Tearing and Surface Preserving Electron Magnetohydrodynamic Modes in A Current Layer

TL;DR

This paper investigates tearing and surface-preserving modes in 2D Electron Magnetohydrodynamics, revealing their distinct behaviors and nonlinear evolution, including magnetic island formation and channel structures.

Contribution

It provides a linear and nonlinear analysis distinguishing tearing and surface-preserving modes in EMHD, highlighting their different conditions and nonlinear outcomes.

Findings

Tearing mode requires a null-line in magnetic field profile.

Surface-preserving mode does not require a null-line.

Nonlinear simulations show magnetic islands form in tearing mode, while channels form in surface-preserving mode.

Abstract

In this paper, we have carried out linear and nonlinear analysis of tearing and surface preserving modes of two dimensional (2D) Electron Magnetohydrodynamics (EMHD). A linear analysis shows that the perturbations parallel to equilibrium magnetic field $B_0$ (characteristic tangent hyperbolic spatial profile), driven by the current gradients, lead to two different modes. The first mode is the tearing mode having a non-local behavior which requires the null-line in the magnetic field profile. Whereas, the second mode is a surface preserving local mode which does not require the null-line in the magnetic field. The quantity $B_0 - B_0^{''}$ should change sign for these modes to exist. In nonlinear simulations, for tearing case we observe formation of magnetic island at the null-line due to the reconnection of magnetic field lines. However, for surface preserving mode, a channel like structure is observed instead of the island structure.