Magnetic Reconnection with a Limited X-line Extent in a Force-free Current Sheet: Applications on Aurora Acceleration

Observational and numerical studies suggested that tearing instability can develop in the upward field aligned current region at around 1~2R_E altitude and is probably responsible for the formation of discrete Aurora arcs. If the Aurora acceleration region is dominated by reconnection, the extent of the reconnection x-line which is nearly parallel to the geomagnetic field lines will have a finite length around several thousand kilometers, or tens of ion inertial length. In this work, three-dimensional particle-in-cell simulation is performed to study reconnection with a limited x-line extent in a force-free current sheet with a guide field. Simulation is conducted in XYZ coordinate, X is the direction of the antiparallel upstream magnetic field, Y is the current or the guide field direction, and Z is the normal direction of the current sheet. X, Y, and Z correspond to the longitude, altitude and latitude direction in reality. Open boundary condition is employed in the Y direction to obtain a localized x-line. We find that the reconnection current sheet is short and is limited around x-line on the ion-drifting (high altitude) side, while on the electron-drifting (low altitude) side, the current sheet elongate along the separatrix and can reach tens of ion inertial length. The current sheet is unstable to oblique tearing mode instability and electron scale flux ropes and filament currents will be generated on the electron-drifting side. This process is quite similar to that small scale Aurora arcs form in a large scale arc. Both large scale potential drop and small scale double layers parallel to the magnetic field are observed. They are responsible for the acceleration of energetic electrons. In the current sheet, the energy flux enhancement of energetic electrons is limited in a narrow band, similar to that observed in inverted-V Aurora. While in the flux ropes, the energy flux enhancement of energetic electrons is in a broad band, similar to that observed in Alfvenic Aurora.