The first model for ‘fast’ magnetic field reconnection at speeds comparable with the Alfvén speed was put forward by Petschek (1964). It involves one shock wave in each quadrant radiating from a central diffusion region and leads to a maximum reconnection rate dependent on the electrical conductivity but typically of order 10-1 or 10-2 of the Alfvén speed. Sonnerup (1970) and Yeh and Axford (1970) then looked for similarity solutions of the magnetohydrodynamic equations, valid at large distances from the diffusion region; by contrast with Petschek's analysis, their models have two waves in each quadrant and produce no sub-Alfvénic limit on the reconnection rate.
Our approach has been, like Yeh and Axford, to look for solutions valid far from the diffusion region, but we allow only one wave in each quadrant, since the second is externally generated and so unphysical for astrophysical applications. The result is a model which qualitatively supports Petschek's picture; in fact it can be regarded as putting Petschek's model on a firm mathematical basis. The differences are that the shock waves are curved rather than straight and the maximum reconnection rate is typically a half of what Petschek gave. The paper is a summary of a much larger one (Soward and Priest, 1976).