Onset of fast "ideal" tearing in thin current sheets: dependence on the equilibrium current profile

TL;DR

This paper investigates the conditions under which fast tearing instabilities occur in various equilibrium current sheet configurations, extending previous models and identifying new scaling laws for the onset of ideal tearing in plasmas.

Contribution

It introduces a generalized analysis of the ideal tearing instability for different equilibrium profiles, revealing new scaling relations and bounds beyond the classic Harris sheet model.

Findings

Critical aspect ratios can be smaller than S^{1/3} for some equilibria.

A lower bound of S^{1/4} for the aspect ratio scaling is established.

Different equilibrium profiles are categorized by their Δ' dependence on wavenumber.

Abstract

In this paper we study the scaling relations for the triggering of the fast, or "ideal", tearing instability starting from equilibrium configurations relevant to astrophysical as well as laboratory plasmas that differ from the simple Harris current sheet configuration. We present the linear tearing instability analysis for equilibrium magnetic fields which a) go to zero at the boundary of the domain and b) contain a double current sheet system (the latter previously studied as a cartesian proxy for the m=1 kink mode in cylindrical plasmas). More generally, we discuss the critical aspect ratio scalings at which the growth rates become independent of the Lundquist number $S$, in terms of the dependence of the $\Delta'$ parameter on the wavenumber $k$ of unstable modes. The scaling $\Delta'(k)$ with $k$ at small $k$ is found to categorize different equilibria broadly: the critical aspect ratios may be even smaller than $L/a \sim S^{\alpha}$ with $\alpha=1/3$ originally found for the Harris current sheet, but there exists a general lower bound $\alpha\ge1/4$.