ABSTRACT
In this and the following chapters we discuss methods for determining the stability and subsequent evolution of configurations that deviate from the equilibrium solutions discussed in Chapters 4, 5, and 6. We begin in this chapter by discussing the theoretical basis for linear methods which are suitable for computing the stability of small deviations from equilibrium using the ideal MHD description of the plasma given in Section 1.2.3. It is shown that a variational form is especially convenient for this. We then discuss special theoretical techniques that have been developed for cylindrical and toroidal geometry to enable efficient computation. In the following chapters we present different computational techniques for solving the equations presented here in both the linear and the non-linear regimes, and for extending the solutions to include non-ideal effects.
