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Fast Steady State Magnetic Reconnection

F. Jamitzky and M. Scholer

We investigate the behaviour of a reconnecting current sheet by performing a boundary layer analysis of the stationary incompressible MHD-equations with spatially inhomogeneous resistivity. Steady state solutions for the diffusion region are constructed and are matched to solutions of the ideal MHD-equations in the outer region.

In the case of uniform resistivity it was found that the reconnection proceeds in a Sweet/Parker type behaviour which leads to a very instationary and slow reconnection for large magnetic Reynolds numbers. The separatrices osculate and the characteristics, which are the rays of the linear waves that emerge from the diffusion region, are confined in the current sheet. They cannot escape into the inflow region where they could steepen and become standing slow shocks. For an elongated current sheet the waves can escape at the ends of the sheet and produce here the observed standing slow shocks.
     In the non-uniform resistivity case the picture changes completely: the reconnection rate increases drastically and the diffusion region stays small even for large magnetic Reynolds numbers. Petschek-type magnetic reconnection is realized. The separatrices cross under a finite angle and, as a result, the slow waves also have a propagation direction in the inflow region. The slow waves can immediately escape from the X-point, be convected back and steepen to standing slow shocks. Slow shocks are much more effective in converting magnetic energy into kinetic energy than an elongated current sheet, which explains the strongly enhanced reconnection rate. The effectiveness of the slow shocks manifests itself in the weak dependence of the reconnection rate on magnetic Reynolds numbers.
     We thus have demonstrated that the important difference between uniform and non-uniform resistivity magnetic reconnection lies in the behaviour of the separatrices near the X-point.
     Summarizing the occurrence of fast magnetic reconnection in resistive astrophysical and space plasmas can be understood on the basis of Petschek type reconnection if a gradient of the resistivity exists near the magnetic null point.
     P. A. Sweet, IAU Symp. 6, 123 (1958). E. N. Parker, Astrophys. J. Supp. 8, 177 (1963). H. E. Petschek, in AAS-NASA Symposium on Physics of Solar Flares; NASA SP-50, 425 (1964). F. Jamitzky and M. Scholer, J. Geophys. Res. 100, 19,277 (1995). M. C. Yan, L. C. Lee, and E. R. Priest, J. Geophys. Res. 97, 8277 (1992). E. R. Priest and S. W. H. Cowley, J. Plasma Physics, 14, 271 (1975).