A model of Hall reconnection

The rate of quasi-stationary, two-dimensional magnetic reconnection is calculated in the framework of incompressible Hall magnetohydrodynamics (MHD). The calculation is based on the solution of Hall-MHD equations that include Hall and electron pressure terms for electric current. These 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 d_i 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 d_i/L, where L is the scale length of the external magnetic field in the upstream region outside the electron layer.