Download - Clayton E. Myers July 9 , 2013
Clayton E. MyersJuly 9, 2013
Line-Tied Magnetic Flux Ropes in the Laboratory:Equilibrium Force Balance & Eruptive Instabilities
MRX Collaborators: M. Yamada, H. Ji, J. Yoo, and J. Jara-AlmonteMHD Simulations: E. Belova
Technical Contributors: R. Cutler, P. Sloboda, and F. Scotti
Hinode MRX
• These are the first results from a new laboratory experiment that is designed to study quasi-statically driven flux ropes
• Overarching physics question:• How do the parameters of the potential field arcade (i.e., its strength,
orientation, and gradient) influence the flux rope evolution?
• Primary topics:• Equilibrium force balance• Sigmoidal flux ropes• The kink & torus instabilities (eruptions)
Overview
Caltech
FlareLab
UCLA
• Several existing experiments have studied flux rope eruptions in the lab
• Caltech & FlareLab dynamically inject poloidal flux at the footpoints
• UCLA uses lasers to inject mass and current at the footpoints
• These dynamically driven eruptions do not qualify as “storage-and-release” events
Other laboratory flux rope experiments
Electrodes
GlassSubstrate Vessel Length ~ 2 m
Line-Current Coil
Arcade Coils
Electrodes
HelmholtzCoils
GlassSubstrate
Line-Current Coil
Arcade Coils
Electrodes
HelmholtzCoils
(1) The flux rope footpoints are line-tied to conducting electrodes
(2) The plasma current (twist) is injected quasi-statically (~100 μs)
(3) The plasma is low-β with significant stored magnetic energy
(4) The applied potential field arcade is highly tunable
Line-tied magnetic flux rope experiments in MRX
Changing the orientation of the potential field arcade
Changing the orientation of the potential field arcade
• The orientation and the strength of the arcade are key knobs in determining the flux rope behavior
• We can also vary the vertical gradient of the arcade to study the torus instability
Distributed in situ magnetic diagnostics• On MRX, we deploy large arrays of internal magnetic probes to
measure the spatial and temporal evolution of the plasma
z
x
z
y
By = poloidal field
Bx = toroidal field
Visible Light
StrengthAngleCurrent
===
1018 G 0°-17.6 kA
StrengthAngleCurrent
===
737 G 0°-18.6 kA
StrengthAngleCurrent
===
300 G 0°-20.8 kA
Parallel potential arcade quiescent flux ropes
Parallel potential arcade quiescent flux ropes
StrengthAngleCurrent
===
149 G 0°-20.5 kA
• Flux ropes that are formed within a parallel potential arcade are confined in a quasi-static equilibrium
• Internal toroidal field is generated during the discharge
• No dynamic eruptions are observed in this regime
• The kink instability saturates at low amplitude, even in cases with large twist (due to line-tying effects)
Minor radius force balance internal toroidal field
Linear flux rope
Adapted from FriedbergRev. Mod. Phys., 1982
• The “toroidal” current in the flux rope produces a pinch force
• If the flux rope is low-β, the force balance must come from toroidal field pressure
Major radius force balance MHD simulations
The HYM Code (E. Belova, PPPL)
Applied Potential FieldPerturbed/Plasma Field
Key results: The induced toroidal field changes both the pressure and the tension within the flux rope
These forces largely prevent dynamic behavior in parallel potential arcade flux ropes
Major radius force balance from the simulations
StrengthAngleCurrent
===
323 G22°-20.9 kA
Oblique potential arcade erupting flux ropes
StrengthAngleCurrent
===
305 G11°-20.4 kA
StrengthAngleCurrent
===
309 G 0°-20.4 kA
Oblique potential arcade erupting flux ropes
StrengthAngleCurrent
===
347 G30°-21.8 kA
Oblique potential arcade sigmoid formation
MRX (Initial Breakdown Image) Adapted from Savcheva et al., ApJ 2012
• Parallel arcades produce parallel flux ropes that are confined by toroidal field forces
• Oblique arcades produce sigmoidal flux ropes that can erupt
• In a sigmoid, the flux rope apex runs perpendicular to the arcade, thereby avoiding the aforementioned toroidal field forces
Many open questions:
• What determines the critical arcade orientation angle that leads to eruptions?
• How much internal axial flux is carried within the sigmoid? Is there a laboratory knob for this?
• What are the specific roles of the kink and torus instabilities in driving the observed eruptions?
The next step: A new 2D in situ magnetic probe array
• Five probes with 54 magnetic field measurements each (270 total channels)
• Full coverage from z = 0 to the vessel wall (~64 cm)
• Arbitrarily rotatable between discharges in order obtain 2D maps of the sigmoidal equilibrium features and erupting structures
Perpendicular to the Arcade Parallel to the Arcade