Dynamic non-null magnetic reconnection in three dimensions. I. Particular solutions

A stationary model of three-dimensional magnetic reconnection in the absence of a null point is presented, with a non-ideal region that is localized in space. Analytical solutions to the resistive magnetohydrodynamic equations are obtained, with the momentum equation included so that the model is fully dynamic, and thus extends the previous kinematic solutions. A splitting of variables allows solutions to be written in terms of a particular non-ideal solution, on which ideal solutions may be superposed. For the non-ideal solution alone, it is shown that only the field lines linking the diffusion region are affected by the reconnection process, and counter-rotating flows above and below the diffusion region are present. It is only the dimensions of the diffusion region along the reconnection line that are important for the reconnection rate. Many features of the previous stationary kinematic model are also observed here.