Plasmoid-dominated Turbulent Reconnection in a Low $\beta$ Plasma

Properties of plasmoid-dominated turbulent reconnection in a low-$\beta$ background plasma are investigated by resistive magnetohydrodynamic (MHD) simulations. In the $\beta_{\rm in} < 1$ regime, where $\beta_{\rm in}$ is plasma $\beta$ in the inflow region, the reconnection site is dominated by shocks and shock-related structures and plasma compression is significant. The effective reconnection rate increases from $0.01$ to $0.02$ as $\beta_{\rm in}$ decreases. We hypothesize that plasma compression allows faster reconnection rate, and then we estimate a speed-up factor, based on a compressible MHD theory. We validate our prediction by a series of MHD simulations. These results suggest that the plasmoid-dominated reconnection can be twice faster than expected in the $\beta \ll 1$ environment in a solar corona.