A nonlinear time-domain analysis of the orotron is presented. The e.m. field in the
cavity is expanded into the Hermite-Gaussian modes with time-dependent amplitudes,
for which a set of ordinary differential equations is obtained from Maxwell's
equations. The equations for the amplitudes are coupled to the equations of motion for
the electrons. The calculations yield transient and steady state behaviour, saturated
efficiency and output power of the device.
S. Lütgert, S. Lütgert,
"Self-consistent nonlinear analysis of the orotron", Proc. SPIE 1514, 15th International Conference on Infrared and Millimeter Waves, 15141G (1 December 1990); doi: 10.1117/12.2301462; https://doi.org/10.1117/12.2301462