       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
*j*coil/*j*max (*B*max)                             ≤ 1      1.00

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

## Typical Systems Code Results

- Plasma Parameters
- central ion temp (keV)                      8.63
- central ion density (1020 m–3)          7.83
- central elec. density (1020 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/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
- Operations & maintenance       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 cost
**modular coil                            12.5%**
**coil structure                          19.9%**
**blanket, first/back wall             8.7%**
**shield and manifolds              26.5%**
- vacuum system + 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 and              1345**
**     ****hot structure                     **
**Total nuclear island                10,962**
- Cryostat mass	  	          1333
- Mass 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 and                 108**
**	****hot structure**
**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 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

## 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 Te

## pn,wall,max Has Impact on Rmin

*p*n,wall,max = 5.26 MW/m2 in
-      code at which *R* = *R*min set by the required plasma-coil space
- As *p*n,wall decreases, *R* and the COE increase
- *B*axis falls to keep *P*fusion constant for fixed **
- The COE increase is partly offset by the reduced cost of coil and structure
- Will examine lower *p*n,wall for the report, which can help design issues

## Bmax Has Modest Impact on R and Costs

*B*max cannot increase above 15.1 T because *p*n,wall at a targeted limit
- As *B*max decreases
- *B*axis decreases, but *R*3*B*axis4 is ≈ constant to keep Pfusion fixed for same **
- cost varies fastest with *R*, so slow increase in *R* results in slow decrease in *B*axis
- coil cost decreases, which partly offsets increase due to larger *R*
*p*n,wall falls, increases lifetime
- Possibility of even lower *B*max may allow use of NbTi and reduced costs

##  = 5% Is not a Hard Constraint 

- As ** decreases below 5%
- *R* = *R*min and decreases, eases space constraints but increases the COE
*p*n,wall falls, increases lifetime
*B*max increases to the 16 T limit
- Above ** = 5%
- *R* is fixed because *p*n,wall at a limit
- slower decrease in the COE; decreasing *B*max impact on cost of coils and structure less than the penalty associated with larger *R* at lower **

## Tapered/Full and Advanced Blanket Cases

- Reference tapered blanket/ shield (min = 131 cm)
- min = 172 cm if no tapered region

- Advanced blanket case, similar to that for AT
- higher th (55-60% vs 42%)
-  min = 130 cm
- Not analyzed in detail yet, will be in final report

## Magnetic Configurations and Blanket/ Shield Options Are Being Studied 

- *for LiPb/FS/He case; LiPb/SiC will be lower because thermal higher
- (a) to keep same neutron wall power density
- (b) requires better confinement, higher ** if same *B*axis

## 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

## 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 building0.62
- 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)                     6.49
- 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

## 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 I&C                         44.19     constant
-      Cost 22 (Reactor Plant)      1642     (inc. 2% spare parts)

## Slide 43

## Slide 44

## Further Modeling of Impurities Is Possible

- Present approach
- assumes *n*C = fC*n*e & *n*Fe = fFe*n*e;  fZ 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 fZ (*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**