Abstract
The dynamics of a plasma in the vicinity of a neutral line of the magnetic field is considered in the framework of incompressible Hall magnetohydrodynamics (MHD). A self-similar solution for the collapse to a current sheet is obtained. Numerical and analytical results are presented. In contrast to the standard incompressible MHD model in two dimensions, the Hall effect leads to the formation of finite-time singularities of the velocity derivatives and the electric current density at the neutral line. Analytical expressions are derived for the collapse time and the form of the solution near the singularity, which agree closely with the numerical results. If the ion skin depth is set to zero, the singularity formation time becomes infinite, corresponding to the standard MHD result. Implications of the results for Hall MHD models of fast magnetic reconnection are discussed.
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