Line-Tied Magnetic Flux Ropes in the Laboratory:
Equilibrium Force Balance & Eruptive Instabilities
Hinode
MRX
Clayton E. Myers
July 9, 2013
MRX Collaborators: M. Yamada, H. Ji, J. Yoo, and J. Jara-Almonte
MHD Simulations: E. Belova
Technical Contributors:
R. Cutler, P. Sloboda, and F. Scotti
Overview
• 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)
Other laboratory flux rope experiments
Caltech
•
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-andrelease” events
FlareLab
UCLA
Line-tied magnetic flux rope experiments in MRX
Line-Current Coil
Electrodes
(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
Glass
Substrate
Arcade Coils
Helmholtz
Coils
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
Visible Light
Bx = toroidal field
z
x
By = poloidal field
z
y
Parallel potential arcade  quiescent flux ropes
737 GG
300
Strength = 1018
Angle
= 0°
-17.6 kA
-18.6
Current = -20.8
Parallel potential arcade  quiescent flux ropes
Strength = 149 G
Angle
= 0°
Current = -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 Friedberg
Rev. 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
Applied
Potential Field
Field
Perturbed/Plasma
The HYM Code (E. Belova, PPPL)
Major radius force balance from the simulations
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
Oblique potential arcade  erupting flux ropes
323 G
305
Strength = 309
11°
0°
Angle
= 22°
-20.9 kA
Current = -20.4
Oblique potential arcade  erupting flux ropes
Strength = 347 G
Angle
= 30°
Current = -21.8 kA
Oblique potential arcade  sigmoid formation
• Parallel arcades produce parallel flux ropes
that are confined by toroidal field forces
• Oblique arcades produce sigmoidal flux ropes
that can erupt
Many open questions:
•
• In a sigmoid, the flux rope apex runs
perpendicular
to the arcade,
What determines the critical
arcade orientation
anglethereby
that avoiding
the aforementioned toroidal field forces
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?
MRX (Initial Breakdown Image)
Adapted from Savcheva et al., ApJ 2012
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