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

TL;DR

This paper investigates how the Hall effect and electron inertia influence collisionless magnetic reconnection, deriving a scaling law for the reconnection rate and confirming it through numerical simulations.

Contribution

It provides a theoretical scaling for the reconnection rate based on the Hall parameter and confirms it with spectral code simulations, highlighting the role of electron inertia.

Findings

Reconnection rate is proportional to the Hall parameter.

Current sheet width is independent of the Hall parameter.

Current sheet thickness is on the order of the electron inertial length.

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 range, thus confirming that the stationary reconnection rate is proportional to the Hall parameter.