MAGNETIC RECONNECTION AT STRESSED X-TYPE NEUTRAL POINTS

The reconnection and relaxation of two-dimensional stressed (nonpotential) X-type neutral point magnetic fields are studied via solution of the nonlinear resistive two-dimensional MHD equations and by analytical solution of the linear eigenvalue problem. Previous linear studies (Craig & McClymont 1991; Hassam 1992; Craig & Watson 1992), have shown that such stressed fields may relax on a time substantially shorter (i.e., approximately \log eta\2, where eta is the resistivity) than the usual time scale for linear reconnection (i.e., eta3/5). We have generalized the linear dispersion relation 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. All of the results presented are for frozen-in (line-tied) boundary conditions at some distance from the X-point, and we emphasize that these boundary conditions are essential in order to obtain our solutions. We find that for nearly azimuthally symmetric magnetic perturbations 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 Liapunov functional for the nonlinear incompressible two-dimensional resistive MHD equations is derived to show that the current-free X-point configuration is a global equilibrium to which general initial conditions relax.