STABILITY THEOREM FOR A SINGLE-SPECIES PLASMA IN A TOROIDAL MAGNETIC-CONFIGURATION

A stability theorem is developed for a single species plasma that is c onfined by a purely toroidal magnetic field. A toroidal conductor is a ssumed to bound the confinement region, and frequencies are ordered so that the cyclotron action and the toroidal action for each particle a re good adiabatic invariants. The cross-field motion is described by t oroidal-average drift dynamics. In this situation, it is possible to f ind plasma equilibria for which the energy is a maximum, as compared t o all neighboring states that are accessible under general constraints on the dynamics. Since the energy is conserved, such states must be s table to small-amplitude perturbations. This theorem is developed form ally using Arnold's method, and examples of stable equilibria are obta ined.