Numerical study of the influence of electron inertial effects and electron dynamics on tearing mode instability

The tearing mode instabilities were numerically studied in two distinct models: the finite electron inertial magnetohydrodynamics (MHD) and the electron MHD (EMHD). The finite electron inertial MHD model employed a modified Hall-MHD model that incorporated the electron inertial effects in the generalized Ohm's Law. On the other hand, the electron dynamics were described by the EMHD model. It is found that both electron inertial effects and electron dynamics significantly influence the linear and nonlinear growth of tearing mode instabilities, with electron dynamics playing a more dominant role. The dependence of the linear growth rate of tearing modes on the electron inertial length d_e was investigated. The results show that electron inertial effects enhance the growth rate but resemble the behavior of resistivity η. Whereas, in the EMHD model, electron inertia plays a dominant role in tearing mode instabilities. Additionally, a study on the nonlinear saturation of (2,1) tearing modes was conducted, demonstrating consistency with relevant analytical theories. The study indicates that, in both models, the magnetic island exhibits faster growth and achieves a larger saturated island width as d_e increases.