Effects of Line-tying on Resistive Tearing Instability in Slab Geometry

Abstract

The effects of line-tying on resistive tearing instability in slab geometry is studied within the framework of reduced magnetohydrodynamics (RMHD).\citep{KadomtsevP1974,Strauss1976} It is found that line-tying has a stabilizing effect. The tearing mode is stabilized when the system length $L$ is shorter than a critical length $L_c$, which is independent of the resistivity $\eta$. When $L$ is not too much longer than $L_c$, the growthrate $\gamma$ is proportional to $\eta$ . When $L$ is sufficiently long, the tearing mode scaling $\gamma \sim {\eta }^{3/5}$ is recovered. The transition from $\gamma \sim \eta$ to $\gamma \sim {\eta }^{3/5}$ occurs at a transition length $L_t\sim {\eta }^{-2/5}$.

Correct a typo

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• $m=1$ Ideal Internal Kink Modes in a Line-tied Screw Pinch

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