Some properties of rotating coherent structures in a non-neutral plasma column

Coherent structures rotating at the angular velocity ω in a two-dimensional pure electron plasma confined inside a conducting grounded cylinder are considered. These structures are described by a streamfunction ψ, obeying a nonlinear boundary value problem. It is shown, in particular, that (i) this problem has a minimal cylindrically symmetric solution if it has a solution at all. (ii) For a nonsymmetric solution, 2ω is necessarily comprised between the minimum and maximum values taken by the local diocotron frequency in the cylinder. (iii) Bifurcation of a symmetric radially decreasing solution to a nonsymmetric one can occur only when 2ω is equal to the mean diocotron frequency