Simple theory of a nonlinear ciiocotron mode

A simple perturbation theory of the frequencies and density distortions of the I= 1 diocotron mode on pure electron plasma columns is presented. This mode is the dynamical state of an off-axis electron column which is orbiting around the containment axis at the ExB drift velocity. The theory predicts shifts in the orbit frequency and quadrupole distortions of the plasma surface, both varying as the offset squared, in good agreement with experiments. The results also apply to a two-dimensional vortex patch in an inviscid fluid with circular boundaries.