A numerical model for nonaxisymmetric MHD instabilities

Abstract A method is described for studying the stability of two-dimensional equilibria of magnetically confined plasmas. The equations of magnetohydrodynamics (MHD) are linearized and the resulting time-dependent first-order system of equations is solved. Unstable equilibria result in exponentially growing solutions. The plasma is assumed to be incompressible and resistivity is included in the model. The equations are solved in cylindrical coordinates and the perturbations vary as f 1 ( r , z , t )exp( inτ ). Nonaxisymmetric modes ( n ≠0) are considered. Tearing mode results for one-dimensional analytic equilibria are compared with earlier work. A numerically generated equilibrium, modeling the field reversed theta pinch experiment, is shown to be unstable to the n =1 tilting mode.