Ideal Tearing in the Hall Regime

Abstract:

Magnetic reconnection is generally believed to be the mechanism that
explains explosive events in astrophysical plasmas, such as flares in
the solar corona, substorms. One of the main questions which remains
concerns how magnetic reconnection may account for the fast magnetic
energy conversion to kinetic and thermal energies. Recently it has
been shown by Pucci and Velli (2014) that, assuming that current
sheets scales as different powers of the magnetic Reynolds number S,
the growth rate of the tearing mode instability in current sheets
increases as the sheets thin and, once the thickness reaches a scaling
a/L ∼ S^−1/3, the time scale for the instability to develop becomes
of the order of the Alfvén time. In Hall reconnection, dispersive
waves introduced by the Hall effect make the energy release rates
faster. This effect becomes important to the collisional tearing mode
instability when the thickness of magnetic reversal layer is
comparable to the ion inertia length, where Hall currents produce a
three-dimensional quadrupole structure of magnetic field. Here we
present a linear study aiming to show how an "ideal tearing mode" is
achieved when Hall effects are included, including scaling laws for
sheet aspect ratios and growth rates.