FIELD-THEORY OF A TRAVELING-WAVE TUBE AMPLIFIER WITH A TAPE HELIX

A self-consistent relativistic field theory of a helix traveling wave tube (TWT) is presented for a configuration in which a magnetized penc il beam propagates through a tape helix enclosed with a loss-free wall . A linear analysis of the interaction is solved subject to the bounda ry conditions imposed by the beam, helix, and wall. The wave equation for the fields within the electron beam corresponds to the Appleton-Ha rtree magnetoionic wave modes that are of mixed electrostatic/electrom agnetic polarization. Hence, the determinantal dispersion equation tha t is obtained implicitly includes beam space-charge effects without re course to a heuristic model of the space-charge field. This dispersion equation includes azimuthal variations and all spatial harmonics of t he tape helix. Solutions are found numerically, which correspond to bo th the extraordinary (X) and ordinary (O) solutions for the Appleton-H artree modes. Note that the O- and X-mode designations are more proper ly applied for waves propagating perpendicular to the ambient magnetic field in a uniform plasma. In the present case, we are interested in the modes propagating parallel to the ambient magnetic field in a boun ded system in which an electron beam is enclosed by a tape helix and a conducting wall. Hence, our use of this nomenclature is merely for co nvenience in designating the specific mode of solution of the dispersi on equation. With this in mind, each solution is found to behave quite differently with variations in the axial magnetic field. For example, maximum gain of the X(O)-mode is found to increase (decrease) with th e axial field up to the point at which the axial field suppresses the transverse electron motion, and to remain relatively constant thereaft er. A detailed numerical example is shown corresponding to an experime nt in progress at the Naval Research Laboratory.