Numerical models of magnetic reconnection

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Abstract
This paper contains a review of numerical experiments concerning steady state magnetic reconnection. The Sweet/Parker current sheet model and Petschek's standing slow mode shock wave model for magnetic reconnection are reviewed briefly along with the recently developed unified theory of Priest and Forbes. All these analytical models do not provide a detailed description of the diffusion layer. Because of the inherent mathematical difficulties involved in solving analytically the full resistive problem, one is forced to perform numerical studies of the reconnection process. All numerical experiments performed so far have not been able to produce fast steady state reconnection at high Reynolds numbers in a system with uniform resistivity. Fast steady state reconnection seems only possible if the resistivity is spatially limited to a small region. In the case of free boundary conditions Petschek-type reconnection results, and in the case of driven reconnection all reconnection regimes derived by Priest and Forbes can be obtained. In a system with uniform resistivity, long current sheets tend to develop, irrespectively whether reconnection is driven or spontaneous, and the reconnection rate is correspondingly small. These long current sheets are unstable and reconnection will then enter a highly dynamic and/or turbulent regime.