Small-signal theory of wave propagation in a uniform electron beam

The object of the paper is to present a detailed study of the fundamental properties of electron beams as waveguides for TM-waves. Electron beams are presented as active systems in contrast with the conventional waveguide, which is a passive system. Three simple systems are analysed and compared: (a) a planar uniform beam between conducting sheets, (b) a planar uniform beam in free space, (c) a planar uniform beam between reactive-impedance sheets. In (a) it is shown in detail how the spectra of the space-charge waves and the field waves discussed by Ramo4 are coupled so that for each mode number there are always four waves. In (b) the complete spectrum for the beam alone is given, from which it is evident that for every frequency and mode number there can be two forward and two reverse waves. In (c) it is shown how the spectral characteristics of the different waves change as the phase velocity of the lowest TM-wave in the empty guide is varied.