Laboratory Study of the Equilibrium and Eruption of Line-Tied Magnetic Flux Ropes in the Solar Corona

Abstract

Ideal magnetohydrodynamic (MHD) instabilities such as the kink instability and the torus instability are leading candidates to explain the sudden onset of eruptive events in the solar corona. These instabilities act on line-tied magnetic flux ropes--long-lived arched structures anchored to the solar surface. In spite of substantial observational and numerical research, however, the role of these instabilities in the corona remains a subject of intense debate. For this thesis, we have constructed and operated a new line-tied flux rope experiment that permits for the first time the study of both the kink and torus instabilities in the laboratory. This experiment has the following key features: (1) the arched flux rope is line-tied to two conducting footpoints; (2) the system is magnetically dominated (low-beta) with significant stored energy; (3) the system is driven quasi-statically, producing a long-lived equilibrium; and (4) the flux rope is generated within a potential (vacuum) magnetic field arcade whose decay index--the predicted torus instability control parameter--can be externally controlled. The flux ropes are diagnosed using a two-dimensional in situ magnetic probe array whose cross-section covers a substantial portion of the plasma.

The central result of this thesis is that toroidal field forces, which are traditionally neglected in the analysis of coronal flux ropes, are identified for the first time as an essential contributor to both the equilibrium and the stability of line-tied flux ropes. Most importantly, experimental measurements show that a tension force derived from a self-generated paramagnetic toroidal field exerts a restoring force on the line-tied plasma and suppresses eruptive behavior in a significant portion of the parameter space. This suppression extends to regimes that are both kink and torus unstable. We find that, in order to explain the measured tension force, low aspect ratio and line-tying effects must be considered. Finally, flux rope eruptions are observed in these experiments, but only in regimes with sufficiently low external toroidal field where the tension force is reduced. These results constitute a new condition for the prediction of line-tied magnetic flux rope eruptions: that of low external toroidal field.