Exact solutions for steady-state, planar, magnetic reconnection in an incompressible viscous plasma

The exact planar reconnection analysis of Craig and Henton [Astrophys. J. 450, 280 (1995)] is extended to include the finite viscosity of the fluid and the presence of nonplanar components in the magnetic and velocity fields. It is shown that fast reconnection can be achieved for sufficiently small values of the kinematic viscosity. In particular, the dissipation rate is sustained by the strong amplification of planar magnetic field components advected toward the neutral point. By contrast, nonplanar field components are advected without amplification and so dissipate energy at the slow Sweet–Parker rate

Dynamic magnetic reconnection in three space dimensions: Fan current solutions

The problem of incompressible, nonlinear magnetic reconnection in three-dimensional "open" geometries is considered. An analytic treatment shows that dynamic "fan current" reconnection may be driven by superposing long wavelength, finite amplitude, plane wave disturbances onto three-dimensional magnetic X-points. The nonlinear reconnection of the field is preceded by an advection phase in which magnetic shear waves drive large currents as they localize in the vicinity of the magnetic null. Analytic arguments, reinforced by detailed simulations, show that the ohmic dissipation rate can be independent of the plasma resistivity if the merging is suitably driven