Resistive convection in a current-carrying cylindrical plasma: An exact model

Abstract

In a previous paper [J. Plasma Phys. 34, 299 (1985)] it was shown that resistivity and thermal conductivity lead to large scale stationary convection in a current-carrying cylindrical plasma under the action of a shearless magnetic field. It was shown there that convection takes place when (η/κ) = 8π/3, where η is the resistivity and κ the thermal conductivity. Convection occurs when either (Bθ/B z) ≫ 1 or when (Bθ/Bz) ≪ 1. In both cases the condition for convection, i.e., R > Rcrit, where R is the Rayleigh number, was shown to be the same. From this fact it was then conjectured that convection takes place for any Bθ/B 2. By solving the model in a closed form, it is shown that the conjecture is correct for large azimuthal wavenumbers, but, otherwise, convection takes place only in the limits mentioned above. © 1989 American Institute of Physics.