A large-scale two-dimensional electromagnetic particle-in-cell simulation was employed to study the magnetic island coalescence/merging process during magnetic reconnection with guide field. The merged island after coalescence is characterized by strong core field and plasma density dip at the island center. We found that the core field enhancement is caused by the out-of-plane magnetic field pileup, as well as the field line twisting due to Hall effect. There is an in-plane electric current loop, which is mainly carried by electrons, circumventing the enhanced core field region. Total force points away or tangentially to the surface of density dip within the merged island, which prevents electrons from higher-density region entering the lower density region between two merging islands. This is contrary to the force in the secondary island, inside which the total force points toward the island center and constrains plasma there. The coalescence process involves a reconnection at the merging sheet between two islands. Electron frozen-in condition is violated locally along the merging sheet. It is contributed by both the divergence of electron pressure tensor and electron inertial. Energy dissipation is concentrated on the merging line during coalescence, while a train of dynamo (j′ · E′ < 0) and dissipation (j′ · E′ > 0) regions are distributed along the merging sheet after coalescence. Electrons and ions within the density dip at the island center are accelerated antiparallel to the ambient magnetic field, i.e., along the out-of-plane direction. The resultant distribution can excite the Buneman instability and two-streaming instability, which probably account for the electrostatic solitary waves observed by satellite.

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 𝐵𝑦 and the Hall electric field 𝐸𝑧 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 𝐵𝑦 and 𝐸𝑧 and the guide field strength. In addition, by analyzing the different terms in the generalized ohm's law, we find that the electric field 𝐸𝑧 is mainly balanced by the Hall term, and the amplitude asymmetry is mainly caused by the Hall effect.