The tearing mode instability of thin current sheets: the transition to fast reconnection in the presence of viscosity
TL;DR: In this article, the authors studied the growth rate of reconnection instabilities in thin current sheets in the presence of resistivity and viscosity and showed that a finite Prandtl number allows current sheets to reach larger aspect ratios before becoming rapidly unstable in pile-up regime.
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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
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Magnetic reconnection: recursive current sheet collapse triggered by “ideal” tearing
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Visco-Resistive Plasmoid Instability
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Visco-resistive plasmoid instability
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TL;DR: In this paper, the authors analyzed the plasmoid instability in visco-resistive current sheets in both the linear and nonlinear regimes, and they showed that the nonlinear growth of the Plasmoids is radically different from the linear one, and it is essential to understand the global current sheet disruption.
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References
Finite‐Resistivity Instabilities of a Sheet Pinch
TL;DR: In this paper, the stability of a plane current layer is analyzed in the hydromagnetic approximation, allowing for finite isotropic resistivity, and the effect of a small layer curvature is simulated by a gravitational field.
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Instability of current sheets and formation of plasmoid chains
TL;DR: In this article, current sheets formed in magnetic reconnection events are found to be unstable to high-wavenumber perturbations, and a chain of plasmoid secondary islands is formed, whose number scales as S3∕8.
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Plasma Instabilities and Magnetic Field Growth in Clusters of Galaxies
TL;DR: In this paper, the authors show that under very general conditions, cluster plasmas threaded by weak magnetic fields are subject to very fast growing plasma instabilities driven by the anisotropy of the plasma pressure (viscous stress) with respect to the local direction of the magnetic field.
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Reconnection of Quasi-singular Current Sheets: The "Ideal" Tearing Mode
TL;DR: In this paper, it was shown that the Sweet-Parker current sheet is unstable to a reconnecting instability which grows without bound as the Lundquist number, S tends to infinity, and that an ideal tearing mode takes over before current sheets reach such a thickness.
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