On the equilibrium of a cylindrical plasma supported horizontally by magnetic fields in uniform gravity

Abstract

We consider the mechanical equilibrium of a cylinder of plasma suspended horizontally by magnetic fields in uniform gravity. This configuration is what may be expected if a quiescent prominence were to condense in a region initially filled with a uniform magnetic field. A set of exact solutions describing the equilibrium situation is presented. Although the plasma distribution is assumed to be cylindrically symmetric to obtain tractibility of the problem, exact force balance between plasma pressure, the Lorentz force and gravity is achieved everywhere in space. The set of solutions covers a particular case of a uniform temperature as well as cases where the temperature rises from zero at the center of the plasma cylinder to rapidly reach a constant asymptotic value outside the cylinder. The physical properties of these solutions are described. A suggestion is made for future development, based on the present work, to construct a prominence model in which the requirements of both mechanical and radiative equilibrium are satisfied.