Self-consistent theory of ring-plane traveling wave tube

Taking the radial thickness and the relativistic effect of the hollow electron, beam into account, the "hot" dispersion relation for the interaction between the electron beam and the symmetrical mode propagating in the ring-plane slow-wave circuit is developed in this paper by the means of the Ritz-Galerkin method. The numerical results are given in terms of the small signal gain and "hot" phase velocity curves. All the influences by the parameters of the geometry and the beam are discussed in detailed. It shows that the thickness of the electron beam influences the beam-wave interaction strongly.