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Compact Stellarators as Reactors. J. F. Lyon, ORNL NCSX PAC meeting June 4, 1999. TOPICS. Earlier Stellarator Reactor Studies Comparison with ARIES Reactors Extrapolation of QA to Reactor. Compact Stellarators Have the Potential for an Attractive Reactor.

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compact stellarators as reactors

Compact Stellarators as Reactors

J. F. Lyon, ORNL

NCSX PAC meeting

June 4, 1999

  • Earlier Stellarator Reactor Studies
  • Comparison with ARIES Reactors
  • Extrapolation of QA to Reactor
compact stellarators have the potential for an attractive reactor
Compact Stellarators Have the Potential for an Attractive Reactor
  • Steady-state operation without external current drive
  • Disruption immunity at the highest plasma parameters
  • Stability against external kinks and vertical instability without a close conducting wall or active feedback systems
  • Reduced size for higher wall loading

• Compact, power density similar to tokamaks

• Without disruptions, feedback, or external current drive

hsr reactor based on wendelstein 7 x
HSR Reactor Based on Wendelstein 7-X
  • R = 22 m, B0= 5 T, Bmax= 10 T (NbTi SC coils)
  • <> = 5%; based on conservative physics, technology

1993-95 ARIES Stellarator Power Plant Study

•SPPS based on W7-X

like configuration but

aimed at smaller size

•R0 = 13.9 m, <> = 5%

•B0 = 4.9 T, Bmax = 16 T

•Pelectric = 1 GW




and shield

plasma surface


ARIES SPPS Study Developed

a Feasible Maintenance Approach

Fusion Power Core

most important measure of reactor attractiveness is coe
Most Important Measure of Reactor Attractiveness is COE
  • R0, pwall not the most important measures!
  • Higher value of Qeng compensates for R0, pwall
minimum reactor size is determined by
Minimum Reactor Size Is Determined by 
  • A configuration is chacterized by the ratios A = R0/, Ap = R0/<a>, and Bmax/B0
  • The minimum reactor size is set by R0 = A(D + ct/2) where D is the space needed for scrapeoff, first wall, blanket, shield, coil case, and assembly gaps
  • B0 is set by (16 T)/(Bmax/B0)
extrapolation of compact stellarators to a reactor
Extrapolation of Compact Stellarators to a Reactor
  • Vary distance  for compact stellarator configurations
    • calculate sheet-current solution at distance  from plasma that recreates desired plasma boundary
    • calculate Bmax/B0 at distance ct/2 radially in from current sheet
  • Choose maximum credible distance R0 = A(D + ct/2)
  • R03Pfusion/B04, so want high B0 for smaller reactor; however
    • B0decreases with increasing  (Bmax/B0 increases)
    • Coil complexity (kinks) increases with increasing 
  • Choose minimum ct/2 that satisfies two constraints
    • Ampere’s law: B0 = 20Njct2/(2R0); coil aspect ratio = 2 assumed
    • B0 = (16 T)/(Bmax/B0); Bmax/B0 increases as ct decreases
  • Bmax/B0 is larger for actual modular coils, so use 1.15Bmax/B0
  • Need to redo in future for real modular coils
minimum credible a value for c82 is 5 8 minimum r 0 9 3 m
Minimum Credible AValue for C82 is 5.8  Minimum R0 ­ 9.3 m


coil contour

poloidal angle

9.67  15.3 m

7.25  11.6 m

5.8  9.3 m

4.83  7.7 m

toroidal angle


Bmax/Bo Scan for Reactor-Scale QA’s

Bmax/Bo calculated at coil inner edge

(on a surface shifted inward by half coil depth)

from Nescoil surface current solution at coil center

P. Valanju

coil half depth is chosen to minimize r 0
Coil Half-Depth Is Chosen to Minimize R0


A = 4.1




  • R0/ = 5.8 case, 21 coils, 2:1 coil aspect ratio; Bmax = 16 T
  • Based on surface current distribution, not modular coils

j = 3 kA/cm2

based on


qa reactors are closer to aries rs than spps
QA Reactors Are Closer to ARIES-RS than SPPS


  • <> = 5%, H’ = 0.64; not optimized yet for a reactor
c82 based reactors are sensitive to plasma coil spacing
C82-Based Reactors Are Sensitiveto Plasma-Coil Spacing
  • ARIES study is needed to determine realistic plasma-coil spacing and estimated COE
compact stellarators could lead to a better reactor
Compact Stellarators Could Lead to a Better Reactor
  • 14-m SPPS (with lower wall power density) was competitive with 6-m ARIES-IV and 5.5-m ARIES-RS because of its low recycled power (high Qeng)
  • C82 can retain low recycled power of SPPS, but has smaller size (lower cost) and higher wall power density
  • However, the power produced is more than the 1 GWe assumed in the ARIES studies ( margin)
  • The details of size, field, and wall power density need to be studied further to optimize a reactor by the ARIES group, as was done for SPPS
plans for reactor scoping studies
Plans for Reactor Scoping Studies
  • Optimize Bmax/B0 vs  for
    • QA sheet-current configurations with Ap = 3.4 and 4.1
  • Simple 0-D spread sheet reactor optimization
    • include variation of Bmax/B0 vs and reactor physics
  • Full systems code reactor optimization (OPTOR)
  • (minimize COE: ARIES algorithms, benchmark with ARIES-RS)
    • simple 0-D transport models
    • solve for Te(r) and Ti(r) for 1-D anomalous e,i and electric-field-dependent e,i with fixed n(r),(r): Shaing, Mynick
    • Self-consistent solution for Te(r),Ti(r), ne(r), ni(r), and (r) with fixed particle source (pellets or gas)
    • study sensitivity to transport models and energetic losses
  • ARIES group look at impact of key issues, COE
  • QA Compact Stellarators lead to more attractive reactors, but not smaller reactors
  • Ultimate figure of merit for a toroidal reactor is the cost of electricity, not major radius or wall power density, when comparing different concepts
  • However, major radius and wall power density are important when optimizing a particular concept
  • R0/<a> = 3.4 and 4.1 QA configurations lead to smaller reactors closer to ARIES-RS than the earlier competitive SPPS
  • QA configurations so far have not been optimized for a reactor; need to reduce A further
  • ARIES study will be needed for better optimization