Dynamic magnetic reconnection at an X-type neutral point

The relaxation of a two-dimensional "X-type" neutral point magnetic field disturbed from equilibrium is considered. Perturbations are shown to possess well-defined azimuthal modes which allow an exact determination of the magnetic annihilation rate. Free magnetic energy is dissipated by oscillatory reconnection which couples resistive diffusion at the neutral point to global advection of the outer field. The decay of azimuthally symmetric (m = 0) modes - the only modes associated with topological reconnection - is limited by the dissipation time scale of the "fundamental" (n = 0) mode with no radial nodes. This mode decays over typically 100 Alfvén times. An analytic treatment shows that the oscillation and decay time scales couple according to τosc ≈ 2 ln S and τdecay ≈ τosc 2/(2π2), where S is the Lundquist number (4π/c2)υA R/η and the times are in units of R/υA, with R the distance from the neutral point to the boundary, υA the Alfvén speed at the boundary, and η the resistivity