Numerical analysis of magnetohydrodynamic instabilities by the finite element method

A finite-element method has been applied to the analysis of magnetohydrodynamic instabilities in a cylindrical current-carrying plasma embedded in a strong longitudinal magnetic field. To examine the applicability of the finite-element method to the stability analysis, the growth rate of instabilities has been calculated numerically using an electronic computer. It has been shown that the numerical results, for which corresponding analytical results are available, are in good agreement with them. Several examples of the analysis of low-m mode instabilities with various current distributions are demonstrated. It is concluded that the finite-element method is a powerful tool for the study of magnetohydrodynamic instabilities in the cylindrical plasma as well as, possibly, plasmas with more complex geometries.