Numerical Integration of the MHD Equations near a Magnetic Null Line

Abstract

The MHD equations are integrated numerically for a homogeneous plasma initially at rest near a null line in a hyperbolic magnetic field. The finite plasma conductivity is taken into account. A solution of the linearized equations far from the null line — a cylindrical potential-perturbation wave converging on the null line - is adopted as a boundary condition. This perturbation arises when a constant external electric field is applied parallel to the null line. As the null line is approached, the wave becomes nonlinear and leads to the appearance of a thin current sheet. There is no evidence of any kind for the system of slow-mode shockwaves corresponding to the Petschek model. Within the current sheet the plasma density increases, while the density just outside the sheet decreases. The plasma flows along the sheet at approximately the Alfvén velocity. A return current flows at the edges of the sheet.