This paper discusses the transition to fast growth of the tearing instability in thin current sheets in the collisionless limit where electron inertia drives the reconnection process. It has been previously suggested that in resistive MHD there is a natural maximum aspect ratio (ratio of sheet length and breadth to thickness) which may be reached for current sheets with a macroscopic length L, the limit being provided by the fact that the tearing mode growth time becomes of the same order as the Alfv`en time calculated on the macroscopic scale (Pucci and Velli (2014)). For current sheets with a smaller aspect ratio than critical the normalized growth rate tends to zero with increasing Lundquist number S, while for current sheets with an aspect ratio greater than critical the growth rate diverges with S. Here we carry out a similar analysis but with electron inertia as the term violating magnetic flux conservation: previously found scalings of critical current sheet aspect ratios with the Lundquist number are generalized to include the dependence on the ratio $(d_e/L)^2$ where de is the electron skin depth, and it is shown that there are limiting scalings which, as in the resistive case, result in reconnecting modes growing on ideal time scales. Finite Larmor Radius effects are then included and the rescaling argument at the basis of ideal reconnection is proposed to explain secondary fast reconnection regimes naturally appearing in numerical simulations of current sheet evolution.
تحميل البحث