Marginal Stability of Current Sheets at Low Lundquist Numbers and the Hall Effect

Magnetohydrodynamic simulations suggest that there exists a non-unique critical Lundquist number S, around S 104, above which current sheets transition from a stationary Sweet-Parker (SP) like reconnecting configuration to a highly tearing-unstable (turbulent) state dominated by plasmoid generation. It is known that the flow along the sheet plays a stabilizing role, as one would expect that the plasmoid evacuation time-scale must be longer than the typical growth time for islands in order for the sheet to be tearing unstable. However, a satisfactory explanation of the existence of such a critical threshold for the tearing instability, and why it is not universal, is still lacking. A detailed understanding of this effect is important even for very large Lundquist number plasmas, because it has been shown that in such cases fast reconnection occurs, at least in 2D, starting from sheets that are much thicker than SP (so-called ideally tearing sheets) and evolving in a self-similar way over smaller and smaller scales (and therefore smalle Lundquist numbers) until a sufficiently low Reynolds number is reached for which sheets are stable and dissipate rapidly. So the ending of this so-called fractal reconnection regime is determined by the low-Lundquist number stabilization of SP-like sheets. Here we present the linear stability analysis of two-dimensional SP current sheets at relatively low-S with flows across and along the sheet, and carry out 2D MHD simulations to validate the linear results, and extend those results by including the Hall effect in order to inspect in which way it affects both the marginal stability of SP-like current sheets at low-S and the disruption of forming current sheets above the critical S.