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.
Highlights
It is expected that the electron magnetohydrodynamics (EMHD) model could identify the electron’s dynamics in the electron diffusion region (EDR) and pertain to the early stage of realistic reconnection at the scale of de by the scaling W/Lc ∝ (de/Lc) ∼ 1
We further delineate and quantify this issue by the “inner region” structures and an external index Δ′ = 2ψ1′,max/ψ1,xs. It shows that Δ′ is much smaller than classical Δ′0 = 2(1/kyLc − kyLc)/Lc when de/Lc = 0.5–2 and approaches classical Δ′0 only when de/Lc ≪ 1
For different Lc/de, we obtain the most unstable mode variation kynaxde ≈ 0.4(Lc/de)−1.07, which leads to the nonlinear evolution of the EMHD tearing mode restricted by the box size
Summary
Magnetic reconnection in the current sheet is a magnetic-toparticle energy conversion process that is fundamental to many space and laboratory plasma systems, such as tokamaks, magnetospheres, and solar flares. In low-density, high-temperature plasmas, the reconnection is always found to be the collisionless one that happens in an electron diffusion region (EDR). The current sheet could thin down to the electron inertial length (de). In this region, the time scale is almost independent of resistive dissipation. resistive magnetohydrodynamics (MHD) theory will no longer be valid and the electron magnetohydrodynamics (EMHD) theory should be included. The theory focuses on the dynamics of electron flow rather than that of heavier ions, which merely provide a stationary neutralizing background. It has been demonstrated to be valid for many fast plasma processes, such as magnetic vortices, EMHD turbulence, and whistler wave propagation.. Earlier works by Jain and Sharma focused on the formation and evolution of the current sheet to predict the dynamic structures. They detected the nested quadrupole structure of the out-of-plane field, the bifurcated filamented triple-peak structures of the current, and observed secondary instabilities in the islands due to subordinate shear flow.. It is expected that the EMHD model could identify the electron’s dynamics in the EDR and pertain to the early stage of realistic reconnection at the scale of de/Lc ∼ 1. In this work, both linear and nonlinear results of the tearing mode at the de/Lc ∼ 1 scale are presented.
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