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Magnetic reconnection is believed to be responsible forvarious explosive processes in the space plasma includingmagnetospheric substorms. The Hall effect is proved to play a keyrole in the reconnection process. An analytical model ofsteady-state magnetic reconnection in a collisionlessincompressible plasma is developed using the electron Hall MHDapproximation. It is shown that the initial complicated system ofequations may split into a system of independent equations, andthe solution of the problem is based on the Grad-Shafranovequation for the magnetic potential.The results of the analytical study are further compared with atwo-dimensional particle-in-cell simulation of reconnection.  Itis shown that both methods demonstrate a close agreement in theelectron current and the magnetic and electric field structuresobtained. The spatial scales of the acceleration region in thesimulation and the analytical study are of the same order. Suchfeatures like particles trajectories and the in-plane electricfield structure appear essentially similar in both models

Collisionless magnetic reconnection: analytical model and PIC simulation comparison