The Tearing Instability of Resistive Magnetohydrodynamics

Abstract

In this Chapter we explore the linear onset of one of the most important instabilities of resistive magnetohydrodynamics, the tearing instability. In particular, we focus on two important aspects of the onset of tearing: asymptotic (modal) stability and transient (non-modal) stability. We discuss the theory required to understand these two aspects of stability, both of which have undergone significant development in recent years.

Connecting theory of plasmoid-modulated reconnection to observations of solar flares

“…Following the arguments for the plasmoid instability (e.g., MacTaggart, 2020), we set that the half-width and half-length of the current sheet are connected by . We can rescale the maximum growth rate and the most unstable wavelength to be in terms of and not .…”

“…To understand how the tearing instability develops in a reconnecting current sheet, it is standard practice to rescale the growth rates and wavenumbers to calculate them in terms of the half-length of the current sheet and not the half-width (which is used normally when calculating the growth rate of the instability; e.g., Furth et al, 1963). To do this, the aspect ratio (with the half-width of the current sheet and the half-length of the current sheet) is given to scale as (e.g., MacTaggart, 2020). After performing this rescaling, the instability is often known as the plasmoid instability.…”