A New Approach of Linear Theory of Tearing Instability in Uniform Resistivity

TL;DR

This paper numerically examines the linear tearing instability theory with uniform resistivity, demonstrating how the outer region's resistivity influences growth rate limits and aligning findings with MHD simulations of plasmoid instability.

Contribution

It introduces a numerical approach to the linear tearing instability theory considering uniform resistivity, refining growth rate limits and connecting theory with simulation results.

Findings

Uniform resistivity improves theoretical conclusions.

Upper limit of growth rate is regulated by the Alfvén speed.

Partial consistency with MHD simulation of plasmoid instability.

Abstract

The linear perturbation equation of the tearing instability derived in LSC theory (Loureiro, Schekochihin, and Cowley, PoP2007) is numerically examined as an initial value problem, where the inner and outer regions are seamlessly solved under uniform resistivity. Hence, all regions are solved as the resistive MHD (magnetohydrodynamics). To comprehensively study physically acceptable perturbation solutions, the behaviors of the local maximum points required for physically acceptable solutions and zero-crossing points, at which \phi=0 and \psi=0, are examined. Eventually, the uniform resistivity assumed in the outer region is shown to play an important role in improving some conclusions derived from the theory. In conclusion, the upper limit \lambda_{up} of the growth rate obtained in the improved (modified) LSC theory is shown to be regulated by the Alfven speed measured in the outer region. It is also shown to be partially consistent with the growth rate in the linear developing stage of the impulsive tearing instability observed in the compressible MHD simulation of the plasmoid instability (PI) based on uniform resistivity.