Electron magnetohydrodynamics Grad–Shafranov reconstruction of the magnetic reconnection electron diffusion region

We present a study of the electron magnetohydrodynamics Grad–Shafranov (GS) reconstruction of the electron diffusion region (EDR) of magnetic reconnection. Two-dimensionality of the magnetoplasma configuration and steady state are the two basic assumptions of the GS reconstruction technique, which represent the method’s fundamental limitations. The present study demonstrates that the GS reconstruction can provide physically meaningful results even when these two assumptions, which are hardly fulfilled in spacecraft observations, are violated. This conclusion is supported by the reconstruction of magnetic configurations of two EDRs, encountered by the Magnetospheric Multiscale (MMS) Mission on July 11, 2017 and September 8, 2018. Here, the former event exhibited a violation of two-dimensionality, and the latter event exhibited a violation of steady state. In both cases, despite the deviations from the ideal model configuration, reasonable reconstruction results are obtained by implementing the herein introduced compressible GS reconstruction model. In addition to the discussed fundamental limitations, all existing versions of the GS reconstruction technique rely on a number of minor simplifying assumptions, which restrict the model scope and efficiency. We study the prospects for further model improvement and generalization analytically. Our analysis reveals that nearly all these minor limitations can be overcome by using a polynomial MMS-tailored reconstruction technique in the space of rotationally invariant variables instead of Cartesian coordinates.