Spontaneous growth of the reconnection electric field during magnetic reconnection with a guide field: A theoretical model and particle-in-cell simulations**Project supported by the National Natural Science of China (Grant Nos. 41527804 and 41774169), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB 41000000), and the Key Research Program of Frontier Sciences of the Chinese Academy

Abstract

Reconnection electric field is a key element of magnetic reconnection. It quantifies the change of magnetic topology and the dissipation of magnetic energy. In this work, two-dimensional (2D) particle-in-cell (PIC) simulations are performed to study the growth of the reconnection electric field in the electron diffusion region (EDR) during magnetic reconnection with a guide field. At first, a seed electric field is produced due to the excitation of the tearing-mode instability. Then, the reconnection electric field in the EDR, which is dominated by the electron pressure tensor term, suffers a spontaneous growth stage and grows exponentially until it saturates. A theoretical model is also proposed to explain such a kind of growth. The reconnection electric field in the EDR is found to be directly proportional to the electron outflow speed. The time derivative of electron outflow speed is proportional to the reconnection electric field in the EDR because the outflow is formed after the inflow electrons are accelerated by the reconnection electric field in the EDR and then directed away along the outflow direction. This kind of reinforcing process at last leads to the exponential growth of the reconnection electric field in the EDR.