Fine structures of electron distribution functions in the electron diffusion region during magnetic reconnection

We study the origin and evolution of fine structures in electron distribution functions in the electron diffusion region (EDR) during anti-parallel magnetic reconnection. In the EDR, electron non-gyrotropic motion causes a variety of fine structures in electron distributions. Recently, Ng et al. 2011 and 2012 reported that striations in the electron distribution near the X-line are due to particle reflections. We have advanced the understanding of the formation mechanism of striations near the X-line by means of analytical analysis and particle tracing in particle-in-cell (PIC) simulations. Based on an approximation that nonlinear terms are negligible in the EDR, we derive a formula for the separation of striations, and explain the triangular shape of the distribution. We also show that an electron distribution with striations in the horizontal (p_x) direction evolves within about 8 ion cyclotron oscillations into a fork-like structure exhibiting three branches in the vertical (p_y) direction. We show by theory and PIC simulation that the length of the EDR is proportional to p_s^2, where p_s is the separation of the outer branches. Away from the X-line toward the end of electron outflows, electron distribution functions show arcs, swirls, and rings. The arcs and swirls are caused by partial gyration of accelerated electrons around the normal magnetic field. Near the end of the EDR, rings are formed in electron distributions due to magnetization process of electrons. Predictions of various structures of the EDR electron distributions will enable identifications of EDR crossings at different locations based on satellite measurements.