Cone focusing of intense relativistic electron beams

An analytic theory, embodying an axially-dependent breakdown model, is presented to explain the focusing experienced by an intense relativistic electron beam upon its injection into a gently-tapered, metallic guide tube (cone) filled with a neutral gas. The mechanism of cone focusing is thereby believed to be identified for the first time. The theory predicts the relative efficiency, relative fluence gain, energy loss along the cone, pressure variation, and cutoffs, with full dependence on the beam, cone, and neutral gas parameters. The theory is in good agreement with experiment. It is emphasized that the axially-dependent nature of the breakdown must be considered to explain the focusing; in addition, it is shown why image charges, image currents, or specular reflections can not explain the focusing.