On the limiting steady configurations of a model plasma

A model equation describing the configuration of a simple plasma maintained by external radiation is studied. A branch of steady solutions of the equation was found by W. Eckhaus et al. to terminate at a finite critical value of the power of the external source, and this is attributed to the discontinuous nature of a nonlinear term in the governing equation. On introducing a small parameter to render the term continuous, a second branch of solutions is constructed in a neighborhood of the termination point of the original branch. This suggests that the termination point is formed as the limit of a subcritical fold in the surface of the steady solution branch.