Studies of ImprovedStability FRCs in MRX

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Studies of Improved-Stability FRCs in MRX

• S. P. Gerhardt, M. Inomoto, E. Belova, M.
  Yamada, H. Ji, Y Ren
• Princeton Plasma Physics Laboratory
• Osaka University

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MRX-FRC program attempts to address outstanding
issues in FRC Research

• Formation of large flux FRCs
• Spheromak merging technique
• Initial toroidal field energy of spheromaks
  converted to thermal energy.
• Previous work indicates the utility of this
  method (TS-3/4, SSX)
• Tilt Stability of FRCs
• Oblate shape is predicted to stabilize
  tilt-instability

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This Talk

• MRX Device, Diagnostics, and Instabilities.
• Spheromak Merging/FRC Formation Sequence.
• 3 Keys to Good FRC formation in MRX-FRC.
• Experimental Study of FRC Stability
• Boundary Between n1 shift and tilt stability.
• Reduction of Instabilities with a center
  conductor
• Experimental regime of n1 stability with center
  conductor.
• Equilibrium and Stability Properties for FRC
  plasmas.
• Custom Grad-Shafranov solution code.
• Establishment of Rigid-body tilt stable regime
• Initial 3D MHD simulation results.
• Conclusions

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Goals of Informal Discussion

• Experimentally Determine Which Instabilities are
  present in MRX FRCs
• Look and Helium and Neon cases
• Determine the stabilizing mechanisms
• Center Column
• Equilibrium Field Shape
• Develop a theoretical understanding of
  equilibrium stability.

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Comprehensive Diagnostic Set For Stability Studies

• 90 Channel Probe 6x5 Array of Coil Triplets,
  4cm resolution, scannable
• 105 Channel Toroidal Array 7 Probes 5 coil
  triplets
• Toroidal Mode Number n0,1,2,3 in BZ, BR, BT
• 16 External and 8 Internal Poloidal Flux Loops
• 14 Channel Wall Mounted Mirnov Array (8 BT and 6
  BZ)

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Two Polarizations of ModesRadial Polarization
(n1?Shifting)
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Two Polarizations of ModesAxial Polarization
(n1?Tilting)
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Flexibility in Equilibrium Field Allows Different
Stability Regimes
Elongated Field Reversed Theta-Pinch ndecay??0
Flux-Core Spheromak (S-1) ndecay??0.2
MRX-FRC 0.3ltndecay?4
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Well Controlled Merging Yields Good FRC
Movie Here
Three Keys to Good FRC formation in MRX 1 Good
Spheromak Balance Two Spheromaks must have
similar size and field strength. 2 Good
Equilibrium Field Configuration Spheromaks must
not be tilting during merging. 3 Passive
stabilization passive stabilization via center
column further reduces tilting/shifting.
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Radially Polarized Co-Interchange Strongest in BZ
BT
BZ
BR
-.0048 to .0048
-.001 to .001
-.0008 to .0008
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Axially Polarized Co-Interchange Strongest in BR
BR and BT phase is ?/n
BR
BT
BZ
-.046 to .046
-.1 to .1
-.02 to .02
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Consider 3 Time Slices of a Single Discharge
Early Merging Strong BR of Spheromaks
Interacting
Late Merging Strong BT of Spheromaks Interacting
Equilibrium/Decay
Merging Excites n1,2,3 modes to Large amplitude.
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Early Merging Axial Motion with n1,2,3, Visible
in BR
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Late Merging Strong Axial n1,2,3, visible in BT
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Signature of n23 CoInterchange Modes
For n2 BR and BT phase differ by ?/2, implying
Axially Polarized mode
For n2 3 Strong BZ indicates radially
polarized mode?
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Strong n1 during tilting spheromak
Flux
Current
BR, n1
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Spheromak Tilt is Dominated by n1
BR, n1
BR, n2
BR, n3
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Strong n1 during Tilting Spheromak
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Systematic Instability Studies

• How do non-axisymmetric modes depend on the

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Helium FRC in MHD Regime For n1 Tilting
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Neon FRC Approaching Kinetic Regime for Tilting
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Axial Motions Increase as Mirror Ratio Decreases
BR, n1
BR, n2
BR, n3

• Large Error Bars Due to Shot-to-Shot
  Reproducibility
• N1 (tilt) dominated the BR spectrum

Helium
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Center Column Reduces Tilt Motions
BR, n1
BR, n2
BR, n3

• Improved reproducibility.
• N1 (tilt) reduced with center column
• n23 not effected by center column
• n23 comparable or larger than n1 (tilt).

Helium
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N1 Shifting Increases With Mirror Ratio
BR, n1
BR, n2
BR, n3
Helium
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Rigid Body Shifting Signature Largely Suppressed
with Center Column
BR, n1
BR, n2
BR, n3
Helium
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Center Column only Weakly Extends Plasma Lifetime
??
?R depends quadratically on poorly known minor
radius.
??/?R
??/?A
Slight Improvement with Center Column
Helium
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Neon Shows Growth in Axial Mode Signature at Low
Mirror Ratio
BR, n1
BR, n2
BR, n3
Neon
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Neon Tilting Apparently Suppressed With Center
Column
BR, n1
BR, n3
BR, n2
N3 mode very small in all casesFLR effect?
Neon
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Neon Radial Shift Signature Increases With Mirror
Ratio without Center Column
BZ, n1
BZ, n2
BZ, n3
Neon
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Center Column Reduces Rigid Body Shift Signature
BZ, n1
BZ, n2
BZ, n3
Neon
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Multiple Tools Used to Model Improved-Stability
Oblate FRCs

• MHD equilibria computed using new free-boundary
  Grad-Shafranov solver.
• Simple rigid-body model used to estimate rigid
  body shifting/tilting.
• Simple check for interchange stability
• MHD computations with the HYM code.

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MRXFIT Solves G-S Eqn. Subject to Magnetic
Constraints
Create Guesses to the ? distribution and p(?) and
F(?).
Create Input Based on MRX Data 1 90 Channel
Probe Scan 2 N0 Component of N-Probes 3 Coil
Current
Find Separatix flux (?sep) using contour
following algorithm
Modify forms of p(?) and F(?), and use ?
calculate from magnetics data.
Store ? as ?old
Reevaluate P and F with new ?
Using p(?) and F(?), calculate new
J?2?Rp2?FF/(R?0)
Store ?2 as ?2old.
Didnt Converge
Didnt Converge
Compare ? to ?old
Use new J? to calculate new ?
Converge
G-S Solver Loop
If not Iteration 1 Compare ?2 to ?2old.
Plotting and post-processing.
Predict diagnostic signals based on Equilibria.
Compute ?2
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Fields Calculated From Axisymmetric Model With
Flux Conserving Vessel
Shaping Field Coils 2 Turns Per Coil
Vacuum Vessel is Treated as a Flux Conserver
Equilibrium Field Coils
Flux Core PF Windings 4 Turns Per Coil
J.K. Anderson et al
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MRXFIT Code Finds MHD Equilibria Consistent with
Magnetics Data
Equilibria computed for a single time for nearly
all Helium discharges
52776 ?0.2 ?1.2
Mirror Ratio2.0
52475 ?-0.1 ?0.8
Mirror Ratio3.2
Helium
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Rigid-Body Stability Theory Predicts
Tilt-Stability Boundary
Model Assume that the plasma is a rigid torus
in a vacuum field. The current profile and
equilibrium field distribution are
known. Procedure Assume a small tilt ?, and
calculate the torque on the torus.
If ngt1, the stabilizing
Ji et. al.
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Oblate Plasmas At Boundary of Rigid-Body Tilt
Stable Regime

• Plasma Approaching Stability to rigid-body n1
  tilt.

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Interchange Unstable Plasmas
Stability criterion
Typical Case shows instability for all
surfaces. What is the experimental signature in
the magnetics?
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Conclusions

• Shift/Tilt conundrum is observed in MRX plasmas
  with a center column.
• Combination of shaping and center-column can
  substantially reduce N1 mode amplitudes.
• FRC does not display rigid body signatures like a
  spheromak.
• N2,3 are still present, probably leading the
  destruction of the configuration.

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Questions

• How Sensitive are n2,3,4axial and radial modes
  to the elongation?
• What would be the signature of interchange modes?

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Everything After Here is Backup/Outdated
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Analytic Equilibrium Model by Zheng Provides
Approximation to Current Profile

• 6 Fit parameters in Model
• 4 Parameters determine the Plasma shape
• 2 Parameters determine Pressure and Toroidal
  field

Poloidal flux specified as
Magnetic Field