Necessary and Sufficient Condition for Hydromagnetic Stability of the Bennett Pinch. II. Finite-Radius Pinch

Abstract

The hydromagnetic energy principle is applied to the derivation of the necessary and sufficient condition for the stability of the linear Bennett pinch. Two models of the finite-radius pinch are considered. In the first model, the radius of the plasma column is assumed to be equal to the radius of a conducive wall. In another model, the radius of the plasma column is assumed to be smaller than the radius of the wall. Though long-wavelength kink disturbances are stabilized by the conductive wall, the stability conditions of both models for all kink disturbances change only slightly from the stability condition of an infinite-radius pinch. Sausage disturbances are stabilized more effectively by the wall. It is shown that the conductive wall has little effect on the stability of the pinch in the Tokamak device if it can be represented by the Bennett pinch.