The tearing mode instability of thin current sheets: the transition to fast reconnection in the presence of 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 $S\to \infty$. 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

Accepted for publication in The Astrophysical Journal on January 16, 2015

References in corpus (2)

• Instability of current sheets and formation of plasmoid chains
• A catastrophe model for fast magnetic reconnection onset

Cited by in corpus (7)

• Plasmoid Instability in Forming Current Sheets
• Extended theory of the Taylor problem in the plasmoid-unstable regime
• "Ideally" unstable current sheets and the triggering of fast magnetic reconnection
• Coronal Heating Topology: the Interplay of Current Sheets and Magnetic Field Lines
• Activation of MHD reconnection on ideal timescales
• Boosting Magnetic Reconnection by Viscosity and Thermal Conduction
• Optimal Energy Growth in Current Sheets