Start-oscillation conditions in nonuniform backward-wave oscillators

The effects of nonuniformities in the circuit phase velocity and the beam potential on the start-oscillation conditions of an O-type backward-wave oscillator (BWO) are investigated. The nonuniformities include linear, quadratic, and exponential circuit phase velocity tapers and beam potential gradients. It is shown that for weak circuit phase velocity tapers or voltage gradients the start-oscillation current may be lower than that of a uniform tube; however, when the taper or gradient is made stronger than a particular value which depends on the operating parameters, a no-oscillation region results. The latter result indicates that such nonuniformities may be utilized to suppress backward-wave oscillations in forward-wave amplifiers.