Steady magnetic reconnection in three dimensions

The concept of magnetic reconnection, defined to occur when there is an electric field parallel to field lines which are potential reconnection locations and near which the field has an X-type topology in a plane normal to the field line, has been generalized to three-dimensional configurations. A continuum of neighboring potential singular lines is found to exist, one of which supports reconnection, depending upon the imposed flow or electric field. For the case of steady reconnection, the nearby flow and electric field are shown to be severely constrained in the ideal region by the condition that the electric field = 0 there. It is noted that reconnection may occur at singularities of the electric field where this constraint fails and there is singular plasma jetting.