Effective Resistivity for Magnetohydrodynamic Simulation of Collisionless Magnetic Reconnection

Abstract

The electron inertia and the off-diagonal electron pressure terms are well-known for the frozen-in condition breakdown in collisionless magnetic reconnection, which are naturally kinetic and difficult to employ in magnetohydrodynamic (MHD) simulations. Considering the limitations of MHD and Hall MHD in neglecting the important electron dynamics such as the inertia and the nongyrotropic pressure, the kinetic characteristics of electrons and ions in the diffusion region are studied and an effective resistivity model involving dynamics of charged particles is proposed (Ma et al. 2018, https://doi.org/10.1038/s41598-018-28851-7 Sci. Rep. 8 10521), where the guide field is omitted to simplify the model by primarily considering the out-of-plane velocity of charged particles and the in-plane reconnecting field. The amplitude of the effective resistivity is mainly determined by electrons in most realistic situations with large ion-electron mass ratios. In this work, the effective resistivity model for collisionless magnetic reconnection is successfully applied in the 2.5D MHD and Hall MHD simulations, which remarkably improves the simulation results compared with traditional MHD models. For the MHD case, the effective resistivity significantly increases the reconnection rate to a reasonable value of $\sim 0.1B_0{v}_A$. For the Hall MHD case with effective resistivity, the peak reconnection rate is $\sim 0.25B_0{v}_A$, and the major structures of the reconnecting field and the current sheet agree well with the particle-in-cell (PIC) simulations. Meanwhile, a more general effective resistivity model incorporating guide field corrections for MHD simulations is under development.