Magnetic reconnection and current-sheet formation at x-type neutral points

Numerical solutions of the nonlinear, resistive magnetohydrodynamic (MHD) equations are used to study the evolution of a perturbed or stressed x-type neutral point. By performing individual simulations for both compressible and incompressible plasmas, we are able to demonstrate that the important physics for this problem involves just the interaction between the plasma flow velocity and the magnetic field and that the thermodynamics has a relatively passive effect. We have also done separate simulations for both solid, conducting wall boundary conditions at a fixed distance from the x-point and for open boundary conditions that adjust as required by the evolving solution within the boundaries. With solid, conducting wall boundary conditions, our solutions for azimuthally symmetric disturbances agree with those obtained in previous analytic linear studies. In this case the stressed x-point relaxes back to the unstressed state on a time scale somewhat shorter than the time scale for the linear resistive tearing mode. Perturbations that are not azimuthally symmetric can relax even faster than the symmetric modes. When the conditions at the boundary are free to adjust, the disturbances grow in amplitude on an Alfven time scale with the eventual formation of a current sheet separating two y-points. This rapid growing behavior is, of course, in sharp contrast to the relatively slow decaying solutions obtained with closed boundaries. The growing solutions qualitatively agree with previous analytic x-point solutions that have been suggested as an explanation for the rapid energy conversion in flares and substorms