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

TL;DR

This study investigates how line-tying influences resistive tearing instability in slab geometry, revealing stabilization effects and scaling transitions dependent on system length and resistivity within the RMHD framework.

Contribution

It demonstrates that line-tying stabilizes tearing modes below a critical length and identifies the scaling transition of growth rates with resistivity as length varies.

Findings

Line-tying stabilizes tearing modes when system length is below a critical value.

Growth rate scales linearly with resistivity for lengths just above the critical.

Transition from linear to -5/5 scaling occurs at a length proportional to resistivity^{-2/5}.

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 $L_{t}\sim\eta^{-2/5}$.