Magnetic Energy Release in Dynamic Fan Reconnection Models

The problem of dynamic, three-dimensional magnetic reconnection is considered. Analytic “fan current” solutions are derived by superposing plane-wave disturbances on magnetic X-point equilibria. The localization of the wave produces a strong current sheet containing the neutral point. It is shown that the classical rate of resistive dissipation in the sheet, namely Wn~n1/2, represents the slowest possible energy-loss rate for the disturbance. The conditions required for fast coronal reconnection are then discussed. It is pointed out that significant “flare-like” energy release may be possible under physically realizable conditions. Moreover, the small length scales associated with the current sheet widths of order ∆x~n1/2 suggest that conditions are probably collisionless close to the neutral point. It is argued that our results are consistent with magnetic reconnection simulations that display “stalling” of the merging rate at small plasma resistivities