Optimization of the ARIES-CS Compact Stellarator Reactor Parameters - - PowerPoint PPT Presentation

Optimization of the ARIES-CS Compact Stellarator Reactor Parameters

• J. F. Lyon, ORNL

for the ARIES Group 15th International Stellarator Workshop Madrid October 3, 2005

Topics

• ARIES Reactor Optimization Approach
• Configuration Properties
• Coil, Blanket/Shield Models
• Systems Optimization Code
• Typical Case Results
• Parameter Variations and Scaling

ARIES-Compact Stellarator Program Has Three Phases

FY 2003/2004: Exploration of Plasma/Coil Configuration and Engineering Options

• 1. Develop physics requirements and

modules (power balance, stability, a confinement, divertor, etc.)

• 2. Develop engineering requirements

and constraints.

• 3. Explore attractive coil topologies.

FY 2003/2004: Exploration of Plasma/Coil Configuration and Engineering Options

• 1. Develop physics requirements and

modules (power balance, stability, a confinement, divertor, etc.)

• 2. Develop engineering requirements

and constraints.

• 3. Explore attractive coil topologies.

FY 2004/2005: Exploration of Configuration Design Space

• 1. Physics: aspect ratio, number of

periods, rotational transform profile, β, α losses, etc.

• 2. Engineering: configuration
• ptimization, management of

space between plasma and coils, etc.

• 3. Focus on two configurations and

choose one for detailed design. FY 2004/2005: Exploration of Configuration Design Space

• 1. Physics: aspect ratio, number of

periods, rotational transform profile, β, α losses, etc.

• 2. Engineering: configuration
• ptimization, management of

space between plasma and coils, etc.

• 3. Focus on two configurations and

choose one for detailed design. FY 2006: Detailed system design and optimization FY 2006: Detailed system design and optimization

Present status

Goal: Stellarator Reactors Similar in Size to Tokamak Reactors

• Need a factor of 2-4 reduction compact stellarators

2 4 6 8 10 12 14 4 8 12 16 20 24

Plasma Aspect Ratio <R>/<a> Average Major Radius <R> (m) Stellarator Reactors

HSR-5 HSR-4 SPPS

Compact Stellarator Reactors ARIES AT ARIES RS

FFHR-1 MHR-S

Circle area ~ plasma area Tokamak Reactors

Parameter Optimization Integrates Plasma/Coil Geometry and Reactor Constraints

Plasma & Coil Geometry Reactor Constraints

• Shape of last closed flux surface

and <Raxis>/<aplasma>, β limit

• Shape of modular coils and

Bmax,coil/Baxis vs coil cross section, <Rcoil>/<Raxis>, ∆min/<Raxis>

• Alpha-particle loss fraction
• Blanket and shield thickness
• Bmax,coil vs jcoil for superconductor
• Acceptable wall power loading
• Access for assembly/disassembly
• Component costs/volume

Parameter Determination

• <Raxis>, <aplasma>, <Baxis>
• Bmax,coil, coil cross section, gaps
• ne,I,Z(r),Te,i(r), <β>, Pfusion, Prad, etc.
• Operating point, path to ignition
• Cost of components, operating

cost cost of electricity

Requires non-linear constrained optimization

Stellarator Properties Affect Reactor Optimization

• Inherently steady state

⇒ no current drive power ignited plasma, small

recirculating power

• No plasma disruptions

⇒ higher density operation than in tokamaks, set by radiation

losses

⇒ confinement time increases with density ⇒ <β

β β β> appears to be limited by equilibrium rather than by stability

• Modular coils determine plasma shape, hence plasma

properties

⇒ higher-order field components needed at plasma

surface decay rapidly with distance from the coils

– Bmax/<Baxis> is a function of the plasma-coil distance

Configuration Optimization Approach

NCSX scale-up Coils

1) Increase plasma-coil separation 2) Simpler coils High leverage in sizing

Physics

1) Confinement of α α α α particle 2) Integrity of equilibrium flux surfaces Critical to 1st wall heat load and divertor

New classes of QA configurations

Reduce consideration on MHD stability in light of W 7-AS and LHD results

MHH2

1) Develop very low aspect ratio geometry 2) Detailed coil design optimization How low should the plasma aspect be?

SNS

1) Nearly flat rotational transforms 2) Excellent flux surface quality How good/robust can

• ne “design” the flux

surfaces?

Friday: L-P Ku, “New Classes of Quasi-axisymmetric Configurations”

First Class of Quasi-Axisymmetric Configurations Studied

NCSX-like configurations Good QA, low effective ripple (<1%), α energy loss ≤7% Stable to MHD modes at <β> ≥ 4% Coils can be designed with aspect ratio ≤ 6 and are able to yield plasmas that capture all essential physics properties Resonance perturbation can be minimized NCSX-like configurations Good QA, low effective ripple (<1%), α energy loss ≤7% Stable to MHD modes at <β> ≥ 4% Coils can be designed with aspect ratio ≤ 6 and are able to yield plasmas that capture all essential physics properties Resonance perturbation can be minimized

Footprints of escaping α α α α’s on LCFS Energy loss ~12% in model calculation Heat load maybe localized and high (~a few MW/m2)

Second Class of Quasi-Axisymmetric Configuration Studied

MHH2

Low plasma aspect ratio (Ap ~ 3.6) in 2 field periods Good QA, low effective ripple (<0.8%), α energy loss ≤5% . Stable to MHD modes at <β> ≥ 4%

MHH2

Low plasma aspect ratio (Ap ~ 3.6) in 2 field periods Good QA, low effective ripple (<0.8%), α energy loss ≤5% . Stable to MHD modes at <β> ≥ 4% 16 simpler coils

Stellarator Geometry Is Characterized by Ratios

• Distances, areas, volumes scale photo-

graphically for fixed plasma and coil configuration

• Plasma aspect ratio Ap = <Raxis>/<a>

– plasma (and wall) surface areas ∝

∝ ∝ ∝ <R>2 (costs ∝ ∝ ∝ ∝ areas for fixed thickness parts) pwall ∝ ∝ ∝ ∝ 1/wall area, often sets <Raxis>min

– surface area ∝

∝ ∝ ∝ A∆

∆ ∆ ∆2/Ap

– plasma volume ∝

∝ ∝ ∝ <R>3

• Coil-plasma distance: A∆

∆ ∆ ∆ = <Raxis>/∆

∆ ∆ ∆

– can also set <Raxis>min = A∆

∆ ∆ ∆(D + ct/2)

where D is the space needed for scrapeoff, first wall, blanket, shield, coil case, and assembly gaps

• Coil volume (cost) ∝

∝ ∝ ∝ <Raxis>2, coil-coil spacing ∝ ∝ ∝ ∝ <Raxis>

∆ ∆ ∆ ∆

Major Radius R0 Plasma Surface

• Ave. Radius <a>

Minimum Distance ∆ ∆ ∆ ∆ between Plasma Edge and Center

• f Coil Winding

Surface Center of Coil Winding Surface B0

Plasma

∆ ∆ ∆ ∆

Bmax Coil ct = coil thickness

Selected Two Main Plasma and Coil Configurations to Study

Key Configuration Properties NCSX MHH2 Plasma aspect ratio Ap = <R>/<a> 4.55 2.66 Wall (plasma) surface area/<R>2 11.78 18.55 Minimum pl-coil dist. ratio A∆

∆ ∆ ∆

= <R >/∆ ∆ ∆ ∆min 5.89 5.55 Minimum coil-coil dist. ratio <R>/(c-c) 10.03 10.33 Total coil length/<R> 89.3 91.0 Bmax/<Baxis>, 0.3 m x 0.3 m coil pack 2.63 2.69

NCSX MHH2

• Bmax/<Baxis> varies rapidly with coil distance

from plasma and coil pack dimensions

• Only quasi-axisymmetric type of compact

stellarators studied: 7 variants of NCSX and 4 of MHH2

Bmax on the Coils Is an Important Parameter

• Larger plasma-coil spacings lead to more convoluted coils and higher

Bmax/<Baxis>; constrains value of <Baxis> if Bmax is limited

• Coil current density and cost depend on Bmax; Nb3Sn examined first

1 2 3 4 5 6 7 8 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Bmax/<B

axis>

d = (cross section)

1/2, m

MHH2-16 MHH2-8

square coil pack cross section (k = 1)

NCSX cases

5 10 15 4 6 8 10 12 14 16 18

Conductor Cost ($/kA-m) B

max (T)

Current Density (10-kA/mm

2)

Nb

3Sn

NbTiTa

Coil Complexity Also Dictates Choice of Superconducting Material

Strains required during winding process are large NbTi-like (at 4K) ⇒ B < ~7-8 T NbTi-like (at 2K) ⇒ B < 9 T, problem with temperature margin Nb3Sn or MgB2 ⇒ B < 16 T, Wind & React: Need to maintain structural integrity during heat treatment (700o C for a few hundred hours) Inorganic insulators Strains required during winding process are large NbTi-like (at 4K) ⇒ B < ~7-8 T NbTi-like (at 2K) ⇒ B < 9 T, problem with temperature margin Nb3Sn or MgB2 ⇒ B < 16 T, Wind & React: Need to maintain structural integrity during heat treatment (700o C for a few hundred hours) Inorganic insulators

• A. Puigsegur et al., Development Of An Innovative

Insulation For Nb3Sn Wind And React Coils

Inorganic insulation is assembled with magnet prior to winding and thus able to withstand the Nb3Sn heat treatment process – Two groups (one in the US, the other in Europe) have developed glass-tape that can withstand the process Inorganic insulation is assembled with magnet prior to winding and thus able to withstand the Nb3Sn heat treatment process – Two groups (one in the US, the other in Europe) have developed glass-tape that can withstand the process

Minimum Coil-Plasma Distance Can Be Reduced By Using a Shield-Only Zone

Resulting Radial & Toroidal Cross Section

• For NCSX-type configurations, coils are far from the plasma

except for ~5% of the wall area, which allows a shield-only build in that area and hence a smaller value for <Raxis>

• MHH2 coil configurations do not allow this

coil structure

Port Assembly Approach

Components Replaced through Three Ports

Modules removed through three ports using an articulated boom. Modules removed through three ports using an articulated boom. Drawbacks: Coolant manifolds increases plasma-coil distance Very complex manifolds and joints Large number of connect/disconnects Drawbacks: Coolant manifolds increases plasma-coil distance Very complex manifolds and joints Large number of connect/disconnects

Component complexity, assembly and maintenance are key issues

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: width/depth of coils – reactor variables: <Baxis>, <R>

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

– Pelectric, β

β β β limit, confinement multiplier, coil j and Bmax, clearance radially and between coils, TBR, neutron wall power density

• 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

Reference Models and Constraints

• Plasma and Coil Geometry from 3-D optimization (L-P. Ku)

⇒ normalized distances for plasma-coil, coil-coil, coil length ⇒ plasma aspect ratio and surface areas for plasma & coils

• Plasma scaling and constraints

– ignited plasma; chosen <β

β β β> limit; slightly hollow ne(r); prad(r)

– stellarator scalings: <ne> < 0.5[PB/Ra2]1/2 and τ

τ τ τE/τ τ τ τE

ISS-95 < 4 where

τ τ τ τE

ISS-95 ~ Pheating –0.59<ne>0.51<Baxis>0.83<R>0.65<a>2.21ι

ι ι ι2/3

0.4

• Coil modeling (L-P. Ku, L. Bromberg)

⇒ Bmax/<Baxis> vs plasma-coil distance and coil pack dimensions – Bmax < 16 T; maximum conductor j and cost vary with Bmax – coil-coil distance allows >2-m port size for maintenance

• Blanket and shield models; Pelectric = 1 GW (L. ElGuebaly)

– dual coolant (Li17Pb, He) blanket and shields (FS, WC) – pn,wall,max < 5 MW/m2, lifetime 15 MW-yr/m2 – thermal efficiency and shielding thickness vary with pn,wall,max

Treatment of Impurities

• A large fraction of the power can be radiated to reduce the power

load on the divertor, so radiation modeling is important

• ne = nDT + Σ

Σ Σ Σ ZnZ, so impurities reduce Pfusion through

– reduced nDT

2 and β

β β β2 (~ ne + nDT)2; Pfusion ~ nDT

2 ~β

β β β2B4

– 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)

0.001 0.01 0.1 1 10 100 1000 0.1 1 10

T

e (keV)

Fe C Impurity Bremsstrahlung H Brems- strahlung f(Te)

Typical Systems Code Summary

NCSX case (ARE) modified LiPb/FS/He H2O-cooled internal vacuum vessel with SiC inserts and tapered blanket, port maintenance

inflation factor 2004 year following CONSTRAINTS were selected: ignition = 1 target 1.0 Electric Power (GW) 1.0 volume averaged beta (%) 5.0 sufficient radial build max neutron wall load (MW/m2) <5.0 maximum jcoil/jSC(Bmax) <1.0 maximum density = 2 x nSudo

• max. ISS-95 confine. multiplier <4.0

minimum port width (m) >2.0 VARIABLES selected for iteration major radius (m) 5.0 16.0 field on axis (T) 3.0 10.0 ion density (1020m–3) 1.0 10.0 ion temperature (keV) 1.0 20.0 coil radial depth (m) 0.03 1.0 confinement multiplier 0.1 9.0 FIGURE OF MERIT ..................... Cost of Electricity (mills/kWhr) 68.4 mass core + LiPb coolant (t) 12,102 FINAL VALUES OF CONSTRAINTS: ignition margin 1.00 Electric Power (GW) 1.00 volume averaged beta (%) 5.00 radial build margin 1.00

• max. neutron wall load (MW/m2) 5.00

jcoil/jSC(Bmax) 1.00 average/maximum density 1.00 ISS-95 confinement multiplier 3.13 maintenance port width (m) 3.64 FINAL DESIGN major radius (m) 6.93 field on axis (T) 6.28

• max. field on coil (T) 14.03

volume avg. density (1020 m–3) 4.59 density averaged temp (keV) 6.93 coil dimensions (m x m) 0.18 x 0.67 current density (MA/m2) 107

Stellarator Geometry-Dependent Components only Part of the Cost

Fractions of reactor core cost modular coil 11.9% coil structure 18.6% bucking cylinder 4.5% blanket, first/back wall 7.3% shield and manifolds 21.9% LiPb coolant compared to reactor core cost 20.3%

• Reactor core is 33.8% of

total direct cost, which includes other reactor plant equipment and buildings

• Total direct cost is 51.8%
• f total capital cost
• Replaceable blanket

components only contribute 2% to COE

Comparing Masses with AT, RS & SPPS

Mass (tonnes) CS AT RS SPPS FW/Blanket/BW 805 255 585 251 Shield, BW, man. 3053 882 4235 9453 Coils + Structure 3999 1525 4907 9556 Vacuum Vessel 1192 1415 1357 2171 Fusion Power Core 9,052 5,226 12,679 21,430 LM Coolant 3,051 5,269 223 175 FPC + Coolant 12,102 10,495 12,902 21,605 COE (in 1992 mills /kWhr) 55.7 56.6 75.7 74.9

Comparing Costs with AT, RS & SPPS

Cost (1994 M$) CS AT RS SPPS 22.1 Reactor Equipment 623.4 519.9 966.4 1115

Cost of stellarator/tokamak components

399.7 64% 274.9 53% 516.3 53% 750.9 67%

22.1.1 blanket & 1st wall

45.5 67.9 74.3 71.5

22.1.2 shield, BW, man.

136.4 73.3 168.0 289.8

22.1.3,5 coils + structure

217.8 163.5 327.4 542.5

22.1.4 heating

53.7 41.0 164.2 54.2

22.1.6 vacuum systems

109.2 109.2 159.2 85.4

22.1.7 power supplies

55.3 56.1 55.3 55.3

22.1.8 impurity control

5.5 4.5 13.6 12.0

22.1.10 ECH startup

4.4 4.3 4.3

COE Decreases with Increasing β β β β

Only 6% decrease in COE as <β β β β> increases from 5% to 10%

56 60 64 68 72 76 80 2 3 4 5 6 7 8 9 10

<β β β β> (%) NCSX plasmas

COE (Mills/kW-hr)

Variation of Reactor Parameters with β β β β

• Increasing <β

β β β> allows reduced <Baxis> and <R> (until pwall limit reached)

4 6 8 10 12 14 16 2 3 4 5 6 7 8 9 10

<β β β β> (%) <B

axis (T)>

NCSX plasmas B

max (T)

5.6 6 6.4 6.8 7.2 2 3 4 5 6 7 8 9 10

<β β β β> (%) <R

axis (m)>

NCSX plasmas 2*<p

wall>

COE Varies as <Raxis>2 ~ 1/pn,wall

• Component costs depend on

– blanket, shield, structure,

vacuum vessel ~ wall area ~ 1/<pn,wall>

– volume of coils ~ LcoilIcoil/jcoil ~

<R>1.2 ~ 1/<pn,wall>0.6

– blanket replacement and other

costs independent of <pn,wall>

* replacement cost ~

1/<pn,wall>, number of replacements ~ <pn,wall>

• For a fixed plasma configuration,

<pn,wall> sets limit on area (hence <Raxis>) unless plasma-coil spacing more constraining

• pmax > 5 MW/m2 requires smaller <Raxis>, but there is insufficent space

for blanket, shield, coils, etc. for this coil set geometry

68 70 72 74 76 78 80 82 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 40 50 60 70 80 90 100 110

COE (mills/kWhr) 1/p

n,wall,max (m 2/MW)

<R

axis> 2 (m 2)

Values for Different pwall Limits

Target pwall,max 2 MW/m2 3 MW/m2 4 MW/m2 5 MW/m2 <R> (m) 10.44 8.63 7.57 6.93 <Baxis> (T) 4.39 5.17 5.80 6.28 Bmax (T) 9.66 11.54 12.99 14.03 pwall,max MW/m2 2.00 3.00 4.00 4.89 <Raxis>/Rmin 1.636 1.305 1.115 1.000 COE 81.90 73.95 70.28 68.45

Variation of Reactor Parameters with pwall

• Increasing pwall decreases <Raxis> and COE until Rmin limit is reached

4 5 6 7 8 9 10 11 2 2.5 3 3.5 4 4.5 5

p

wall,max (m 2/MW)

NCSX plasmas <R

axis> (m)

R

min (m)

COE/10 <B

axis> (T)

B

max/ 2 (T)

Different NCSX Coil Configurations

A∆

∆ ∆ ∆

5.69 5.89 6.1 6.82 <R> (m) 6.82 6.92 7.08 7.75 <Baxis> (T) 6.33 6.23 6.11 5.64 Bmax (T) 14.8 14.0 13.4 12.0 pwall,max MW/m2 5.00 4.92 4.57 3.73 <Raxis>/Rmin 1.001 1.000 1.000 1.000 CoE 68.6 68.2 68.7 70.7

Lower <Raxis>/∆ ∆ ∆ ∆min Reduces <Raxis> and COE until <pwall> Limit is Reached

increase due to increased Bmax

68 68.5 69 69.5 70 70.5 71 4.5 5 5.5 6 6.5 7 7.5 8 5.6 5.8 6 6.2 6.4 6.6 6.8 7

COE (mills/kWhr) <R

axis> (m), 2<p wall> (MW/m 2)

<R

axis>/∆

∆ ∆ ∆

min

<R

axis>

2<p

wall>

p

max = 5 MW/m 2

COE

Lower <Raxis>/∆ ∆ ∆ ∆min Requires Higher Magnetic Field

11 11.5 12 12.5 13 13.5 14 14.5 15 5.6 5.8 6 6.2 6.4 6.6 6.8 7

<R

axis>/∆

∆ ∆ ∆

min

NCSX plasmas

2<B

axis> (T)

B

max (T)

Code Minimizes COE

• Since radial thicknesses of most components are
• approx. fixed, volumes (and costs) ~ areas ~R2, so

code minimizes <Raxis>

• <Raxis> set by larger of (5/pwall,max)1/2 or A∆

∆ ∆ ∆D

– fixes Icoil, lcoil, coil-coil spacing and hence coil elongation

• Maximum half-coil-radial-

depth set by space between vacuum vessel and coil winding surface

⇒ minimize cost by using maximum coil thickness – jcoil and Bmax decrease, cost decreases faster than coil volume (thickness) 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) Cost x Pack Depth

Field Period Maintenance Approach

Components Replaced from Ends of a Field Period

30-deg 60-deg 0-deg Takes advantage of net force balance in a field period Life-time components (shield) need to be shaped so that replacement components can be withdrawn Takes advantage of net force balance in a field period Life-time components (shield) need to be shaped so that replacement components can be withdrawn Drawbacks: Complex shield (lifetime components) geometry Very complex initial assembly (of lifetime components) Complex warm/cold interfaces (magnet structure) and/or magnet need to be warmed up during maintenance Drawbacks: Complex shield (lifetime components) geometry Very complex initial assembly (of lifetime components) Complex warm/cold interfaces (magnet structure) and/or magnet need to be warmed up during maintenance

Summary

• Parameter determination integrates plasma,

reactor components, and coil geometry with physics & engineering constraints and assumptions

• The dominant factors in determining size and

cost are pwall and the plasma-coil distance

• Study leads to factor ~2 smaller stellarator

reactors (<R> ~ 7 m), closer to tokamaks in size

• CoE is relatively insensitive to assumptions for

a fixed plasma/coil configuration