Classical diffusion of a stationary toroidal plasma

Abstract

The classical resistive diffusion of a stationary toroidal plasma is treated on the basis of the one-fluid magneto-hydrodynamic equations. The Kruskal-Kulsrud conditions for the existence of a stationary solution are generalized to include an external longitudinal electric field. One of these conditions shows that there are unidirectional longitudinal currents connected with the diffusion velocity, even in the absence of an external electric field. A general expression for the mean velocity of diffusion through a magnetic surface is obtained. This expression is applied to different magnetic configurations of the Stellarator and Tokamak type by using an expansion in the neighborhood of a magnetic axis. The validity of a formula given by Pfirsch and Schluter is essentially confirmed.