Numerical studies on electron magnetohydrodynamics tearing mode instability

Abstract

The 2D electron-magnetohydrodynamics (EMHD) dominant tearing mode in an electron-skin-depth-scale current sheet (ECS) is further studied. The resistive diffusion is proved to be insignificant at the scale. Electron inertia leads to the expansion of the “inner region” as well as a wider saturation island and the invalidity of the boundary layer approximation. The unstable tearing mode index Δ′ thus decreases dramatically from that in classical asymptotic theory. As for nonlinear evaluation, the inverse spectral cascade and the flattening of the m = 0 anti-parallel asymptotic magnetic field will result in an m = 1 final island after nonlinear coupling in a long ECS. A rapid normal saturation transition is observed and only expected for a larger wave number due to the growth rate dependence on the wave number being a single humped function. A linear analysis of the EMHD tearing mode is also presented for the force-free equilibrium. With a strong guide field, it shows that the tearing mode can be suppressed by the shear flow. Nonlinear simulation results with specific parameters then showed that the dynamic structures in the current sheet are consistent with the observation in the Earth’s turbulent magnetosheath.