Space-Charge Wave Harmonics and Noise Propagation in Rotating Electron Beams

Interest in the ac behavior of cylindrical electron beams issuing from magnetically shielded or partly shielded guns has been stimulated in recent years by their increasing application in medium- and high-power traveling-wave tubes. As yet, however, such beams have received considerably less attention in the literature than have those in confined flow. The properties of the fundamental (axial-symmetric) space-charge mode in the former type of beam have been studied by liigrod and Lewis, and by Brewer." Waves of this type provide a first-order description of the beam interaction with its environment, such as a drift tube or helix. The present paper will supplement this work by considering higher-order modes of wave propagation in such beams, in which the fields have azimuthal, but not radial, periodicity. Following an analysis of the waves themselves, several problems will be discussed in which they play important roles: the excitation in a helix of spatialharmonic modes, the propagation of noise excitation and possible new 1