Abstract
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 magnetic field (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 magnetic field in the corresponding steady problem.
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