Magnetic reconnection mediated by hyper-resistive plasmoid instability

TL;DR

This study investigates how hyper-resistive plasmoid instability influences magnetic reconnection, revealing specific scaling laws and statistical distributions through linear analysis and nonlinear simulations, advancing understanding of plasma physics phenomena.

Contribution

It provides the first detailed analysis of hyper-resistive plasmoid-mediated reconnection, including scaling laws and plasmoid distribution, extending previous resistive MHD results.

Findings

Linear growth rate scales as S_H^{1/6}.

Reconnection rate becomes nearly independent of S_H in nonlinear regime.

Number of plasmoids scales as S_H^{1/2}.

Abstract

Magnetic reconnection mediated by the hyper-resistive plasmoid instability is studied with both linear analysis and nonlinear simulations. The linear growth rate is found to scale as $S_{H}^{1/6}$ with respect to the hyper-resistive Lundquist number $S_{H}\equiv L^{3}V_{A}/\eta_{H}$, where $L$ is the system size, $V_{A}$ is the Alfv\'en velocity, and $\eta_{H}$ is the hyper-resistivity. In the nonlinear regime, reconnection rate becomes nearly independent of $S_{H}$, the number of plasmoids scales as $S_{H}^{1/2}$, and the secondary current sheet length and width both scale as $S_{H}^{-1/2}$. These scalings are consistent with a heuristic argument assuming secondary current sheets are close to marginal stability. The distribution of plasmoids as a function of the enclosed flux $\psi$ is found to obey a $\psi^{-1}$ power law over an extended range, followed by a rapid fall off for large plasmoids. These results are compared with those from resistive magnetohydrodynamic studies.