IRREVERSIBLE-PROCESSES IN A MAGNETOPLASMA

Magnetically confined plasmas exhibit some interesting instabilities t hat have somewhat bedeviled the long quest for fusion power in tokamak machines. The magnetic fields employed are strong in the sense that t he parameter omegaBAR = omega(c)tau, where omega(c) is the cyclotron f requency and tau is the collision interval, is a very large number. Th e purpose of the paper is to relate these instabilities to sigma, the entropy production rate per unit volume. In a neutral gas sigma is non -negative, which result can be obtained as a local form of Boltzmann's H-theorem. With sigma expanded in the Knudsen number (epsilon) power series, sigma = sigma1 + sigma2 + ..., where sigma1 is the familiar, n on-negative quadratic form, the second-order term sigma2 = O(epsilon2) , may have either sign. In the usual case, for epsilon smal enough, si gma1 >> \sigma2\ and the inequality sigma greater-than-or-equal-to 0 f ollows. However in a magnetoplasma, we shall show that sigma1 = O(omeg aBAR-2), whereas sigma2 = O(omegaBAR-1). This means that in tokamaks s igma2 (which may have either sign) dominates sigma1. It is therefore p ossible that in some circumstances sigma is negative and the outcome i s an unstable fluctuation. Another way of expressing this result, is t hat the heat flows up the temperature gradient, albeit only for a shor t time. In the course of establishing this surprising result, we shall give a method of calculating sigma2 that is independent of the form o f Boltzmann's collision integral. Our conclusions are supported by ref erence to tokamak experiments.