Abstract
A simple zero-dimensional model is proposed that synthesizes the complex dynamics of driven, two-dimensional, magnetically reconnecting systems within the resistive magnetohydrodynamics (MHD) framework. The model applies to the so-called asymptotic regime of the well-known magnetic island coalescence problem, where well-separated macroscopic “ideal” and microscopic “resistive” regions are assumed to exist. The dynamics of the ideal region is described in terms of the Lorentz and pressure gradient forces on current filaments, and conservation of magnetic flux; that of the resistive region is described in terms of plasma flow and magnetic field magnitudes at the current sheet boundaries. Matching of the two regions provides the evolution equation for the current sheet thickness. The results for the O-point position versus time, reconnection rate, current sheet thickness, etc., at different resistivities obtained from the model agree well with those from the fully nonlinear two-dimensional reduced MHD simulation.
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