Reconnection of inhomogeneous magnetic fields

Magnetic reconnection is a universal energy conversion process which is expected to take place in current sheets of various geometries. We present here a theoretical investigation of specific features of inhomogeneous magnetic field reconnection in the framework of a two-dimensional and time-dependent Petschek-type model for the case of an incompressible plasma, with an inhomogeneous field strength along the current sheet. Two field-reversal regions (FRRs) appear on opposite sides of the reconnection line, as was the case for homogeneous fields. However, the inhomogeneous field gives rise to a different type of boundary for the FRR: the boundary consists of both Petschek-type shock waves and tangential discontinuities. Here we show that the method of strings restricts our ability to solve the reconnection problem, and suggest ways of improvement.