Steady Hall Magnetohydrodynamics Near a X-type Magnetic Neutral Line

TL;DR

This paper investigates steady-state Hall magnetohydrodynamics near an X-type magnetic neutral line, revealing that Hall effects can sustain a more open magnetic configuration and influence reconnection rates.

Contribution

It demonstrates that Hall effects can maintain hyperbolic magnetic fields in steady state, linking steady and time-dependent problems, and explains the independence of reconnection rate from the flux-breaking mechanism.

Findings

Hall effects sustain hyperbolic magnetic fields near the neutral line.

Steady state can be viewed as an asymptotic limit of the time-dependent problem.

Reconnection rate is independent of the flux-breaking mechanism.

Abstract

Hall magnetohydrodynamics (MHD) properties near a two-dimensional (2D) X-type magnetic neutral line in the steady state are considered via heuristic and rigorous developments. Upon considering the steady-state as the asymptotic limit of the corresponding \textit{time-dependent} problem and using a rigorous development, Hall effects are shown to be able to sustain the hyperbolicity of the magnetic field (and hence a more open X-point configuration) near the neutral line in the steady state. The heuristic development misses this subtle connection of the steady state with the corresponding \textit{time-dependent} problem and predicts only an elongated current-sheet configuration (as in resistive MHD). However, the heuristic development turns out to be useful in providing insight into the lack of dependence of the reconnection rate on the mechanism breaking the frozen-in condition of the magnetic field lines. The latter result can be understood in terms of the ability of the ions and electrons to transport equal amounts of magnetic flux per unit time out of the reconnection region.