Hall magnetohydrodynamics near an X-type magnetic neutral line

Hall magnetohydrodynamics (MHD) near a two-dimensional (2D) X-type magnetic neutral line is considered. The Hall effects are shown to be able to sustain the hyperbolicity of the magneticfield (and hence a more open X-point configuration) near the neutral line in the steady state. This result is predicated on considering the steady Hall MHD state as the temporal asymptotic limit of the corresponding time-dependent problem. For the time-dependent Hall MHD problem, the Hall effects are shown to have a negligible impact on the current-sheet formation process near the X-type magnetic neutral line at short times but, subsequently, to quench the finite-time singularity exhibited in ideal MHD and, hence to prevent the plasma collapse, in consistency with the sustenance of the hyperbolicity of the magneticfield in the corresponding steady problem. Copyright (C) EPLA, 200