Intuitive approach to magnetic reconnection

Two reconnection problems are considered. The first problem concerns global physics. The plasma in the global reconnection region is in magnetostatic equilibrium. It is shown that this equilibrium can be uniquely characterized by a set of constraints. During reconnection and independently of the local reconnection physics, these constraints can be uniquely evolved from any initial state. The second problem concerns Petschek reconnection. Petschek's model for fast reconnection, which is governed by resistive MHD equations with constant resistivity is not validated by numerical simulations. Malyshkin et al.[Phys. Plasmas 12, 102920 (2005)], showed that the reason for the discrepancy is that Petschek did not employ Ohm's law throughout the local diffusion region, but only at the X-point. A derivation of Petschek reconnection, including Ohm's law throughout the entire diffusion region, removes the discrepancy. This derivation is based largely on Petschek's original 1964 calculation [in AAS-NASA Symposium on Solar Flares (National Aeronautics and Space Administration, Washington, D.C., 1964), NASA SP50, p. 425]. A useful physical interpretation of the role which Ohm's law plays in the diffusion region is presented.