Introduction

In the remainder of the book, it is assumed that an MHD equilibrium has been calculated, either analytically or numerically. The next basic question to ask is whether or not the equilibrium is MHD stable. Qualitatively, the question of stability can be stated as follows. The existence of an MHD equilibrium implies a plasma state in which the sum of all forces acting on the plasma is zero. Assume now that the plasma is perturbed from this state producing a set of corresponding perturbed forces. If the direction of these forces is such as to restore the plasma to its original equilibrium position then the plasma is stable. If, on the other hand, the direction of the forces tends to enhance the initial perturbation then the plasma is unstable.

The question of ideal MHD stability is a crucial one, since plasmas, in general, suffer serious degradation in performance, ranging from enhanced transport to catastrophic termination, as a consequence of such instabilities. Not surprisingly, there is consensus in the international fusion community that a plasma must be MHD stable to be viable in a fusion reactor. Indeed, it is fair to say that MHD stability considerations are a primary driver in the design of virtually all the magnetic geometries that have been proposed as fusion reactors.