Further studies of a simple gyrotron model equation

Work with other authors, \textit{J. Phys. A: Math. Theor.}\textbf{ 40}, 2203 (2007), is extended. Analytic and computational methods are applied to examine desirable start-up conditions in a gyrotron and to minimize deleterious bunching effects. Analysis permits extensive, but incomplete exploration of the dynamics, while computation with the simple model provides essential, more complete results. Several of the conclusions of the cited paper are significantly modified.