Effect of the Reconnection Electric Field on Electron Distribution Functions in the Diffusion Region of Magnetotail Reconnection

Electron distribution functions in the electron diffusion region during symmetric magnetic reconnection are investigated by means of theory and fully kinetic simulations. Crescent-like striations are formed in distribution functions in the velocity plane perpendicular to the magnetic field. Using an analytical current sheet, we solve the equation of motion for electrons, and derive the shape of a crescent distribution, as a function of the distance from the neutral line, field gradients, and the reconnection electric field. Each crescent is tilted in the velocity plane because of the acceleration by the reconnection electric field, and multiple stripes appear due to multiple meandering bounces. Applying the theory to distribution functions observed in Earth's magnetotail, we deduce the amplitude of the reconnection electric field. Plain Language Summary Magnetic reconnection is a mechanism to rapidly release magnetic energy, causing, for example, magnetic substorms in Earth's magnetosphere. Understanding particle motion and energy release during reconnection is highly important in space plasma physics. Reconnection can occur where electrons are moving back and forth across a current sheet. When reconnection occurs, electrons are accelerated by the electric field generated by reconnection. Evidence of such electron motion and acceleration should be seen in particle data in spacecraft orbiting Earth. In this study, using computer simulations and space observations by National Aeronautics and Space Administration's Magnetospheric Multiscale Mission, we demonstrate characteristic shapes in the electron data from reconnection in Earth's nightside magnetosphere. We derive a formula to explain multiple stripes seen in the electron data. The theory successfully explains the simulation data. This formula is applied to space observation data to extract the electric field amplitude during magnetic reconnection. Direct measurement of this electric field is challenging because of its small amplitude and the presence of other simultaneous fluctuations. Our method can be used to estimate the electric field from electron data.