Hydromagnetic-Instability Growth Rates of a Plasma Column —Application of Ritz-Galerkin Method—

Abstract

A procedure is developed for evaluating the hydromagnetic-instability growth rates of a fixed boundary plasma. The procedure is based on the energy principle. Three components of a plasma displacement are treated as independent variables and are expanded in terms of complete systems of functions. The potential-energy change δW and the kinetic energy δK are expressed as quadratic forms of the expansion coefficients. The growth rates are obtained by minimizing δW⁄δK with respect to the expansion coefficients. As an example of application, the growth rates of the Bennett pinch are evaluated for incompressible displacements. Results show that the expansion with only 3 or 4 terms for each variable gives satisfactory values of growth rates.