Bifurcations in elliptical, asymmetric non-neutral plasmas

A pure electron plasma held in a Malmberg-Penning trap deforms into an ellipse when subjected to a stationary, l = 2 voltage perturbation on the trap wall. At first, the plasma's ellipticity is proportional to the strength of the perturbation, but once the perturbation increases beyond a critical value, the plasma equilibrium bifurcates into two stable off-axis equilibria and an unstable saddle. At the bifurcation point, the l = 1 diocotron frequency dips to near zero. The diocotron orbits become very elliptical just below the bifurcation, and, after the bifurcation, split into three classes delimited by a separatrix: two classes surrounding the individual new equilibria, and one class surrounding both equilibria. The mode frequencies slow near the separatrix, and the trajectories themselves slow near the saddle at the origin. Interaction with the elliptical mode causes the diocotron mode to spontaneously and revcrsibly jump across the separatrix.