Extracting the reconnection electric field from electron distribution functions

Electron velocity distribution functions (VDFs) in the electron diffusion region (EDR) in magnetic reconnection are in a crescent shape in the velocity plane perpendicular to the magnetic field, due to meandering motion across a current sheet. In reconnection in Earth’s magnetotail, however, the crescent shape is significantly modified because of the reconnection electric field. We study the formation of multiple striations in an electron crescent VDF in magnetotail reconnection, by means of 2-D particle-in-cell simulations, theory, and space observations by Magnetospheric Multiscale (MMS).

During the meandering motion in the EDR, electrons are accelerated by the reconnection electric field, which makes the crescent asymmetric in the velocity plane perpendicular to the magnetic field, and generates multiple striations. Analyzing electron motion in a simplified 1-D current sheet, we derive an equation to describe multiple striations of electron VDF, as a function of the distance from the magnetic neutral line and the strength of the reconnection electric field. The theory and simulations show excellent agreement. Applying the theory to VDF data obtained in observations by MMS, we derive the amplitude of the reconnection electric field in Earth’s magnetotail.