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The off-diagonal electron pressure terms are well-known for the frozen-incondition breakdown in collisionless magnetic reconnection, but are naturallykinetic and hard to employ in magnetohydrodynamics (MHD) simulations.Considering the inadequacy of MHD and Hall MHD in neglecting the importantelectron dynamics like inertia item and nongyrotropic pressure, we studied thekinetic features of electrons and ions in the diffusion region and suggested anew effective resistivity model involving basic dynamics of charged particlesin diffusion region, which is found to be electron dominated in most of largeion-electron mass ratio cases [Z W Ma et al., Scientific Reports (2018)8:10521]. The application of the effective resistivity in MHD and Hall MHDremarkably improves the simulation results compared with traditional models.Especially for the Hall MHD case with effective resistivity, the peakreconnection rate, major topological structures of the reconnection field andthe current sheet are quite consistent with the reported particle-in-cell (PIC)and hybrid simulation results.

Application of the effective resistivity in MHD and Hall MHD simulations for collisionless magnetic reconnection