Particle-in-cell Simulation of Electromagnetic Field Structure in the Electron-only Reconnection

Standard collisionless magnetic reconnection couples with both electron and ion dynamics. Recently, a new type of magnetic reconnection, electron-only magnetic reconnection without ion outflow, has been observed. Using 2.5D particle-in-cell simulation, the electromagnetic field structure in the electron-only reconnection with a strong guide field was studied. At the moment of the maximum reconnection rate, the electron inflow and outflow are observed on either side of the separatrix. The spatial distribution of the electron bulk velocity is approximately symmetric, which generates the nearly symmetrically distributed Hall current, resulting in the quadrupole Hall magnetic field. The Hall magnetic field is not obviously distorted despite the presence of the strong guide field. Meanwhile, the charge separation is caused in the separatrix region, which generates the nearly symmetrically distributed Hall electric field. Besides, the evolution of the spatial distribution of the electron bulk velocity was studied. The equation of motion for the frozen electrons was analytically obtained: $v_e=v_{ey}B/B_y+E\times \left(B_y{e}_y\right)/B_y^2$. According to the equation of motion for the electrons, we divide the electron-only reconnection with a strong guide field into two stages. In the first stage, the $E\times B$ drift is negligible because of the weaker Hall electric field, and then the electrons flow mainly along the magnetic field line following the equation $v_e\approx v_{ey}B/B_y$. In the second stage, the Hall electric field is so strong that the motion of electrons is dominated by the $E\times B$ drift following the equation $v_e\approx E\times \left(B_y{e}_y\right)/B_y^2$. The simulation shows that extremely strong charge separation can be caused in electron-only reconnection, which generates the nearly symmetrically distributed Hall electric field. With a guide field, this Hall electric field leads to the $E\times B$ drift, which dominates the spatial distribution of the electron bulk velocity. Therefore nearly symmetrically distributed Hall current is formed, which generates the nearly symmetrically distributed quadrupole Hall magnetic field.