Plasmoid Instability in High-Lundquist-Number Magnetic Reconnection

Our understanding of magnetic reconnection in resistive magnetohydrodynamics has gone through a fundamental change in recent years. The conventional wisdom is that magnetic reconnection mediated by resistivity is slow in laminar high Lundquist ($S$) plasmas, constrained by the scaling of the reconnection rate predicted by Sweet-Parker theory. However, recent studies have shown that when $S$ exceeds a critical value $\sim10^{4}$, the Sweet-Parker current sheet is unstable to a super-Alfv\'enic plasmoid instability, with a linear growth rate that scales as $S^{1/4}$. In the fully developed statistical steady state of two-dimensional resistive magnetohydrodynamic simulations, the normalized average reconnection rate is approximately 0.01, nearly independent of $S$, and the distribution function $f(\psi)$ of plasmoid magnetic flux $\psi$ follows a power law $f(\psi)\sim\psi^{-1}$. When Hall effects are included, the plasmoid instability may trigger onset of Hall reconnection even when the conventional criterion for onset is not satisfied. The rich variety of possible reconnection dynamics is organized in the framework of a phase diagram.