Ideal Tearing in the Hall Regime

Magnetic reconnection is generally believed to be the mechanism thatexplains explosive events in astrophysical plasmas, such as flares inthe solar corona, substorms. One of the main questions which remainsconcerns how magnetic reconnection may account for the fast magneticenergy conversion to kinetic and thermal energies. Recently it hasbeen shown by Pucci and Velli (2014) that, assuming that currentsheets scales as different powers of the magnetic Reynolds number S,the growth rate of the tearing mode instability in current sheetsincreases as the sheets thin and, once the thickness reaches a scalinga/L ∼ S-1/3, the time scale for the instability to develop becomesof the order of the Alfvén time. In Hall reconnection, dispersivewaves introduced by the Hall effect make the energy release ratesfaster. This effect becomes important to the collisional tearing modeinstability when the thickness of magnetic reversal layer iscomparable to the ion inertia length, where Hall currents produce athree-dimensional quadrupole structure of magnetic field. Here wepresent a linear study aiming to show how an "ideal tearing mode" isachieved when Hall effects are included, including scaling laws forsheet aspect ratios and growth rates.