Physics Basis for ARIES-CS

1
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

2
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 Configuration
The baseline plasma is a three field-period,
aspect ratio 4.5, quasi-axisymmtric configuration
with R7.75 m.
Reference parameters for baseline R7.75 m,
ltagt1.72 m, ltngt3.61020 m-3, ltTgt5.73 keV,
B5.7 T, b5, Ip3.5 MA, P(fusion) 2.364
GW, P(electric) 1 GW
Plane and perspective view of the geometry and
B of the last closed magnetic surface
J. Lyon, this meeting
4
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.
B in u-v space on surfaces at r/a0.5, 0.7 and
1.0
Collisionless orbits improved with 1-2 B(0,1)
as seen in an earlier study. N3AEC, toroidal
transit limit500, R10 m, B5.5 T, a born on
r/a0.5.
5
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.
Noise ?
1.8
3.5
r/a0.5
B(0,1)
r/a0.7
H. Mynick, A. Boozer and L. P. Ku, to appear in
Phys. Plasmas
6
The plasma may be described by
where D2,0-0.25, D2,1-0.41, D3,00.14,
D-1,00.11, D3,10.15, D-1,-10.17,
D0,10.07, D3,20.06, D4,0-0.06, with
D0,0 1.
k1.7, d0.7
D0,10.04 for NCSX
Plasma cross section seen in four equally spaced
toroidal angles.
L. P. Ku P. Garabedian, FST, 50, 207 (2006)
7
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 a
slowing down calculations with the temperature
profile chosen to provide a consistent pressure
profile.
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.
Temperature
p?1-(r/a)2.11.21
Density
p(peak)/p(average)2.1
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Equilibrium calculations indicate small Shafranov
shifts at high b 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.
Equilibrium calculated _at_ 5 b by VMEC
External and finite b total transform
VMECS. P. Hirshman, W. I. van Rij, P. Merkel,
Comp. Phys. Commun. 43, 143 (1986)
9
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.
Poincaré plot of an equilibrium at 5 b by PIES
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).
10
The configuration is stable to the vertical mode
(1,0) as i(ext)/i?75. The configuration is also
stable to the external kink modes at 5 b
without passive stabilization (Terpsichore
calculations).

• 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 (??????????

HSR 3.5 for global modes.
TerpsichoreD. 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).
11
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 b, indicating the configuration
has favorable characteristics for global mode
stability.
Current Density
kink stable using the reference J profile.
kink stable at 5 b using a broad J profile.
12
The configuration has good stability
characteristics to the Mercier and ballooning
modes (COBRA calculations).
unstable
unstable
FLR correction typically leads to a higher
ballooning b limit (50). Local pressure
flattening also leads to higher limits.
b3, 4, 5, 6
b3, 4, 5, 6
stable
stable
COBRAR. Sanchez, S. P. Hirshman, J. C. Whitson,
A. Ware, J. Comput. Phys., 161, 589 (2000)
13
Recent W7AS and LHD Experiments Steady High-b,
Above Linear Limit. (courtesy of M. Zarnstorff)
Germany
PPPL MP/IPP Collaboration
Japan

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

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The configuration has very low effective ripple,
being everywhere lt 0.5, despite the existence of
1-2 of B(0,1) and B(1,1).
e-eff calculated by NEO
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 H1.5 (J Lyon, this meeting).
HSR-18 lt0.6 FFHR 10
ISS04 has a more favorable scaling.
20 MW auxiliary power is required during startup
to reach ignition. Paths of startup have not been
studied.
NEOV. V. Nemov, S. V. Kasilov, W. Kernbichler
and M. F. Heyn, Phys. Plasma, 6(12), 4622 (1999)
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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.
B6.5 T, 5 b
R7 m
R10 m
HSR-18 2.5 FFHR 10
Footprint of lost a in (q,f), lost particle
energy distribution and cumulative particle loss
versus time for the baseline configuration
(ORBIT3D calculations).
ORBIT3DR. B. White and M. S. Chance, Phys.
fluids, 27, 2455 (1984)
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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
Modular coil winding pack 0.194 m x 0.743 m
I(max)13.5 MA, B(max)15 T, R/D(C-P)5.9,
R/D(C-C)10.
PF coils are designed for startup and equilibrium
position control. I(max)lt 5 MA.
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.

plate/baffle area lt15 A(1st wall) peak heat load
10 MW/m2
0?
30?
Poincare plots for solutions obtained by
MFBE/GOURDON.
E. Strumberger, Nucl. Fusion 37, 19, 1997.
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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 (51019 m-3) and good
radiated power fraction in SOL and divertors
(gt50).
w(i,j)max/w(avg)15
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.
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Basis for Configuration Design Approachmotivatio
n and goals
Lower COE
L.P. Ku, ARIES-CS project meeting presentation,
San Diego, Nov 4-5 (2004).

• Compact reactor system

QAS, QPS
QHS?
Courtesy of J. Lyon
HSR ltjgt/ltj?gt
FFHRD(c-p)
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Important Issues and Configuration Optimization

• Critical considerations for QA reactors ( in
  addition to MHD stability and thermal confinement
  for experimental QA devices)
• Confinement of a,
• 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 a
  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.

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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
  boundary
• m6, n4
• Rotational transform due to external coils ?50
• MHD stability to Mercier/ballooning/kinks 4-5
  b using the ideal, linear theory (vary plasma
  shape but not the pressure profile)
• Effective ripple 1, a 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 a loss, reduce e-eff
• MHH2/3/4
• Reduce A, design coils for finite b (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 Advanced and Other Interesting Configurations
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.
i0.15 per field period
A1.9 per period
A1.2 per period
B(0,1)/B(0,0)0
B(0,1)/B(0,0)4
i0.21 per field period
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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.
r/a0.7
R/Dmin(coil-plasma)5.5
P. Garabedian L. P. Ku, FST, 47, 400 (2005)
L. P. Ku, Proc. 21st IEEE/NPSS Symposium on
Fusion Engineering, Knoxville, TN, Sept. 26-29
(2005).
25
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 A4.5 in
which the iota profile lies in a region without
low order resonances at 5 b. Coils with good
physics and engineering properties need to be
designed.
Equilibrium at 5 b calcuated by the PIES code,
showing the excellent flux surface integrity
i2.1/period
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 b operations. Divertors have been
  designed for particle and power handling.
• The baseline coils have sufficient space for
  blanket/shielding so that reactors of R8 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.