Pinch Instability

Abstract

A simple and thoroughly investigated hydromagnetic instability is the instability discovered in the course of studying a plasma column (pinch) compressed by the magnetic field produced by current flowing through the column itself. The pinch instability is essentially the same as the instability of any flexible conductor along which current flows. There is a circular magnetic field around the straight conductor; the strength of this field is inversely proportional to the radial distance from the axis. The field lines are everywhere convex outward and their center of curvature lies on the axis, i.e., inside the plasma. Therefore, it follows from the energy principle that if there is no magnetic field inside the plasma (completely diamagnetic) the pinch must be unstable with respect to convective motion. It is possible to give a clear picture of the instability.