How Does the Guide Field Affect the Asymmetry of Hall Magnetic and Electric Fields in Fast Magnetic Reconnection?

Recent studies show that the out-of-plane quadrupolar magnetic field in fast magnetic reconnection is distorted in the presence of a guide field. It is asymmetric with respect to the current sheet. In this work, we analyze the spatial and amplitude asymmetries of the Hall magnetic field B_y and the Hall electric field E_z in reconnection with different guide fields by a series of 2.5-D particle-in-cell simulations. We derive the relation between the asymmetry of B_y and E_z and the guide field strength. In addition, by analyzing the different terms in the generalized ohm's law, we find that the electric field E_z is mainly balanced by the Hall term, and the amplitude asymmetry is mainly caused by the Hall effect.