### Abstract

Numerical results of two and three dimensional magnetic reconnection in the Hall limit (L < c/wpi where c/wpi ion inertial length) are presented. Two dimensional Hall magnetohydrodynamic (MHD) simulations are used to determine the magnetic reconnection rate in the Hall limit. The simulations are run until a steady state is achieved for four initial current sheet thicknesses: L = 1,5,10, and 20 c/wpi It is found that the asymptotic (i.e., time independent) state of the system is nearly independent of the initial current sheet width. Specifically, the Hall reconnection rate is weakly dependent on the initial current layer width and is ~ 0.1 V_A0B_0 where V_A0 and B_0 are the Alfven velocity and magnetic field strength in the upstream region. Moreover, this rate appears to be independent of the scale length on which the electron `frozen-in' condition is broken (as long as it is < c/wpi). The 3D reconnection process is initiated with a magnetic field perturbation localized along the current channel in a reversed field plasma configuration. The perturbation induces a magnetic wave structure that propagates opposite to the current, and leads to the asymmetric thinning of the plasma layer, strong plasma flows in the direction of the current, and rapid magnetic reconnection. The propagating wave structure is a Hall phenomenon associated with magnetic field curvature. The results are applied to reconnection processes in space.