Radial boundary layers in diffusing toroidal equilibria

Analytic results in straight cylindrical geometry imply sharp density gradients near the boundary of a plasma decaying by classical diffusion. Utilizing an isothermal one‐fluid magnetohydrodynamic model, these results are applied to toroidal configurations and a set of nonlinear equations for a radial boundary layer are obtained. A dominant effect in this region is convective plasma flow along magnetic lines of force, with velocity in the sonic range. This flow pattern matches onto the interior solution of Pfirsch–Schluter convective flow. Solutions separable in the radial and poloidal directions are found that fulfill both boundary and periodicity conditions, and that result in both smooth subsonic poloidal flow, and weak shock transonic flows. Effects of the flow patterns on diffusion are discussed.