TY - JOUR

T1 - Grad-Shafranov reconstruction of the magnetic configuration in the reconnection X-point vicinity in compressible plasma

AU - Korovinskiy, D. B.

AU - Divin, A. V.

AU - Semenov, V. S.

AU - Erkaev, N. V.

AU - Kiehas, Stefan A.

AU - Kubyshkin, I. V.

N1 - Funding Information: This study has been supported by the Austrian Science Fund (FWF): No. I 3506-N27 and by Russian Science Foundation (RSF): No. 18-47-05001. The authors thank the reviewers for their help in improving the manuscript. Publisher Copyright: © 2020 Author(s). Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/8/1

Y1 - 2020/8/1

N2 - The reconstruction problem for steady symmetrical two-dimensional magnetic reconnection is addressed in the frame of a two-fluid approximation with neglected ion current. This approach yields Poisson's equation for the magnetic potential of the in-plane magnetic field, where the right-hand side contains the out-of-plane electron current density with the reversed sign. In the simplest case of uniform electron temperature and number density and neglecting the electron inertia, Poisson's equation turns to the Grad-Shafranov one. With boundary conditions fixed at any unclosed curve (the satellite trajectory), both equations result in an ill-posed problem. Since the magnetic configuration in the reconnection region is highly stretched, one can make use of the boundary layer approximation; hence, the problem becomes well-posed. The described approach is generalized for the case of nonuniform electron temperature and number density. The benchmark reconstruction of the PIC simulations data has shown that the main contribution for inaccuracy arises from replacing Poisson's equation by the equation of Grad-Shafranov. Under this substitution, the reachable cross-size of the reconstructed region is shrinking down to fractions of the proton inertial length. Artificial smoothing, demanded by solving the ill-posed problem, boundary layer approximation represent two alternative methods of problem regularization. In terms of the reconstruction error, they perform nearly the same; the second method benefits from the comparative simplicity and less restrictions imposed on the boundary shape.

AB - The reconstruction problem for steady symmetrical two-dimensional magnetic reconnection is addressed in the frame of a two-fluid approximation with neglected ion current. This approach yields Poisson's equation for the magnetic potential of the in-plane magnetic field, where the right-hand side contains the out-of-plane electron current density with the reversed sign. In the simplest case of uniform electron temperature and number density and neglecting the electron inertia, Poisson's equation turns to the Grad-Shafranov one. With boundary conditions fixed at any unclosed curve (the satellite trajectory), both equations result in an ill-posed problem. Since the magnetic configuration in the reconnection region is highly stretched, one can make use of the boundary layer approximation; hence, the problem becomes well-posed. The described approach is generalized for the case of nonuniform electron temperature and number density. The benchmark reconstruction of the PIC simulations data has shown that the main contribution for inaccuracy arises from replacing Poisson's equation by the equation of Grad-Shafranov. Under this substitution, the reachable cross-size of the reconstructed region is shrinking down to fractions of the proton inertial length. Artificial smoothing, demanded by solving the ill-posed problem, boundary layer approximation represent two alternative methods of problem regularization. In terms of the reconstruction error, they perform nearly the same; the second method benefits from the comparative simplicity and less restrictions imposed on the boundary shape.

UR - http://www.scopus.com/inward/record.url?scp=85094938176&partnerID=8YFLogxK

U2 - 10.1063/5.0015240

DO - 10.1063/5.0015240

M3 - Article

AN - SCOPUS:85094938176

VL - 27

JO - Physics of Plasmas

JF - Physics of Plasmas

SN - 1070-664X

IS - 8

M1 - 082905

ER -