The influence of electron velocity spread on parameters of microwave vacuum microelectronics devices

A one-dimensional linear theory of the interaction between an electron beam and an electro-magnetic wave in a delay line, where the effect of the velocity distribution of the electron beam is taken care of, is considered. Vlasov's kinetic equation is used for analysis of the velocity distribution effect on the start oscillation regime of a low-voltage backward-wave oscillator (BWO). Equations obtained are applicable practically for any velocity distribution function. Some typical results for a Maxwellian kind of distribution are presented.