Optimal Energy Growth in Current Sheets

TL;DR

This paper explores how transient energy growth in linear perturbations of current sheets, especially due to damped modes, can accelerate current sheet disruption and influence solar phenomena like flares.

Contribution

It demonstrates that damped modes in resistive MHD current sheets can cause significant transient energy growth, impacting the understanding of current sheet evolution and instability onset.

Findings

Damped modes can produce transient energy growth exceeding normal tearing modes.

Transient growth can accelerate current sheet disruption and plasmoid instability.

Results have implications for solar flares and coronal heating processes.

Abstract

In this paper, we investigate the possibility of transient growth in the linear perturbation of current sheets. The resistive magnetohydrodynamic (MHD) operator for a background field consisting of a current sheet is non-normal, meaning that associated eigenvalues and eigenmodes can be very sensitive to perturbation. In a linear stability analysis of a tearing current sheet, we show that modes that are damped as $t\rightarrow\infty$ can produce transient energy growth, contributing faster growth rates and higher energy attainment (within a fixed finite time) than the unstable tearing mode found from normal-mode analysis. We determine the transient growth for tearing-stable and tearing-unstable regimes and discuss the consequences of our results for processes in the solar atmosphere, such as flares and coronal heating. Our results have significant potential impact on how fast current sheets can be disrupted. In particular, transient energy growth due to (asymptotically) damped modes may lead to accelerated current sheet thinning and, hence, a faster onset of the plasmoid instability, compared to the rate determined by the tearing mode alone.