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Studies of ImprovedStability FRCs in MRX

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Oblate shape is predicted to stabilize tilt-instability ... Used to Model Improved-Stability Oblate FRCs ... Oblate Plasmas At Boundary of Rigid-Body Tilt ... – PowerPoint PPT presentation

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Title: Studies of ImprovedStability FRCs in MRX


1
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

2
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

3
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

4
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.

5
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)

6
Two Polarizations of ModesRadial Polarization
(n1?Shifting)
7
Two Polarizations of ModesAxial Polarization
(n1?Tilting)
8
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
9
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.
10
Radially Polarized Co-Interchange Strongest in BZ
BT
BZ
BR
-.0048 to .0048
-.001 to .001
-.0008 to .0008
11
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
12
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.
13
Early Merging Axial Motion with n1,2,3, Visible
in BR
14
Late Merging Strong Axial n1,2,3, visible in BT
15
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?
16
Strong n1 during tilting spheromak
Flux
Current
BR, n1
17
Spheromak Tilt is Dominated by n1
BR, n1
BR, n2
BR, n3
18
Strong n1 during Tilting Spheromak
19
Systematic Instability Studies
  • How do non-axisymmetric modes depend on the

20
Helium FRC in MHD Regime For n1 Tilting
21
Neon FRC Approaching Kinetic Regime for Tilting
22
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
23
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
24
N1 Shifting Increases With Mirror Ratio
BR, n1
BR, n2
BR, n3
Helium
25
Rigid Body Shifting Signature Largely Suppressed
with Center Column
BR, n1
BR, n2
BR, n3
Helium
26
Center Column only Weakly Extends Plasma Lifetime
??
?R depends quadratically on poorly known minor
radius.
??/?R
??/?A
Slight Improvement with Center Column
Helium
27
Neon Shows Growth in Axial Mode Signature at Low
Mirror Ratio
BR, n1
BR, n2
BR, n3
Neon
28
Neon Tilting Apparently Suppressed With Center
Column
BR, n1
BR, n3
BR, n2
N3 mode very small in all casesFLR effect?
Neon
29
Neon Radial Shift Signature Increases With Mirror
Ratio without Center Column
BZ, n1
BZ, n2
BZ, n3
Neon
30
Center Column Reduces Rigid Body Shift Signature
BZ, n1
BZ, n2
BZ, n3
Neon
31
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.

32
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
33
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
34
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
35
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.
36
Oblate Plasmas At Boundary of Rigid-Body Tilt
Stable Regime
  • Plasma Approaching Stability to rigid-body n1
    tilt.

37
Interchange Unstable Plasmas
Stability criterion
Typical Case shows instability for all
surfaces. What is the experimental signature in
the magnetics?
38
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.

39
Questions
  • How Sensitive are n2,3,4axial and radial modes
    to the elongation?
  • What would be the signature of interchange modes?

40
Everything After Here is Backup/Outdated
41
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
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