A CRITERION FOR SPLITTING OF A RECONNECTING CURRENT SHEET INTO MHD DISCONTINUITIES

We consider the splitting of a reconnecting current sheet into MHD dis continuities, which is observed in many numerical simulations of the m agnetic reconnection process, We suppose that the splitting takes plac e as a consequence of non-evolutionarity of the reconnecting current s heet as a one-dimensional discontinuity. This means that the problem o f the time evolution of its small perturbations does not have a unique solution. Since a physical problem must always have a unique solution ; a non-evolutionary discontinuity cannot exist in a real plasma, and splits into evolutionary discontinuities. However, this approach canno t be immediately applied to a current sheet, because tile flow velocit y inside the sheet is two-dimensional and it cannot be generally treat ed as a one-dimensional discontinuity. Solving the linear MHD equation s inside and outside tile sheet, we show that for large enough plasma conductivity, certain small perturbations interact with the sheet as w ith a discontinuity. On the basis of the non-evolutionarity criterion, with respect to these perturbations, we obtain a condition on the flo w velocity at the sheet surface, under which the splitting takes place .