Onset of Fast Reconnection in Hall Magnetohydrodynamics Mediated by the Plasmoid Instability

The role of a super-Alfv\'enic plasmoid instability in the onset of fast reconnection is studied by means of the largest Hall magnetohydrodynamics simulations to date, with system sizes up to $10^{4}$ ion skin depths ($d_{i}$). It is demonstrated that the plasmoid instability can facilitate the onset of rapid Hall reconnection, in a regime where the onset would otherwise be inaccessible because the Sweet-Parker width is significantly above $d_{i}$. However, the topology of Hall reconnection is not inevitably a single stable X-point. There exists an intermediate regime where the single X-point topology itself exhibits instability, causing the system to alternate between a single X-point geometry and an extended current sheet with multiple X-points produced by the plasmoid instability. Through a series of simulations with various system sizes relative to $d_{i}$, it is shown that system size affects the accessibility of the intermediate regime. The larger the system size is, the easier it is to realize the intermediate regime. Although our Hall MHD model lacks many important physical effects included in fully kinetic models, the fact that a single X-point geometry is not inevitable raises the interesting possibility for the first time that Hall MHD simulations may have the potential to realize reconnection with geometrical features similar to those seen in fully kinetic simulations, namely, extended current sheets and plasmoid formation.