Wave Propagation Along a Magnetically-Focused Cylindrical Electron Beam

This paper analyses the nature of wave propagation along a cylindrical electron beam, focused in Brillouin flow by means of a finite axial magnetic field. Two different types of conducting boundaries external to the beam are treated: (1) the concentric cylindrical tube, forming a drift region; and (2) the sheath helix, forming a model of the helix traveling-wave tube. The field solution of the helix problem is used to evaluate the normal-mode parameters of an equivalent circuit seen by a thin beam, thereby permitting computation of the gain constant of growing waves. The gain constant of the cylindrical beam with Brillouin flow is found to exceed that of a similar beam with rectilinear flow, presumably because of the transverse component of electron motion in the former