Magnetic reconnection with anomalous resistivity in two-and-a-half dimensions. I. Quasistationary case

In this paper quasistationary, “two-and-a-half-dimensional” magnetic reconnection is studied in the framework of incompressible resistive magnetohydrodynamics. A new theoretical approach for the calculation of the reconnection rate is presented. This approach is based on the local analytical derivations in a thin reconnection layer, and it is applicable to the case when resistivity is anomalous and is an arbitrary function of the electric current and the spatial coordinates. It is found that a quasistationary reconnection rate is fully determined by a particular functional form of the anomalous resistivity and by the local configuration of the magnetic field just outside the reconnection layer. It is also found that, in the special case of constant resistivity, reconnection is Sweet-Parker [Electromagnetic Phenomena, edited by B. Lehnert (Cambridge University Press, New York, 1958), p. 123; Astrophys. J., Suppl. 8, 177 (1963)] and not Petschek [AAS-NASA Symposium on Solar Flares NASA SP5 (National Aeronautics and Space Administration, Washington, D.C., 1964), p. 425].