ANALYSIS OF PETSCHEK-TYPE RECONNECTION IN A Y-TYPE MAGNETIC-FIELD DISTRIBUTION

An analytical investigation is performed of Petschek-type reconnection in an incompressible plasma medium with a non-uniform magnetic field distribution, given by B = root (2 (z) over bar) in complex variable n otation. The initial two-dimensional (2D) configuration contains a cur rent sheet, modelled as a tangential discontinuity, which runs along t he positive x-axis in the complex plane, and which terminates in a Y-t ype neutral point at one end (x = 0). In the model, reconnection is in itiated through the introduction of tangential electric field componen t in a localized part of the current sheet referred to as the diffusio n region. Outside the diffusion region, which we approximate as an X-t ype neutral point, the behaviour of the magnetic field and plasma flow is governed by the equations of ideal magnetohydrodynamics (MHD), whi ch for the purpose of this analysis are transformed into a Lagrangian coordinate system. With the restriction of a small reconnection rate, a perturbation method is applied to solve the MHD equations for the ou tflow region, containing the reconnected plasma, and the surrounding i nflow region. The outflow region is treated as a thin boundary layer, and the usual matching procedure for problems of this type is used. in agreement with the results of previous studies of Petschek-type recon nection in non-uniform, asymmetric magnetic field and velocity distrib utions, the boundary and interior structure of the outflow region is f ound to consist of a combination of Petschek-type shocks and tangentia l discontinuities. This is in contrast to the case of an initially uni form magnetic field distribution, analysed originally by Petschek, whe re the outflow region is entirely bounded by Petschek-type shocks and contains no interior discontinuities. The new features arise because t he shocks propagate at the local Alfven velocity in the medium, wherea s plasma entering the outflow region is accelerated to the Alfven velo city as measured at the reconnection site. As a result of the discrepa ncy between the plasma outflow speed and the shock propagation speed i n the model configuration analysed here, the behaviour of the field an d flow is qualitatively and quantitatively different on opposite sides of the X-line. In particular, the outflow region propagating into the direction of increasing field strength (i.e. x increasing) is bounded entirely by Petschek-type shocks, but contains a tangential discontin uity which extends the original current sheet through the leading poin t (or nose) into the interior of the outflow region. On the other hand , the outflow region propagating into the direction of decreasing fiel d strength (x decreasing, but remaining positive) is bounded on the fr ont by tangential discontinuities, which emerge out of Petschek-type s hocks, and merge into the original current sheet at the nose. When the reconnection rate drops to zero, there is an additional reverse type of behaviour which occurs in the trailing part tangential discontinuit ies develop to form the tail end boundary of the outflow region in the former case, and in the latter case a tangential discontinuity develo ps which penetrates through the tail into the outflow region. We also investigate the consequences of a reconnection site which moves along the current sheet, analyse what happens when there are two successive pulses of reconnection, and briefly discuss the situation when the out flow region propagates beyond the edge of the current sheet.