Optimal Energy Growth in Current Sheets

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 $t\to \infty$ 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.

Accepted for Solar Physics

References in corpus (7)

• Instability of current sheets and formation of plasmoid chains
• Self-Feeding Turbulent Magnetic Reconnection on Macroscopic Scales
• General Theory of the Plasmoid Instability
• The tearing mode instability of thin current sheets: the transition to fast reconnection in the presence of viscosity
• "Ideally" unstable current sheets and the triggering of fast magnetic reconnection
• The magnetic structure of surges in small-scale emerging flux regions
• Transient growth in stable collisionless plasma