Analytic solutions of the magnetic annihilation and reconnection problems. II. Three-dimensional flows

Abstract

Analytic solutions for magnetic annihilation and reconnection in three-dimensional velocity fields are constructed. Exact and approximate solutions for three-dimensional fan current reconnection can be derived using prototype fields based on simple, one-component magnetic annihilation models. Certain reconnection solutions are found to be “fast,” in the sense that the Ohmic dissipation rate scales independently of any positive power of the plasma resistivity η. Three-dimensional models can also possess novel features not contained in two-dimensional planar reconnection solutions. In particular, classes of solutions involving separated field nulls are found to possess multiple scalings for the Ohmic dissipation rate—a feature that has not been observed before. Several solutions are shown to have the potential to meet the extreme energy release characteristics of the solar flare.