Optimal energy growth in current sheets

MacTaggart, D. and Stewart, P. (2017) Optimal energy growth in current sheets. Solar Physics, 292(10), 148. (doi: 10.1007/s11207-017-1177-1)

Abstract

In this article, we investigate the possibility of transient growth in the linear perturbation of current sheets. The resistive magnetohydrodynamics 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→∞ 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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Mactaggart, Dr David and Stewart, Professor Peter
• Authors: MacTaggart, D., and Stewart, P.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Solar Physics
• Publisher: Springer
• ISSN: 0038-0938
• ISSN (Online): 1573-093X
• Published Online: 09 October 2017
• Copyright Holders: Copyright © 2017 Springer Science+Business Media
• First Published: First published in Solar Physics 292(10): 148
• Publisher Policy: Reproduced in accordance with the publisher copyright policy