1. Clayton E. Myers July 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-Almonte MHD Simulations:E. Belova Technical Contributors:R. Cutler, P. Sloboda, and F. Scotti Hinode MRX

2. 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

3. 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

4. Electrodes Glass Substrate Vessel Length ~ 2 m Line-Current Coil Arcade Coils Electrodes Helmholtz Coils Glass Substrate Line-Current Coil Arcade Coils Electrodes Helmholtz Coils (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

5. Changing the orientation of the potential field arcade

6. 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

7. 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 B y = poloidal field B x = toroidal field Visible Light

8. 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

9. 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)

10. 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

11. Major radius force balance  MHD simulations The HYM Code (E. Belova, PPPL) Applied Potential Field Perturbed/Plasma Field

12. 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

13. 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

14. Oblique potential arcade  erupting flux ropes Strength Angle Current ====== 347 G 30° -21.8 kA

15. 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?

16. 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 ArcadeParallel to the Arcade