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


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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 $L/asim S^alpha$ with $alpha > 1/3$ because the growth rate of the tearing mode would then diverge in the ideal limit $Srightarrowinfty$. 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

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