Mode coupling of Trivelpiece-Gould (TG) and diocotron modes in a nonneutral plasma column

When an l = 2 diocotron mode is launched to amplitude A, a single l = 0 TG mode is observed to branch out into three waves: an upper and lower frequency TG wave, and a weaker central TG wave, whose frequencies all approach one-another as A decreases with time (due to weak diocotron mode damping). The frequency splitting of the TG waves is proportional to A at larger A values. For infinite magnetic field B this splitting is analogous to the behavior of the eigenmodes of an elliptical drumhead. At finite B it may be analyzed using four-wave mode-coupling theory with the diocotron mode acting as a low-frequency pump wave, and the upper and lower TG waves acting as daughter waves that are admixtures of nearly degenerate l = ±2 and l = 0 TG waves, mode-coupled by the pump. The central TG wave is a third more weakly-coupled daughter wave with θ symmetry that differs from the other branches; hence the weaker coupling. The mode-coupling theory of this effect compares well with the experiments.