The tearing mode instability of thin current sheets: the transition to fast reconnection in the presence of viscosity

TL;DR

This paper extends the analysis of tearing mode instability in thin current sheets by including viscosity effects, showing how viscosity influences the growth rate and aspect ratio limits, and discusses the transition to fast kinetic reconnection.

Contribution

It introduces viscosity into the tearing mode instability analysis, revealing its impact on current sheet stability and the transition to fast reconnection regimes.

Findings

Viscosity allows larger aspect ratios before instability.

Finite Prandtl number stabilizes current sheets.

Transition to kinetic reconnection is influenced by viscosity.

Abstract

This paper studies the growth rate of reconnection instabilities in thin current sheets in the presence of both resistivity and viscosity. In a previous paper, Pucci and Velli (2014), it was argued that at sufficiently high Lundquist number S it is impossible to form current sheets with aspect ratios L/a which scale as $L/a\sim S^\alpha$ with $\alpha > 1/3$ because the growth rate of the tearing mode would then diverge in the ideal limit $S\rightarrow\infty$. Here we extend their analysis to include the effects of viscosity, (always present in numerical simulations along with resistivity) and which may play a role in the solar corona and other astrophysical environments. A finite Prandtl number allows current sheets to reach larger aspect ratios before becoming rapidly unstable in pile-up type regimes. Scalings with Lundquist and Prandtl numbers are discussed as well as the transition to kinetic reconnection