Physics Basis for ARIES-CS

L. P. Ku, J. Lyon, T. K. Mau, A. Turnbull, M. Zarnstorff, A. Grossman, T. Kaiser &

The ARIES Team

ARIES-CS Project Review, October 5, 2006 Princeton Plasma Physics Laboratory

Princeton, New Jersey

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Outline of Discussions

• Physics basis for the baseline configuration– Unique features– Equilibrium and MHD stability– Transport and confinement– Coils– Magnetic topology outside LCMS

• Basis for configuration design approach– Critical considerations in QA reactors– Configuration optimization

• Advanced configurations– Family in which the baseline configuration is a member– Extra-low aspect ratio – High rotational transforms

• Connection to NCSX

• Summary/Conclusions

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The baseline plasma is a three field-period, aspect ratio 4.5, quasi-axisymmtric configuration with R=7.75 m.

Plane and perspective view of the geometry and |B|

of the last closed magnetic surface

Reference parameters for baseline:

R=7.75 m,

<a>=1.72 m,

<n>=3.6·1020 m-3,

<T>=5.73 keV,

B=5.7 T,

=5%,

Ip=3.5 MA,

P(fusion)= 2.364 GW,

P(electric)= 1 GWJ. Lyon, this meeting

The Baseline Configuration

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|B| in u-v space on surfaces at r/a~0.5, 0.7 and 1.0

The configuration has “good” quasi-axisymmetry, but it also has a “not so small” amount of mirror (B1,0) and its side-band helical (B1,1) component. The “residues” are specifically introduced to improve confinement of fast ions.

0

50

100

150

200

250

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0

B(0,1) as percent of B(0,0)

Ave

rag

e N

o. o

f T

ran

sit

Co

mp

lete

d

Collisionless orbits improved with ~1-2% B(0,1) as seen in an earlier study. N3AEC, toroidal transit limit=500, R=10 m, B=5.5 T, born on r/a=0.5.

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Noise 1.8% 3.5%

componentssymmetric,energymagnetic

componentsicnonsymmetr,energymagneticnoise

ιm]φ)[n(mθcosBB mn

B(0,1)

The 1-2% mirror field helps modify ripple distribution along field lines to reduce the overall B drift loss* without compromising the equilibrium and MHD stability properties.

*H. Mynick, A. Boozer and L. P. Ku, to appear in Phys. Plasmas

r/a~0.5

r/a~0.7

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Plasma cross section seen in four equally spaced toroidal angles.

The plasma may be described by*

invimunm

iu eeizr ,

where 2,0=-0.25, 2,1=-0.41, 3,0=0.14, -1,0=0.11, 3,1=0.15, -1,-1=0.17, 0,1=0.07, 3,2=0.06, 4,0=-0.06,

with 0,0 =1.

~1.7, ~0.7

0,1=0.04 for NCSX

*L. P. Ku & P. Garabedian, FS&T, 50, 207 (2006)

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The baseline equilibrium is calculated assuming a peaked pressure profile and shifted current profile derived from ARIES-RS studies to assure favorable MHD stability. A hollow density profile is assumed in the systems code and also in some slowing down calculations with the temperature profile chosen to provide a consistent pressure profile.

p{1-(r/a)2.1}1.21

Sensitivities of MHD stability and particle transport to different profiles have been examined in a limited number of cases. In these cases, most favorable characteristics remain unchanged.

p(peak)/p(average)~2.1

Temperature

Density

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Equilibrium calculated @ 5% by VMEC*

External and finite total transform

Equilibrium calculations indicate small Shafranov shifts at high thanks to the significant transform from plasma shaping and the small plasma aspect ratio. The rotational transform increases nearly monotonically as the plasma radius increases.

<< 1/2

2

Aa

*VMEC—S. P. Hirshman, W. I. van Rij, P. Merkel, Comp. Phys. Commun. 43, 143 (1986)

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Poincaré plot of an equilibrium at 5% by PIES*

Fixed-boundary equilibrium calculation without presupposition of the existence of nested flux surfaces indicates the configuration has good surface integrity. Islands do exist but the widths are small and so is the potential loss of fluxes.

*PIES– A. Reiman and H. Greenside, Comp. Phys. Commun. 43, 157 (1986)

**L.P. Ku, ARIES-CS project meeting presentation, Princeton, Dec 3 (2003). Also, San Diego, Jan 23 (2006).

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• Terpsichore stability calculations with conformal wall at twice plasma radius**:

— 197 radial flux surfaces— Up to 101 toroidal-poloidal mode combinations

• Varying at constant :— Reference case = 4.06%: Marginal unstable ()

# 9/6 (10/6 5/3) peaked at edge and# 6/4 3/2 7/4 2/1 10/7 peaked at edge

— Decreasing = 3.24%, 2.01% at constant is weakly destabilizing— Increasing = 4.88%, 6.13%, 8.22% at constant is stabilizing:

# Stable still at 8.22% for this profile— Interpreted as a weakly unstable current driven mode— Otherwise, robustly stable

• Varying profile at constant : b= 0.698: Unstable 3/2 7/5 6/4 8/5 4/2 peaked at edge ( b= 0.599: Marginal unstable 13/5 14/5 12/5 11/5 peaked in core ( b= 0.732: Unstable 3/2 7/5 1/1 4/2 8/5 peaked at edge (

The configuration is stable to the vertical mode (1,0) as (ext)/75%. The configuration is also stable to the external kink modes at ~5% without passive stabilization (Terpsichore* calculations).

*Terpsichore—D. V. Anderson, W. A. Cooper, R. Gruber, S. Merazzi and U. Schwenn, Sci. Comput. Supercomput. II, 159 (1990).

**A. Turnbull, ARIES-CS project meeting presentation, Princeton, Oct 4 (2006).

HSR: ~3.5% for global modes.

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When a broader current profile is used in sensitivity studies, a small modification of the plasma shape will suffice to re-stabilize the kink modes at 5% indicating the configuration has favorable characteristics for global mode stability

kink stable using the reference J profile.

kink stable at 5% using a broad J profile.

Current Density

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Infi

nite

-n B

allo

onin

g

The configuration has good stability characteristics to the Mercier and ballooning modes (COBRA* calculations).

unstableunstable

stablestable

=3, 4, 5, 6%

=3, 4, 5, 6%

*COBRA—R. Sanchez, S. P. Hirshman, J. C. Whitson, A. Ware, J. Comput. Phys., 161, 589 (2000)

FLR correction typically leads to a higher ballooning limit (~50%). Local pressure flattening also leads to higher limits.

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Recent W7AS and LHD Experiments: Steady High-, Above Linear Limit. (courtesy of M. Zarnstorff)

• In both cases, well above theoretical stability limit < 2%• Not limited by MHD activity. No disruptions observed. Sustained without CD.

Germany JapanPPPL & MP/IPPCollaboration

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The configuration has very low effective ripple, being everywhere < 0.5%, despite the existence of 1-2% of B(0,1) and B(1,1).

Anomalous transport is expected to dominate the thermal loss. Power balance will be achieved without auxiliary heating if the energy confinement (~1 s) follows the ISS-95 scaling with H~1.5 (J Lyon, this meeting).

4083051020

59065021295 2560 ....

MW..

iss ιBnPRa.τ

-eff calculated by NEO*

NEO—V. V. Nemov, S. V. Kasilov, W. Kernbichler and M. F. Heyn, Phys. Plasma, 6(12), 4622 (1999)

~20 MW auxiliary power is required during startup to reach ignition. Paths of startup have not been studied.

HSR-18: <0.6%FFHR; ~10%

ISS04 has a more favorable scaling.

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Alpha loss scales approximately with R2 and B2 and also scales with collisionality.

The density at operating temperature is chosen to provide high collisionality subject to the constraint of Sudo density limit such that the energy loss fraction of alphas is limited to ~5%.

B=6.5 T, 5% R=7 m

R=10 m

Footprint of lost in (,), lost particle energy distribution and cumulative particle loss versus time for the baseline configuration (ORBIT3D* calculations).

*ORBIT3D—R. B. White and M. S. Chance, Phys. fluids, 27, 2455 (1984)

HSR-18: ~2.5%FFHR: ~10%

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Modular and PF coils are designed following the NCSX design principles but are optimized to minimize the coil aspect ratio.

Courtesy of Xueren Wang

PF coils are designed for startup and equilibrium position control. I(max)< 5 MA.

Modular coil winding pack: 0.194 m x 0.743 m I(max)~13.5 MA, B(max)~15 T, R/(C-P)~5.9, R/(C-C)~10.

HSR: 10 T (NbTi)FFHR: 13 T

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Field topology outside LCMS is similar to that of NCSX with a natural flux expansion at tips of the crescent shaped section. Divertor plates are designed in this region by allowing sufficiently long connection lengths for the field lines, maximizing field line intersections with plates and minimizing the heat load peaking factor.

Poincare plots for solutions obtained by MFBE/GOURDON*.

E. Strumberger, Nucl. Fusion 37, 19, 1997.

0 30

plate/baffle area <15% A(1st wall)peak heat load ≤ 10 MW/m2

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An initial divertor design with 0.2 m offset from LCMS and with 25 toroidal 20 poloidal extension, respectively, shows that the plates/baffles provide 99.5% field line intersection with an average connection length ~220 m*, leading to adequate upstream to target temperature separations (300 eV) at high separatrix densities (~5·1019 m-3) and good radiated power fraction in SOL and divertors (>50%)**.

*T. K. Mau, ARIES-CS project meeting presentation, Oct 4 (2006). **Self-consistent edge modeling has not yet been studied in detail. A brief study was done by J. Lyon and R. Maingi using the Borrass model.

Power flow – J. Lyon (this meeting),

Thermomechanical – R. Raffray (this meeting).

~2% fusion power deposited on divertors as conductive/convective processes.

w(i,j)max/w(avg)~15

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Basis for Configuration Design Approach

motivation and goals

• Compact reactor systemQAS, QPS

Lower COE

Courtesy of J. Lyon

0

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0 4 8 12 16 20 24

Pla

sma

Asp

ect

Rat

io <R

>/<a

>

Average Major Radius <R> (m)

Stellarator Reactors

HSR-5

HSR-4SPPS

CompactStellaratorReactorsARIES

AT ARIESRS

FFHR-1

MHR-S

Circle area ~ plasma areaTokamak Reactors

FFHR-2

QHS?

HSR: <j||>/<j>

FFHR:(c-p)

L.P. Ku, ARIES-CS project meeting presentation, San Diego, Nov 4-5 (2004).

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• Critical considerations for QA reactors ( in addition to MHD stability and thermal confinement for experimental QA devices)

– Confinement of , – flux surface integrity, – space for blanket/shielding, – maximum field in superconductors, – coils for ease of machine maintenance

• HSR: low PS and BS, quasi-idodynamicity for confinement, flux surface, B(max) in coils, space for blanket/shielding.

• FFHR: B(max) in coils, space for blanket, long-life components.• Tokamaks: P(recirculation) for CD and alignment of J for MHD stability, vertical

stability and feedback control, kink stability and stabilizing shell, inboard standoff distance between plasma/coils.

Important Issues and Configuration Optimization

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• Configuration development is a non-linear, constrained

mathematical optimization problem, one that is to maximize the symmetry property subject to additional constraints by varying the shape of the LCMS.

– In QAS, bootstrap currents may drive the kink instability– Pressure may drive ballooning and other interchange instabilities– Pressure may enhance the effects of resonance perturbation– Engineering constraints for blanket/shielding and coils

• Consideration given in the development of baseline configuration

– Using limited Fourier modes in describing plasma boundarym≤6, n≤4

– Rotational transform due to external coils 50%– MHD stability to Mercier/ballooning/kinks ~ 4-5% using the ideal,

linear theory (vary plasma shape but not the pressure profile)– Effective ripple ≤1%, energy loss ≤10%– Coil aspect ratio ≤6, separation ratio ≤12

Important, but not included: (1) minimizing resonance perturbation, (2) optimizing pressure profile for both minimizing the peaking of neutron wall load and maximizing MHD stability, (3) optimizing first wall shape to minimize heat load variations, (4) maximizing maintenance port size in coil design, (5) minimizing B peaking in coils.

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• We build upon previous design studies:– NCSX

• Minimizing loss, reduce -eff

– MHH2/3/4 • Reduce A, design coils for finite (P. Garabedian)

• We broaden the search of the configuration landscape, leading to the discovery of many additional interesting configurations.– Generalized baseline configuration family

– “Ultra-low” plasma aspect ratio QAS with “low” coil aspect ratio coils comparable to tokamak reactors

– Configurations with carefully tailored rotational transforms.

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The baseline configuration is a member of the family having the characteristic mirror and helical components in the magnetic spectrum. Configurations in this family spans a wide range of aspect ratios and rotational transforms.

A=3.5 A=4.0 A=4.5 A=5.0 A=5.6

~0.15 per field period

~0.21 per field period

A~1.2 per period A~1.9 per period

The Advanced and Other Interesting Configurations

B(0,1)/B(0,0)~4% B(0,1)/B(0,0)~0%

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It appears that the lower end of the aspect ratio to maintain good quasi-axisymmetry is ~1.2 per field period, leading to the possibility of designing configurations with A as small as 2.5 for two field-period machines. Here is an example of the MHH2 family (MHH2-K14) chosen for its “gentle” shape. MHD stability and flux surface quality need more studies.

*P. Garabedian & L. P. Ku, FS&T, 47, 400 (2005)*L. P. Ku, Proc. 21st IEEE/NPSS Symposium on Fusion Engineering, Knoxville, TN, Sept. 26-29 (2005).

r/a~0.7

R/min(coil-plasma)~5.5

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We have also developed the “SNS” family of configurations whose rotational transform profiles are specifically designed to minimize the effects of resonance on the surface integrity. There are members in the family of the baseline configuration that also have similar properties. Here is an example with A~4.5 in which the iota profile lies in a region without low order resonances at 5% . Coils with good physics and engineering properties need to be designed.

~2.1/period

Equilibrium at 5% calcuated by the PIES code, showing the excellent flux surface integrity

L.P. Ku, ARIES-CS project meeting presentation, San Diego, June 14 (2006).

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NCSX experiment will provide necessary physics data base for design improvement.

• Design involves tradeoffs. Experimental data will help to quantify (courtesy of M. Zarnstorff):

– Rotational transform from coils and self-generated bootstrap current (how much of each?)

– bootstrap current affected by levels of non-axisymmetric residues (how sensitive?)

– 3D plasma shaping to stabilize instabilities (how strong?)– Quasi-axisymmetry to reduce ripple transport, alpha losses, flow damping

(how low must ripple be?)– Role of non-axisymmetric residues in ripple transport (good/bad? which

one? how much?)– Power and particle exhaust via a divertor (what topology?)– R/a (how low?) and (how high?)

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Summary and Conclusion

• The baseline configuration meets requirements of MHD stability and particle confinement necessary for high operations. Divertors have been designed for particle and power handling.

• The baseline coils have sufficient space for blanket/shielding so that reactors of R≤8 m to yield 1 GW electric power is achievable. Coil to coil spacing is also sufficient for the implementation of port maintenance scheme.

• Our efforts have revealed a rich landscape for QA configurations. Still better reactor designs may be found when given more efforts to improve coil designs and system trade-offs.

• The experimental results of NCSX should provide a physics data base using which the uncertainties of the present day design will be reduced and improved design criteria established.