Reconstruction of the electron diffusion region

Abstract We discuss mathematical tools for the reconstruction of two‐dimensional, time‐independent magnetic field and flow in the electron diffusion region, at a site of antiparallel magnetic reconnection. The basic assumptions are that the ions are stationary and have constant density. The width of the reconnection layer is of the order of the electron gyroradius or the electron inertial length. Our model includes the axial electron pressure term in Ohm's law developed by M. Hesse and coworkers. We demonstrate the feasibility of doing reconstruction of electron magnetohydrodynamic (EMHD) structures for a simplified system with zero electron inertia. The code is benchmarked using an exact solution that has antiparallel unidirectional magnetic fields, plus out‐of‐plane quadrupolar Hall fields, as well as the expected slow electron inflow and rapid exit jets. The inertialess reconstruction is then applied to synthetic data from a 2‐D, particle‐in‐cell, simulation of antiparallel reconnection. We find that the inertialess reconstruction of its electron diffusion region works reasonably well only when the spacecraft path passes close to the center of the reconnection site where the magnetic field is zero and the electron flow has a stagnation point. When the path is located farther away, the effects of electron inertia, and probably also deviations from the Hesse formula, cause the quality of the reconstruction to deteriorate. Electron inertia is included in the theoretical development presented here but requires a more complicated numerical reconstruction code. The development and testing of such a code is underway and will be presented separately.