Effects of Line-tying on Magnetohydrodynamic Instabilities and Current Sheet Formation

TL;DR

This paper reviews recent advances in understanding magnetohydrodynamic stability and current sheet formation in line-tied systems, highlighting key stability results, challenging recent claims, and discussing open questions and strategies.

Contribution

It provides a summary of stability analyses, presents a counterexample to recent claims of current sheet formation, and derives equations for quasi-static evolution in line-tied magnetic fields.

Findings

Linear stability of internal kink and tearing modes summarized.

Counterexample to recent claims of current sheet formation provided.

Governing equations for boundary-driven magnetic field evolution derived.

Abstract

An overview of some recent progress on magnetohydrodynamic stability and current sheet formation in a line-tied system is given. Key results on the linear stability of the ideal internal kink mode and resistive tearing mode are summarized. For nonlinear problems, a counterexample to the recent demonstration of current sheet formation by Low \emph{et al}. [B. C. Low and \AA. M. Janse, Astrophys. J. \textbf{696}, 821 (2009)] is presented, and the governing equations for quasi-static evolution of a boundary driven, line-tied magnetic field are derived. Some open questions and possible strategies to resolve them are discussed.