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Magnetic reconnection in a plane current sheet is investigated by means of a two-dimensional time dependent compressible resistive MHD code. The system length is large compared to the current sheet half thickness. A spatially limited resistivity is applied in the center of the current sheet. The resistivity falls off along the current sheet with some e-folding distance xl. For sufficiently small xl, quasi-steady reconnection with a small diffusion region develops. The reconnection exhibits all Petscheklike features, such as two pairs of slow mode shocks attached to the diffusion region, a strongly converging flow toward the field line reversal region, and a weak fast mode expansion of the inflowing plasma. At larger xl values, long current sheets develop; i.e., the length of the diffusion region is always such as to occupy the largest permitted space. The flow in the long current sheet cases is also of the fast mode expansion type. However, the flow turns in these cases upstream of the separatrices into a wedge-shaped reconnection layer, whereas in the case with a small diffusion region the separatrices are well outside the reconnection layer. The reconnection rate measured in terms of the inflow Alfv¿n Mach number well upstream of the diffusion region decreases with increasing current sheet length and reaches the Sweet-Parker rate for a current sheet corresponding to the system size. Starting the simulation with a small xl and increasing xl as a function of time to the total system size inevitably also leads to long extended current sheets with a correspondingly small reconnection rate. It is thus impossible to retain a diffusion region with a comparable width and length in a large-sized system with spatially extended finite resistivity. By artificially limiting the length of the diffusion region, the maximum reconnection rate has been determined for several simulation runs with different magnetic Reynolds numbers Rm. Over a limited Rm range the numerically obtained rate is consistent with the classical Petschek rate. ¿ American Geophysical Union 1989 |
