Self-Consistent Models of Incompressible Stationary Magnetic Reconnection by Weakly Two-dimensional Extension of Magnetic Annihilation

Weakly two-dimensional self-consistent solutions of the stationary resistive magnetohydrodynamic equations are presented The solutions are found by applying an asymptotic expansion procedure to the stationary resistive MHD equations with the annihilation Solution as lowest order solution. Two different approximation schemes are investigated. Whereas the first scheme allows the introduction of a normal magnetic field component in the lowest order, the second scheme also introduces a weak variation of the current density along the current sheet in the lowest order. This is closely related to the fact that in the first case the inflow velocity does not vary along the current sheet, whereas in the second case the inflow velocity may vary weakly along the current sheet.