Title: Studies of ImprovedStability FRCs in MRX
1Studies 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
2MRX-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 -
3This 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
4Goals 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.
5Comprehensive 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)
6Two Polarizations of ModesRadial Polarization
(n1?Shifting)
7Two Polarizations of ModesAxial Polarization
(n1?Tilting)
8Flexibility 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
9Well 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.
10Radially Polarized Co-Interchange Strongest in BZ
BT
BZ
BR
-.0048 to .0048
-.001 to .001
-.0008 to .0008
11Axially Polarized Co-Interchange Strongest in BR
BR and BT phase is ?/n
BR
BT
BZ
-.046 to .046
-.1 to .1
-.02 to .02
12Consider 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.
13Early Merging Axial Motion with n1,2,3, Visible
in BR
14Late Merging Strong Axial n1,2,3, visible in BT
15Signature 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?
16Strong n1 during tilting spheromak
Flux
Current
BR, n1
17Spheromak Tilt is Dominated by n1
BR, n1
BR, n2
BR, n3
18Strong n1 during Tilting Spheromak
19Systematic Instability Studies
- How do non-axisymmetric modes depend on the
20Helium FRC in MHD Regime For n1 Tilting
21Neon FRC Approaching Kinetic Regime for Tilting
22Axial 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
23Center 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
24N1 Shifting Increases With Mirror Ratio
BR, n1
BR, n2
BR, n3
Helium
25Rigid Body Shifting Signature Largely Suppressed
with Center Column
BR, n1
BR, n2
BR, n3
Helium
26Center Column only Weakly Extends Plasma Lifetime
??
?R depends quadratically on poorly known minor
radius.
??/?R
??/?A
Slight Improvement with Center Column
Helium
27Neon Shows Growth in Axial Mode Signature at Low
Mirror Ratio
BR, n1
BR, n2
BR, n3
Neon
28Neon Tilting Apparently Suppressed With Center
Column
BR, n1
BR, n3
BR, n2
N3 mode very small in all casesFLR effect?
Neon
29Neon Radial Shift Signature Increases With Mirror
Ratio without Center Column
BZ, n1
BZ, n2
BZ, n3
Neon
30Center Column Reduces Rigid Body Shift Signature
BZ, n1
BZ, n2
BZ, n3
Neon
31Multiple 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.
32MRXFIT 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
33Fields 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
34MRXFIT 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
35Rigid-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.
36Oblate Plasmas At Boundary of Rigid-Body Tilt
Stable Regime
- Plasma Approaching Stability to rigid-body n1
tilt.
37Interchange Unstable Plasmas
Stability criterion
Typical Case shows instability for all
surfaces. What is the experimental signature in
the magnetics?
38Conclusions
- 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.
39Questions
- How Sensitive are n2,3,4axial and radial modes
to the elongation? - What would be the signature of interchange modes?
40Everything After Here is Backup/Outdated
41Analytic 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