Influence of the Hall effect and electron inertia in collisionless magnetic reconnection

Abstract

We study the role of the Hall current and electron inertia in collisionless magnetic reconnection within the framework of full two-fluid MHD. At spatial scales smaller than the electron inertial length, a topological change of magnetic field lines exclusively due to electron inertia becomes possible. Assuming stationary conditions, we derive a theoretical scaling for the reconnection rate, which is simply proportional to the Hall parameter. Using a pseudo-spectral code with no dissipative effects, our numerical results confirm this theoretical scaling. In particular, for a sequence of different Hall parameter values, our numerical results show that the width of the current sheet is independent of the Hall parameter while its thickness is of the order of the electron inertial length, thus confirming that the stationary reconnection rate is proportional to the Hall parameter.

von Kármán–Howarth equation for three-dimensional two-fluid plasmas

“…The equations of motion for a quasi-neutral incompressible plasma of ions and electrons with mass m i,e , charge ±e, densities n i = n e = n, pressures p (i,e) , and respective velocities v and u are [41][42][43] m e n du dt…”

Exact scaling laws for helical three-dimensional two-fluid turbulent plasmas

“…The equations of motion for a quasi-neutral incompressible plasma of ions and electrons with masses m i,e , charges ±e, constant densities n p = n e = n, pressures p e,p , and respective velocities u e and u p are [33]…”

On the value of the reconnection rate

“…Porcelli et al. 2002; Fitzpatrick 2004; Bhattacharjee, Germaschewski & Ng 2005; Andrés, Dmitruk & Gómez 2016). In light of the subtlety of the problem, we shall elucidate the conditions under which one should expect a maximum/steady-state reconnection rate .…”

“…(1.3) (e.g., Daughton & Karimabadi 2007;Liu et al 2014;Stanier et al 2015). There are also some works that have argued against the ∼ 0.1 value of the maximum/steady-state reconnection rate (e.g., Porcelli et al 2002;Fitzpatrick 2004;Bhattacharjee et al 2005;Andrés et al 2016). In light of the subtlety of the problem, we shall elucidate the conditions under which one should expect a maximum/steady-state reconnection rate ∼ 0.1.…”