Rate of unsteady reconnection in an incompressible plasma

Abstract

Using a two-dimensional, incompressible magnetohydrodynamic (MHD) model, we study unsteady reconnection of antiparallel magnetic fields in the symmetric case. The magnetic reconnection process is initiated by variation of a local resistivity assumed to be a given function of time and spatial coordinates. The diffusion region of reconnection is treated as a thin boundary layer where the perpendicular components of magnetic field and velocity are much smaller than the components of these quantities along the layer. The unsteady MHD equations are solved by a two-step finite difference numerical scheme with an implicit approximation of the magnetic diffusion terms in a uniform right angle grid. In the numerical study, we use the initial conditions related to a uniform current layer without any motion of the plasma. The time-dependent reconnection process is characterized by the following important parameters: A timescale of the local resistivity, a length scale of the local resistivity, a local Reynolds number determined for the maximum resistivity and the length scale of the diffusion region. The numerical results show that the Petschek type reconnection is realized for the sufficiently small length scale andlarge time scale of the local resistivity, and a moderate local Reynolds number. Using unsteady numerical MHD solution obtained for the diffusion region, we determine the reconnection rate as a function of time by matching of the outer Petschek solution and the internal diffusion region solution.