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

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 Å. 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.

To appear in Phys. Plasmas

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• High-Lundquist Number Scaling in Three-Dimensional Simulations of Parker's Model of Coronal Heating
• Rapid Change of Field Line Connectivity and Reconnection in Stochastic Magnetic Fields
• Equilibria, Dynamics and Current Sheets Formation in Magnetically Confined Coronae
• Do chaotic field lines cause fast reconnection in coronal loops?