The evolution of disturbed neutral point equilibria

We consider the linear and nonlinear evolution of a perturbed X-type neutral point. A semianalytic treatment is given for the case of small disturbances of the equilibrium field. This problem admits well defined azimuthal modes which allow a formally exact determination of the magnetic annihilation rate. It is shown that the longest lived modes are purely radial and decay of the timescale is approximately equal to the absolute value of ln-eta where eta defines the resistivity of the coronal plasma. Higher azimuthal modes decay much faster, generally on a fraction (O/m) of the Alfven timescale for the outer field. We go on to perform finite amplitude calculations that demonstrate the implosive current build-up that precedes the reconnective phase of the relaxation. In general, both linear and nonlinear studies support the idea of an initial implosive stage which rapidly releases the bulk of the energy associated with arbitrary field disturbances.