Magnetic reconnection at stressed x-type neutral points

Abstract

The reconnection and relaxation of two-dimensional stressed (non-potential) x-type neutral point magnetic fields are studied via solution of the nonlinear resistive 2-D MHD equations and by analytical solution of the linear eigenvalue problem. The linear dispersion relation was generalized for azimuthally nonsymmetric perturbations, and have found that for modes with azimuthal mode numbers m > 0, the relaxation can occur at a rate faster than that for n = m = 0, where n is the radial ``quantum`` number. One finds that for nearly azimuthally symmetric magnetic perturbations that are zero at the boundary; i.e. the ``frozen-in`` (sometimes called ``fine-tied``) boundary conditions, the fields relax incompressibly and nonlinearly to the unstressed x-type neutral point at a rate close to that predicted by linear theory. Also, fully compressible nonlinear MHD simulations have been performed, which show that the interaction between the plasma flow velocity and the magnetic field is the important physical effect, while the inclusion of thermodynamics does not affect the evolution considerably. A Lyapunov functional for the nonlinear incompressible 2-D resistive MHD equations is derived to show that the current-free x-point configuration is a global equilibrium to which general initial conditions relax.