Model of Hall Reconnection

The rate of quasistationary, two-dimensional magnetic reconnection is calculated in the framework of incompressible Hall magnetohydrodynamics, which includes the Hall and electron pressure terms in Ohm's law. The Hall-magnetohydrodynamics equations are solved in a local region across the reconnection electron layer, including only the upstream region and the layer center. In the case when the ion inertial length di is larger than the Sweet-Parker reconnection layer thickness, the dimensionless reconnection rate is found to be independent of the electrical resistivity and equal to di/L, where L is the scale length of the external magnetic field in the upstream region outside the electron layer and the ion layer thickness is found to be di.