SSPX

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SSPX Physics results from experiment and
simulation Presented at Princeton Plasma Physics
Laboratory Princeton, NJ January 7, 2008 Bick
Hooper Fusion Energy Program, LLNL
Work performed under the auspices of the U. S.
Department of Energy by Lawrence Livermore
National Laboratory under contracts W7405-ENG-48
and DE-AC52-07NA27344.
UCRL-PRES-400218
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This work was conducted with a large number of
collaborators, both experimentalists and theorists
The entire SSPX team contributed through SSPX
operation, critique of the NIMROD studies, and
comparisons with experimental results Collaborato
rs include Dave Hill Harry McLean Carlos
Romero-Talamás Simon Woodruff Ken Fowler Lynda
LoDestro Additional collaborators came from
Caltech, U. Washington, FAMU, LANL, U.C.
Berkeley, U.C. Davis. We are members of NSF
Frontier Science CMSO NIMROD resistive MHD
simulations conducted with Bruce Cohen and in
close collaboration with Carl Sovinec
(Wisconsin) Computer facility support provided
by NERSC and Bill Meyer at LLNL
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The Sustained Spheromak Physics Experiment (SSPX)
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Sustained Spheromak Physics Experiment
Thick wall (.015 m) copper flux conserver (dia1
m). Tungsten coating reduces sputtering. Ti
gettered to reduce impurities 4 msec
discharges. 500 kA peak formation, 250 kA
sustained 9 solenoidal coils provide flexible
vacuum field programming
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Experiment Above a gun-current threshold the
spheromak field builds
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SSPX Summary of results
Te 500 eV nTe(peak) B2 ?e lt 10 m2/s in
spheromak core Magnetic fluctuation spectrum
correlates well with q-profile Confinement has
no (or weak) scaling with mass Energy
confinement improves with Te and low-level
fluctuations Charge-exchange losses are not
dominant Basic understanding of magnetic
reconnection in the spheromak NIMROD
whole-device simulations agree well with many
experimental results
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Whole-device model of SSPX includes power systems
and bias-coil magnets (not shown)
New, lower resistance cables
Sustainment Bank 5kV, 120mF
SSPX
Modular Bank (5 kV, 40 mF) ? 30
Formation Bank 10kV, 10mF
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Whole-device, resistive MHD simulations of SSPX
discharges and physics have contributed
significantly to understanding experimental
results Generally good agreement with
experiment Predictive capability guide
experiments and permit exploratory
modeling NIMROD's capabilities
extended Resistive MHD physics studies in
tokamaks and alternative concepts complemented
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Improved Match of NIMROD Simulations to
Experiment

• Improved NIMROD simulations with
• Spitzer-Braginski resistivity and parallel
  thermal conduction
• more detailed representation of gun geometry
• careful match to current-drive time history with
  experiment
• give improved agreement with Bz and Te in SSPX.

• As current ramps down, a large amplitude n2 mode
  is observed in both experiment and simulation.

From B. I. Cohen, APS invited talk, Nov. 2004
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NIMROD Edge-Probe Fluctuation History Is Similar
To SSPX Data.
During the strong drive period t lt 0.4ms the
n1 mode is active,
, and the closed field lines begin to form
after 0.4 ms. The n2 mode emerges for
0.4ms lt t lt 2ms and gradually subsides,
but re-emerges at the end of the simulation,
gt 4 ms and The amplitudes of the magnetic
fluctuations and their temporal history
are very much like those measured in SSPX.
B. Cohen, Hooper, et al.
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NIMROD Simulations Show Good Flux Surfaces and
Electron Temperatures Similar to SSPX.

• NIMROD simulations show regions of good
  confinement (0.25ltRlt0.4) surrounded by islands
  and chaotic lines (0.15ltRlt0.25,0.4ltRlt0.48) and
  then open field lines.
• Electron temperature contours align with the
  magnetic field lines.
• Local flattening in the electron temperature
  profile due to the presence of islands
• Transition from good flux surfaces to chaotic and
  then open field lines leads to steep drop in Te

From B. I. Cohen, APS invited talk, Nov. 2004
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Spheromak formation Magnetic reconnection Magnetic
field buildup
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Experiment and NIMROD Voltage spikes occur in
both have the same effect on building and
sustaining the plasma
SSPX and NIMROD with identical gun currents The
bubble-burst of plasma from the gun is followed
by voltage spikes Toroidal flux is converted into
poloidal flux at each spike  Reconnection Magnet
ic oscillations (esp. n1) driven by the gun
current grow between voltage spikes relax
at the reconnection event
Same as experiment
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NIMROD  Reconnection events continue if the
current is flat-topped with??gun gt ?threshold
Simulation (shown) and experiment both show
voltage bursts when strongly driven here, ?gun gt
2X?threshold
Poloidal flux amplification 5.6 (extrapolates
to 6.7)
NIMROD simulations
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NIMROD Reconnection occurs when the amplitudes
of modes on the current column become large a
bursting behavior
The poloidal magnetic field and flux increase
with each event the temperature collapses
The n1 mode dominates the spectrum
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NIMROD Magnetic surfaces are destroyed at each
spike
Magnetic surfaces may form soon after the
event The plasma heats until the next event
The magnetic lines become stochastic and the
plasma cools rapidly
70 µs
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NIMROD Thin current sheets form and allow rapid
resistive reconnection
Current sheets are important for
reconnection Resistive diffusion times across
the sheet are comparable to reconnection
times Azimuthal structure is n1 the sheet
is diffuse p?radians azimuthally Current
reverses and large flows perpendicular to B are
localized at the sheet Sheet forms near the
mean-field separatrix
Trajectories of fieldlines which pass close to
the current sheets are very sensitive to their
precise location as expected for generation of
chaos
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The mean-field generation is insensitive to the
max. toroidal mode number for n gt 5
NIMROD
SSPX
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NIMROD (slowly decaying) Mode magnetic energy
drops rapidly with toroidal mode number (n 21)
at high n Most studies can use n
5
kin_visc1000 m2/s
kin_visc100 m2/s
kin_visc10 m2/s
A transition from mode energies constant to a
"cascade" at high n Slope of the "cascade" is
roughly proportional to kinetic viscosity
squared index for (mode energy)1/2
const.log(kin_visc) Hypothesis The transition
occurs when viscosity is strong enough to
stabilize the modes The "cascade" results from
mode coupling with viscous damping (
)
q-profiles depend slightly on viscosity
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Viscosity affects detailed time history but the
generation of the mean field is only weakly
affected
Viscosity (100 m2/s and 1000 m2/s) More
structure in the time histories of current,
field, etc.at low viscosity However, the n0
magnetic field strength is insensitive to the
value of viscosity, dropping about 20 with an
order of magnitude increase in ?
NIMROD (ntor,max5, density 5.0x1019 m3)
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Formation studies successfully reproduce the
mean-field buildup
Resistive MHD is a good model for spheromak
formation by helicity injection into a
flux-conserving geometry Mean-field
(azimuthally-averaged) parameters are generally
reproduced well and are relatively insensitive to
assumed number of toroidal modes, viscosity,
etc. Field ejection from the gun timing and
voltage response (compared to nearly-axisymmetric
experimental ejection) Magnitude of the gun
voltage and current experimental
values Azumuthally-averaged magnetic field
experimental values Detailed time histories are
relatively sensitive to assumed number of
toroidal modes, viscosity and similar
parameters Several parameters require low
kinetic viscosity and ntor,maxgt1 Sharp voltage
spikes Structure in the time-history of the
magnetic field Precise time histories
(including fluctuation timing) differ from the
experiment
These results suggest that field buildup is
insensitive to the detailed physics in the
reconnection layer
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Magnetic field sustainment and Flux
Amplification
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Sustained NIMROD discharges Steady-state with
?gun20.3 m1, and 13.6 m1
(bias flux51 mWb)
?gun13.6 m1
?gun20.3 m1
Gun current
Gun voltage
Note the different time scales
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NIMROD Poloidal flux amplification increases
with ?gun above threshold simulations show this
clearly
Flux Amplification ?mag.axis/?sep Shown is the
flux amplification in a constant gun current
pulse Larger ?gun yields higher flux
amplification, consistent with experiment
It is clear from the simulations and from a
hyper-resistivity model that the poloidal-field
buildup above threshold is a balance between
reconnection and resistive losses. We do not have
a simple model that makes quantitative predictions
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NIMROD Simulations Agree with Flux Amplification
at moderate ?gun in SSPX
NIMROD predicts the flux amplification in SSPX
for current constant Experimental flux
amplification scales with ?gun as predicted by
NIMROD.
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Maximum amplification of the bias magnetic flux
For strong drive, experiment and
simulation differ
Poloidal flux Use Bessel function model and
measured Bp(edge) Shots with lower amplification
result from several causes Formation pulse too
short to reach saturation Lack of density
control Other "kitchen physics" problems There
appears to be a consistent problem at high
?gun The amplitude of the n1 mode becomes very
large, perhaps exacerbating other effects
Data Wood, Hudson, et al.
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Flux Amplification in an Extended Flux Conserver
A series of experiments have been conducted with
the flux conserver length increased from 0.5 to
0.6 m (L/R from 1 to 1.2)
Spheromak poloidal flux (magnetic axis) in SSPX
is determined from Bz at the wall Bessel
function model (midplane probe) ??/Bz332
Wb/T NIMROD (probe near midplane)
??/Bz3245Wb/T Correction (from NIMROD) for
SSPX Probe 9 position ??/Bz354
Wb/T NIMROD Flux Amp.
FA10.56(?gun7.5)
Data Wood
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Flux Amplification scaling with L/R
We have two threshold determinations from NIMROD,
both of the form ????????gun10.56(??th)
In a cylindrical spheromak The tilt (n1,m1)
mode is stable for L/R lt 1.67 The approximate
agreement with the threshold (extrapolated to
?th0) suggests that Coupling to the
spheromak is stabilizing for the column (n1)
mode when the spheromak is stable to the n1, m1
modes Note Scaling as ?thLconst. would yield
?th8.3 for L/R1.2 J. M. Finn and W.
Manheimer, Phys. Fluids 24, 1336 (1981). A.
Bondeson, et al., Phys. Fluids 24, q682 (1981).
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Studies of slowly-decaying plasmas
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Te 500eV in SSPX obtained by extending the
formation
Extended formation
Te Shot 17096 _at_ 1.50 ms
Lower density (less gas)
X2 flux higher Bp edge
Similar fluctuations
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Optimum ?edge ( ?gun) and strong heating
produces high Te
Nimrod simulations show a similar optimum
associated with reduced mode activity
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Equilibrium reconstructions optimal ledge
results in slightly-peaked safety factor profile
with 1/2 lt q lt 2/3
Fluctuations grow when low-order mode-rational
surfaces appear in plasma.
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The safety factor in the simulation is similar
but not identical to that in the best SSPX
shots
Nimrod
SSPX
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Parameter sensitivities in slowly-decaying
plasmas Effects of mode amplitudes and
q-profiles
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Simulation parameter effects on evolution of
magnetic field and detailed time-history of
temperature
The best SSPX shots have higher electron
temperatures than NIMROD!
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Sensitivity to simulation parameters
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NIMROD has successfully modeled many experimental
results, providing insight into spheromak MHD
physics
Magnetic-field buildup by reconnection Buildup
of the spheromak field is insensitive to
simulation parameters The time history of the
mean-field field, Te, etc. are sensitive to
parameters Voltage spikes on the gun result
from reconnection events Stochastic fieldlines
during reconnection result in observed low Te
during magnetic buildup and sustainment Flux
amplification at moderate ?gun agrees with
experiment Amplification simulations (to date)
suggest that the spheromak helps stabilize the
n1 column mode Flux amplification at high ?gun
is less in the experiment for reasons that are
not understood High Te results when flux
surfaces close Surfaces form when magnetic
fluctuations are low Te is thus very sensitive
to the q-profile Simulations helped guide the
experiment and are being used to explore
alternative spheromak configurations
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Backup slides
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Limiting ?e is observed experimentally Likely
due to ohmic heating, but a stability limit
cannot be excluded
Te vs. nk/PB
Need external heat source to differentiate
transport limit from pressure limit
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Electron thermal diffusivity in core of SSPX is
well below Bohm, and scales as Te-5/2

• Power balance between ohmic heating and radial
  transport yields thermal diffusivity

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Using NIMROD for studying possible advanced
spheromak experiments High flux amplification by
Ramp-down of gun flux and current Active Bias
Reduction (ABR) Reduced power losses in edge
plasma and improving MHD stability
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Reducing the bias flux and gun current by a
factor of 10 increases the volume of good flux as
the current column shrinks
Start
Finish
Ramp down in 1 ms
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Reducing the bias flux and gun current by a
factor of 10 decreases the amplitudes of the MHD
modes by a large factor
Amplitude at flux conserver drops to 103 of n0
Total mode energies
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Topics for continuing spheromak simulations
Simulations and other modeling can continue to
advance spheromak physics even if the experiment
ends Use the SSPX data base to interpret
results and improve physics Explore options for
advanced experiments Strengthen comparative
studies with RFP and FRC Analysis of SSPX
data Linear calculations to identify modes
(ideal MHD, tearing) Finite beta is the
limiting beta in SSPX due to MHD
modes? Simulate multipulse discharges Reconnec
tion physics Recovery of good confinement, high
Te Explore effects of increased flux-conserver
Length/Radius Clarify saturation of flux
amplification and develop analytical
approximation Calculate flux amplification at
fixed Te (verify role of power balance) Compare
with hyper-resistive model obtain
hyper-resistive diffusion coefficient for use in
Grad-Shafranov model used in Corsica Model
experimental limits of peak B/I (flux
amplification) current distribution on cathode?
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Continuing spheromak simulations
Analysis of spheromak opportunities Explore
effects of geometry A new grid has been
developed for exploring geometry changes but not
yet used in NIMROD Vary the gun radius  Does
it matter? Is there an optimum
Length/Radius? Extend ABR calculations to more
general geometries Demonstrate quasi-steady
state with ABR and multi-pulse rebuilding of the
magnetic field Do 2-fluid effects matter?
(plasma rotation, reconnection) Explore
auxiliary heating and current drive, e.g. with a
simple model for neutral-beams Explore
current-profile control establish requirements
and examine options
The program presented on these two slides will
take several man-years and substantial computer
time. The goal is to generate the maximum
physics results from the SSPX experiment and
provide a substantial knowledge base for any
future experiments