Effective Resistivity in Collisionless Magnetic Reconnection

Magnetic reconnection (MR) in collisionless plasma is often attributed to the off-diagonal electron Reynolds stress, which can give rise to a large induction electric field in the reconnection region. However, in magneto-hydro-dynamics (MHD) simulations of MR, it is difficult to implement the full Reynolds stress, which is kinetic in nature. In this paper, we propose a theoretical model of effective resistivity from the first principle of particle dynamics. The derived theoretical formulation of the effective resistivity is verified by full particle-in-cell (PIC) simulations, and the corresponding physics is discussed.