On the solutions of three-dimensional non-null magnetic reconnection

Here we present solutions of a stationary magnetohydrodynamic (MHD) model for three-dimensional (3D) magnetic reconnection in the absence of a null point. The solutions are found in the form of an expansion scheme with a localized nonideal region. A wide variety of both analytical and numerical solutions of the resistive MHD equations can be obtained via an integration scheme, which includes free functions to match boundary conditions. General analytical solutions are obtained for the first few orders, whereas higher order solutions require numerical integration. Thus, numerical techniques have been used to examine the contribution of some higher order terms. The obtained solutions show important differences between 3D solutions and the commonly used two-dimensional models. In particular, they show the existence of more complicated current and flow structures in the reconnection region.