Scaling laws of resistive magnetohydrodynamic reconnection in the high-Lundquist-number, plasmoid-unstable regime

Yi-Min Huang; A. Bhattacharjee

doi:10.1063/1.3420208

paper

Scaling laws of resistive magnetohydrodynamic reconnection in the high-Lundquist-number, plasmoid-unstable regime

arXiv:1003.5951 · doi:10.1063/1.3420208

Abstract

The Sweet-Parker layer in a system that exceeds a critical value of the Lundquist number ( $S$ ) is unstable to the plasmoid instability. In this paper, a numerical scaling study has been done with an island coalescing system driven by a low level of random noise. In the early stage, a primary Sweet-Parker layer forms between the two coalescing islands. The primary Sweet-Parker layer breaks into multiple plasmoids and even thinner current sheets through multiple levels of cascading if the Lundquist number is greater than a critical value $S_{c} ≃ 4 \times 1 0^{4}$ . As a result of the plasmoid instability, the system realizes a fast nonlinear reconnection rate that is nearly independent of $S$ , and is only weakly dependent on the level of noise. The number of plasmoids in the linear regime is found to scales as $S^{3/8}$ , as predicted by an earlier asymptotic analysis (Loureiro \emph{et al.}, Phys. Plasmas \textbf{14}, 100703 (2007)). In the nonlinear regime, the number of plasmoids follows a steeper scaling, and is proportional to $S$ . The thickness and length of current sheets are found to scale as $S^{- 1}$ , and the local current densities of current sheets scale as $S^{- 1}$ . Heuristic arguments are given in support of theses scaling relations.

Submitted to Phys. Plasmas

Scaling laws of resistive magnetohydrodynamic reconnection in the high-Lundquist-number, plasmoid-unstable regime

Abstract

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