Electronic Magnetic Fluid In Magnetic Reconnection Instability Theory

Magnetic reconnection is a fundamental transport mechanism in plasma. During the process, magnetic energy is converted to hear, kinetic energy, and fast particle energy. It is probably the most important one for explaining releases of magnetic energy. Magnetic reconnection plays a crucial role in almost all rapid macroscale plasma precess. Tearing mode instability is the unsteady magnetic reconnection, which is one of the most dangerous instabilities in tokamak discharge and can cause disruption. Therefore, it is necessary to investigate magnetic reconnection and tearing mode instability.The mechanism of onset of magnetic reconnection is one of the hot problems about magnetic reconnection. Now, it is believed that magnetic reconnection takes place at the scale of electron inertia skin depth, and the electron inertial probably plays an important role in magnetic reconnection. To investigate the mechanism of onset of magnetic reconnection more better, electron magnetohydrodynamics (EMHD) is used to study reconnection instability. The electron magnetohydrodynamic theory (EMHD) describes plasma phenomena in the whistler frequency regime and below the ion skin depth scale which is proper to investigate the onset of magnetic instability. The characters of magnetic reconnection in the whistler frequency regime and electron skin depth scale are different from that in MHD model, and EMHD theory provides a simple description of reconnection, it is needed to reexamine various aspects of magnetic reconnection which arc well-known in MHD model. In this article, we employ EMHD model to investigate reconnection instability, especially tearing mode instability. There are three aspects we investigated as follows:1, The general dispersion relation of collisionless reconnection instability due to electron viscosityμ_e in the whistler frequency is derived. In the framework of electron magnetohydrodynamics (EMHD), the evolution of magnetic reconnection instability is studied, and the linear growth rates are obtained. The scaling laws of growth rate of reconnection instability with respect to electron viscosity in constant-ψ(used in the tearing mode) and low-k regimes are obtained respectively, and compare with those obtained in standard magnetohydrodynamic theory. In the constant-ψregime for 'tearing mode like' instability, the growth rate is proportional toμ_e^1/4 ; while in low-k regime,it is proportional toμ_e^1/8. It can be seen that the growth rates due to the electron inertial skin depth d_e are different in EMHD and MHD regimes. The EMHD growth rate decreases less rapidly for R→0, and the reconnection rate is more fast.2, The general dispersion relation of tearing mode with electron pressure gradient effect in the whistler frequency is analytically derived in the framework of compressible electron magnetohydrodynamics (EMHD). It is shown that electron pressure gradient effect enhances the growth rate, which is contrary to it in MHD. In MHD, tearing mode instability is suppressed by pressure gradient effect. Due to the existence of electron pressure gradient, EMHD tearing mode becomes drift, and there are three modes: unstable mode, pure oscillating mode and stable modes. For the large electron pressure gradient (χ_p0). the growth rate of tearing mode in compressible EMHD fluid isγ∝d_e²Î»^-2/3χ_p0^1/3 (λdenotes compressible effects); while in incompressible EMHD fluid,γ∝d_e^4/5χ_p0^3/5(d_e is electron inertial skin depth). The growth rate in the compressible EMHD fluid is much different from that in the incompressible EMHD fluid.3, The general time evolution of tearing mode due to electron viscosityμ_e from linear to nonlinear phase in the framework of electron magnetohydrodynamics (EMHD) is derived by quasilinear theory. We did not used the flux-average method, since it would cancel the convective terms in the flux and motion equation. It is found that the linear phase and nonlinear phase are separated by a transition, during which the growth behavior is much different from that in the linear and nonlinear phases.