Magnetic Prandtl number dependence of plasmoid-mediated reconnection

Abstract

We investigate the dependence of the plasmoid-mediated magnetic reconnection rate on the magnetic Prandtl number using two-dimensional magnetohydrodynamic simulations of two coalescing magnetic islands. For Lundquist numbers below the onset of the plasmoid instability, the reconnection rate follows the expected Sweet-Parker scaling and decreases with increasing magnetic Prandtl number. However, once the current sheet becomes plasmoid unstable, the dependence on the magnetic Prandtl number weakens considerably. In the fully plasmoid-mediated regime, we find reconnection rates that remain nearly independent of the magnetic Prandtl number over the explored parameter range. We show that the largest reconnection rates are associated with strongly non-linear phases involving plasmoid interactions and mergers. We further compare our results with simulations of the boundary-driven Taylor problem, where previous studies reported a stronger magnetic Prandtl number dependence, and provide a possible explanation for the differing scalings obtained in the two setups. These results may have implications for reconnection-mediated decay in magnetically dominated turbulence and related astrophysical systems.