Magnetic reconnection mediated by hyper-resistive plasmoid instability

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 ≡ L 3 V A / η H , where L is the system size, VA is the Alfvén velocity, and η H is the hyper-resistivity. In the nonlinear regime, reconnection rate becomes nearly independent of SH , 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 ψ is found to obey a ψ − 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.