Exact solutions for reconnective annihilation in magnetic configurations with three sources

Exact solutions of the steady resistive three dimensional (3D) magnetohydrodynamics (MHD) equations in cylindrical coordinates for an incompressible plasma are presented. The solutions are translationally invariant along one direction and in general they describe a process of reconnective annihilation in a curved current layer with non vanishing magnetic field. In the derivation of the solutions the ideal case with vanishing resistivity and electric field is considered first and then generalized to include the effects of finite electric field and resistivity. Particular attention is devoted to the analysis how the latter ones influence the presence of singularities in the solutions. In this respect comparisons with the purely two-dimensional case are made and the resulting important differences are highlighted. Finally, applications of the solutions for modeling an important class of solar flares are discussed.