Fluctuations in the oscillations of a magnetron type backward-wave oscillator

An attempt is made at developing a simple approximation procedure for calculating the spectral density of amplitude and phase fluctuations in the oscillations of a magnetron type backward-wave oscillator (M-BWO) due to low-frequency fluctuations in the electron beam current. The initial equations used are those expressing the equivalent line length, continuity, and motion. The amplitude and phase noise power, and rms fluctuations in frequency due to random variations in electron beam current, in particular shot effect, are determined. All calculations were carried out within the framework of the adiabatic approximation based on the thin beam model, for sake of simplification.