On the role of system size in Hall MHD magnetic reconnection

We study the effects of the Hall electric field on magnetic island coalescence in the large island limit and find evidence for both an elongated electron current sheet layer with a Sweet-Parker-like reconnection rate and a collapsed, Petschek-like electron sheet with a peak reconnection rate approaching the 0.1vAB0 Hall MHD rate. The state observed in our simulations appears to depend on the grid scale. Furthermore, even at the largest system sizes, we find that flux-pileup effects cause the islands to “bounce” despite the presence of a collapsed current sheet allowing fast instantaneous reconnection. The average reconnection rate in the large island limit is slow though the peak reconnection rate is fast.