Theory of Multimode Resonant Backward-Wave Oscillator With an Inclined Electron Beam

A multimode theory of the resonant backward-wave oscillator (BWO) with an electron beam inclined with respect to the surface of a periodic structure-a clinotron-is presented. It is shown that mode interaction provides phase velocity variation in the interaction space. The beam-wave interaction power increases at a favorable phase velocity profile along the interaction space, which manifests as power peaks in the clinotron zone. In contrast, when it is nonfavorable, there is power drop in the bandwidth. Developed multimode theory results are in satisfactory agreement with the theory of a BWO with reflections and with particle-in-cell simulations.