Theory of Relativistic Backward-Wave Oscillators with End Reflections

Microwave sources based on backward-wave oscillators with relativistic electron beams are capable of producing high-power coherent radiation in the centimeter and millimeter-wavelength regimes. Although there have been a number of experiments reported over the last decade on this topic, there are only a few publications providing a theoretical description of these devices. Thus, there is a need for theoretical models which can be compared in detail with the experimental data. This work is devoted to fill this need. The linear and and nonlinear theory of backward-wave oscillators is developed taking into account reflection of the electromagnetic wave at the boundaries of the slow-wave structure. It is found that owing to end reflections the start oscillation current and the efficiency are sensitive functions of the operating parameters. Regions of stable single-frequency operation in these devices are determined numerically. The effects of finite duration and rise time of the electron beam pulse on device operation are discussed.