The variation of shot-effect noise in an accelerated electron stream with a 'semi-Maxwell' distribution of velocities

Difficulties regarding the statistical description of the disturbed state of an accelerated (retarded) electron stream on the basis of a system of Vlasov equations have been overcome with the aid of numerical methods. The effect of the thermal motion of the electrons on the process of the variation of noise disturbances in electron beams is important from an application-oriented point of view and for an appraisal of the limits inherent in a theory based on considerations of one velocity. Shtyrov (1974) has solved analytically the problem of regular disturbances in the drift electron flow with a 'semi-Maxwell' velocity distribution. Shtyrov's analysis is based on the method of the 'characteristic function' which had been proposed by one of the authors of the present investigation. In the present investigation, the same method is employed for an analysis of the variations of shot-effect noise in a multivelocity flow. An accelerating potential with a linear relationship regarding the longitudinal coordinate is considered.