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A Parametric Study of the Structure of Hall Magnetic Field Based on Kinetic Simulations. I. Anti-parallel Magnetic Reconnection in an Asymmetric Current Sheet

The generation of the Hall magnetic field is considered one of the most important characteristics in collisionless magnetic reconnection. Here, in this paper, with two-dimensional particle-in-cell simulations, we study the structure of the Hall magnetic field generated during anti-parallel magnetic reconnection in an asymmetric current sheet. A quadrupolar structure of the Hall magnetic field is first formed, and then it evolves into a hexapolar structure with the proceeding magnetic reconnection. In the quadrupolar structure of the Hall magnetic field, the quadrants on the side of the current sheet with the weaker magnetic field (the dominant Hall magnetic field) are much stronger than those on the other side, and they can cross the center of the current sheet. With the increase of the ratio of the magnetic fields or the decrease of the density ratio (here, the ratio is defined as the values between the side with the stronger magnetic field to that with the weaker magnetic field), the tendency will become more salient. However, with a decrease of the temperature ratio, the tendency reverses. With the proceeding reconnection, two ribbons with an enhanced Hall magnetic field are generated in the region below the dominant Hall magnetic field, and then a hexapolar structure of the Hall magnetic field is formed, which will become stronger with an increase of the ratio of the magnetic field or decrease of the density, while the effect of the temperature asymmetry is much weaker than that of the magnetic field and density asymmetry. The generation of the Hall magnetic field can be explained by the in-plane current carried mainly by the electrons.