Coalescence of magnetic islands in the low-resistivity, Hall-MHD regime

The coalescence of magnetic islands in the low-resistivity eta, Hall-MHD regime is studied. The interaction between the ion inertial length d(i) and the dynamically evolving current sheet scale length deltaJ is established. Initially, d(i) << deltaJ. If eta is such that deltaJ dynamically thins down to d(i) prior to the well-known sloshing phenomena, then sloshing is avoided. This results in eta independent peak reconnection rates. However, if d(i) is small enough that deltaJ cannot be thinned down to this scale prior to sloshing, then sloshing proceeds as in the resistive MHD model.