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

Strength

Angle

Current

=

=

=

1018 G

0°

-17.6 kA

Strength

Angle

Current

=

=

=

737 G

0°

-18.6 kA

Strength

Angle

Current

=

=

=

300 G

0°

-20.8 kA

Parallel potential arcade quiescent flux ropes

Parallel potential arcade quiescent flux ropes

Strength

Angle

Current

=

=

=

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

Strength

Angle

Current

=

=

=

323 G

22°

-20.9 kA

Oblique potential arcade erupting flux ropes

Strength

Angle

Current

=

=

=

305 G

11°

-20.4 kA

Strength

Angle

Current

=

=

=

309 G

0°

-20.4 kA

Oblique potential arcade erupting flux ropes

Strength

Angle

Current

=

=

=

347 G

30°

-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