Reactor Configuration Development for ARIES-CS

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Reactor Configuration Development for ARIES-CS

• L. P. Ku and the ARIES-CS Team
• Princeton Plasma Physics Laboratory
• Princeton University, Princeton, NJ 08543

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Abstract

• Progress has been made in developing new classes
  of quasi-axially symmetric configurations for
  ARIES-CS that have good a particle confinement
  properties and good integrity of equilibrium flux
  surfaces at high b.

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• For each new class of configurations, we have
  designed coils to ensure that the new
  configurations are realizable and
  engineering-wise feasible.
• R/Dmin (Coil-Plasma) 6
• R/Dmin (Coil-Coil) 10.
• The physics and coil properties of new
  configurations allow power producing reactors of
  2 GW be designed with Rlt9 m with DT fuels and
  with a full breeding blanket. The good
  quasi-axisymmetry limits the energy loss of a to
  lt 10.

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• We showcase two new classes of configurations
• Configurations with low magnetic shear even in
  the presence of large amount of bootstrap
  current.
• Configurations of very low aspect ratios (A2.5)

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What Is ARIES-CS

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F. Najmabadi, UCSD
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Goals of Configuration Design Study

• Identify plasma engineering issues relevant to a
  compact stellarator reactor
• Find configurations that are optimized with
  respect to the components critical to reactor
  performance
• Aspect ratios versus QA
• a loss and its minimization
• Equilibrium and MHD b limits
• Integrity of flux surfaces

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Minimum requirements in configuration
optimization for MHD stable QA plasmas at high b
are not well known at present. The following are
acceptance criteria generally considered.

• Maximum residues of non-axisymmetry in magnetic
  spectrum.
• neo-classical transport ltlt anomalous transport
• ovall allowable noise content lt 2.
• effective ripple in 1/n transport, e-eff lt 1
• ripple transport and energetic particle loss
• a energy loss lt 10
• rotational damping (?)
• Stability beta limits based on linear, ideal MHD
  theories.
• vertical modes
• interchange stability
• V?2-4.
• LHD, CHS stable while having a hill.

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• ballooning modes
• stable to infinite-n modes (eigenvalues
  calculated by COBRA code).
• LHD exceeds infinite-n results. High-n
  calculation typically gives higher b limits.
• kink modes
• stable to n1 and 2 modes without a conducting
  wall (eigenvalues calculated by Terpsichore
  code).
• W7AS results showed mode (2,1) saturation and
  plasma remained quiescent.
• tearing modes
• di/ds gt 0
• Equilibrium and equilibrium beta limits
• Shafranov shift
• large islands associated with low order rational
  surfaces
• flux loss due to all isolated islands lt 5
• overlapping of islands due to high shears
  associated with the bootstrap current
• limit di/ds

The ability to achieve our goals is often
compromised by the conflicting demands of various
constraints. Typically, we impose different
weights depending upon the characteristics of a
configuration we are looking for. There is also
an issue of convergence and accuracy in numerical
calculations.
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Configuration Design Targets (Cont.)
To establish minimum requirements for coil design
optimization, we need more feedback from and
iteration with systems analysis and engineering
design. Presently, we include

• Coil design
• coil to coil and coil to plasma separation
• R/Dmin(c-c) lt 12
• R/Dmin(c-p) lt 6
• radius of curvature and complexity
• Bmax/B0 2.5 for 0.3 m x 0.3 m conductor _at_R8 m.
• adequate space for pumping, diagnostics, plasma
  heating and maintenance
• R/Dout (c-p) lt Ap (R/ltagt)

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Methods of Exploring Configuration Space

• Broaden search of aspect ratio rotational
  transform space, identifying regions endowed with
  particularly interesting features.
• Build sophisticated computational systems to
  design configurations and coils which target the
  physics and engineering goals.

See companion poster Modular Coil Design for
the Ultra-Low Aspect Ratio Quasi-Axially
Symmetric Stellarator MHH2
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Plasma Optimization System

1. Select p, J profiles, b, B, FP
2. Iota target
3. MHD stability target (Mercier, ballooning, kink)
4. Transport target (QA, ripple)
5. Coil target (complexity, current density)

Constraints/weights
Initial guess. Plasma boundary represented as
Fourier coefficients.

ballooning

1) Evaluate equilibrium (VMEC, NSTAB), 2)
Jacobian calculations, 3) determine direction of
descent, 4) perform functional minimization
(Levenberg-Marquardt, GA).
kink
a loss
transport
shape/position
coil complexity
No
Targets met?
Modify weights
Yes
Flux surface quality, islands healing, PIES
Refined calculation and detailed analysis
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I. SNS family of configurations
KJC167 a showcase for essentially flat iota
profile, demonstrating the existence of
excellence of flux surface integrity

Plane and perspective views of last LCMS geometry
and B in real space.
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Why low overall shear is of interest?

• The integrity of equilibrium flux surfaces places
  a limit on the attainable beta
• Shafranov shift
• Formation of magnetic islands
• Spacing between island chains and magnetic field
  stochasticity
• We generally require
• Shafranov shift
• large islands associated with low order rational
  surfaces
• flux loss due to all isolated islands lt 5
• overlapping of islands due to high shears
  associated with the bootstrap current
• limit di/ds

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How flux surface integrity might be achieved in
QAS?

• Bootstrap currents in QAS are expected to be of
  similar magnitude to those in tokamaks.
• High magnetic shear possible
• Rotational transform crossing large number of
  rational surfaces likely
• Rational surfaces may be close to each other
• One solution is to carefully tailor the
  rotational transform profile
• Select regions free of low order resonances
• Shape the plasma such that the rising rotational
  transform due to the bootstrap current is
  compensated for by the decreasing transform from
  the shaping.

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KJC167 is a 3 field-period, aspect ratio 6
configuration of the SNS family in which the iota
profile is selected to minimize the impact of low
order resonance on the flux surface integrity. In
this case, the external iota has a strong
negative shear, but the iota at operating b is
expected to have a small but positive shear in
most of the plasma volume.
Shear 5
Total transform including contribution from
bootstrap current at 6 b.
External transform from plasma shaping
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Excellent quality of flux surfaces is observed in
most of the plasma for KJC167 at 6 b as seen
below based on a PIES calculation.
Equilibrium calculated by PIES _at_6 b.
Poincaré plot in r-q at j0.
In Cartesian
m16
PIES and VMEC solutions are consistent.
Equilibrium calculated by VMEC
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Minimizing non-axisymmetric residues and
effective ripples resulted in good
quasi-axisymmetry. The effective ripple _at_s1 is
only 0.35 at 6 b and the overall noise is
lt2.5. Loss of a energy is 8 in one slowing
down time in our model calculation.
B on last LCMS in U-V space
Effective ripple
2.5 _at_s1
0.5
Ovall noise content
vacuum
Eight major non-symmetric components in the
magnetic spectrum plotted as function of
normalized toroidal flux.
With pressure at 6 b
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KJC167 is stable to the m1, n0 vertical mode
according to the Terpsichore calculation (no
feedback control necessary) and is slightly
unstable to both low and high-n internal modes at
b4.
Infinite-n ballooning modes (Cobra calculation) _at_
Low-n modes g R/vA0.001
P-profile
6 b
5 b
3 b
J-profile
2 b
Note stability analyses were based on the
pressure and current profiles given above.
Profiles may be further optimized to improve MHD
stabilities to both the local and global modes.
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KJC167 may be unstable to free-boundary modes for
b6 according to the Terpsichore calculation
primarily due to the m2, n1 mode, but it could
be made stable with more flux surface shaping to
improve the local shear. It may also be made more
stable by choosing more optimized pressure and
current profiles.
g R/vA0.15
Radial displacement eigenfunction
N0
N1
Wall _at_3.5x plasma-vacuum interface
Plasma-wall interface
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A proposed design for the modular coils is to
have 6 coils/period with coil aspect ratio
R/Dmin(C-P)6. The example given here,
KJC167-M05, based on equal coil currents, has
smooth contours with small toroidal excursion.
Coil contours viewed on U-V plane of the
winding surface in one field period.
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II. MHH2 Family of Configurations
MHH2-K14 a showcase for very low aspect ratio
A2.65 configuration having low field ripples and
excellent confinement of a particles.

Plane and perspective views of the last LCMS
geometry and B in real space.
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Why low aspect ratio is of interest?

• Fusion power, P, is inversely proportional to the
  square of plasma aspect ratio, A
• A R/ltagt, Rmajor radius, ltagtaverage minor
  radius
• P ? B4b2R3/A2
• Lower A allows lower B or b or R.
• Smaller sized-reactor (R)
• Less stress and power for magnets (B)
• Less MHD stability issues (b)

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MHH2-K14 is a configuration of the ultra-low A
family with relatively simple shaping and
optimized for quasi-axisymmetry at 5 b without
any other driven currents.
Expected at 5 b with NCSX-like pressure/current
profile
Assumed in configuration optimization
External transform due to plasma shaping
LCMS in four toroidal angles over half period.
Rotational transform as function of toroidal flux.
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MHH2-K14 has reasonably good QA, but it is not as
good as 1104. The B(2,1) and B(3,2) components
remain to be significant in the magnetic
spectrum. The loss of a energy is still
reasonable, being lt 10 (6 in one slowing down
time in our model calculation).
(2,1)
(0,1)
(0,2)
(3,2)
Max. noise content 3.4 _at_s1
B on last LCMS in U-V space
Eight major non-symmetric components in the
magnetic spectrum plotted as function of
normalized toroidal flux.
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Plots of B along field lines show an increased
amount of secondary ripples and the
epsilon-effective (calculated by the NEO code) at
the edge is now 0.8.
r/a0.5
r/a0.7
effevtive ripple (1/n)
B versus poloidal angle q in radians along
field lines starting _at_ j0, q0.
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A vacuum magnetic well, 4 _at_ s1, was imposed as
one of the constraints in the configuration
optimization.
Total _at_ 5 b, p ? (1-s1.5)1.5
From plasma shaping. Well depth3.8 _at_s1.
Magnetic well depth as function of normalized
toroidal flux.
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But it is slightly unstable to both low- and
high-n internal modes at b4.
Infinite-n ballooning modes (Cobra calculation)
Low-n modes g R/vA0.0009
p ? (1-s1.5)1.5
5 b
Radial displacement eigenfunction
3 b
2 b
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MHH2-K14 may be also unstable to the external
modes for bgt5 according to the Terpsichore
calculation, primarily due to modes of
intermediate toroidal mode numbers 5 and 7.
g R/vA0.12
Radial displacement eigenfunction
Plasma-wall interface
Wall _at_3.5x plasma average minor radius
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A modular coil design for MHH2-K14 (K14LA).
Details see the companion paper.

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Summary Conclusions

• Taking advantage of recent experimental results
  which generally showed that stellarator plasmas
  are more resilient to MHD perturbations than
  predicted by the linerar theories, we searched
  the rotational transform-aspect ratio space for
  configurations endowed with better
  quasi-axisymmetry, low a-particale loss and
  better integrity of flux surfaces at high
  equilibrium beta.
• We have found configurations whose rotational
  transform have small but positive shear even with
  the presence of large amounts of bootstrap
  current, making the avoidance of low order
  rational surfaces possible. We have also found
  configurations in two field periods having very
  low aspect ratios, making reactors of high power
  density and smaller sizes likely.
• The most attractive configurations will
  ultimately be determined by results of systems
  optimization and other constraints arising from
  engineering designs. To this end, we have
  included in our effort also the initial coil
  designs to ensure the realizability of the
  configurations we found and have provided
  configuration and coil parameters to the systems
  study to allow a better understanding of the
  optimal parameters for a competitive power plant.