A sufficient condition for the lack of cellular convection in a dissipative plasma column

A one-dimensional boundary-value problem of dissipative plasma equilibrium in a cylinder is formulated and analytically solved. As regards the data, axial symmetry and uniformity along the axis of the cylinder are assumed; as regards the solution(s), a given periodicity along the axis of the cylinder is imposed. Viscous stresses and resistance are the dissipation processes taken into account, while a particle source and an externally driven electric field sustain the pressure gradient in the plasma. Plasma density, coefficients of viscosity and resistivity are given smooth functions of the radius. After analytically solving the boundary-value problem, a functional setting of the equations is established and a problem for weak solutions is formulated. The main achievement of the analysis is a rigorous uniqueness and nonlinear stability result for the analytical solution found; since such a solution describes a merely radial flow of the plasma across nested magnetic surfaces, what is derived is a sufficient condition for the lack of cellular convection. Finally, the significance of the physical model introduced in this paper, and herein theoretically analysed, is pointed out in view of possible computational work which might yield valuable insight. (orig.)