Resistive instabilities in a diffuse linear pinch

Abstract

The effects of small electrical resistivity, viscosity, and thermal conductivity on hydromagnetic instabilities for diffuse linear pinch configurations are considered. For finite-pressure systems, higher order equations must be solved than in previous work that was applicable to stellarator or slab geometries. A careful treatment of the problem of matching the perturbed solution across the boundaries that separate a resistive layer from outer hydromagnetic regions clarifies the relationship between resistive instabilities and the ordinary hydromagnetic instabilities that are obtained from the ideal equations. In a similar way consideration of various limiting cases brings out the connection between the different resistive modes. The manner in which thermal conductivity and viscosity assert themselves is exhibited, and for a special configuration it is shown explicitly how viscosity can exert a small stabilizing effect. Aside from this, instabilities are found whenever the pressure decrease is outward.