Effects of Hall electric fields on the saturation of forced antiparallel magnetic field merging

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Abstract
The role of Hall electric fields in flux pile-up antiparallel magnetic field merging is addressed. Analytical solutions of the resistive Hall magnetohydrodynamics (Hall-MHD) equations are obtained, describing stagnation point flows in a thin current sheet. The stagnation point flow solutions explain a number of interesting effects observed in two-dimensional resistive Hall-MHD simulations of forced magnetic reconnection. In particular, when Hall electric fields are important within the current sheet, less pile-up of magnetic energy is required upstream of the current sheet to support a given reconnection electric field. Fast electron flows transport magnetic flux into the diffusion layer without requiring a compensating drop in plasma pressure upstream of the current sheet. The maximum flux pile-up merging rate allowed by the external plasma pressure becomes independent of the Lundquist number, scaling like the square root of the ratio of the ion inertial length to the spatial scale of the stagnation point flow. Thus, Hall electric fields provide a possible solution to the problem of flux pile-up saturation in two-dimensional, resistive MHD models of forced magnetic reconnection.