Two-dimensional small signal analysis of backward-wave oscillation in a helix traveling-wave tube under Brillouin-flow, periodic permanent magnetic focusing

The phenomenon of electron beam rotation in the axial magnetic field of a magnetically focused helix TWT results in more complicated parasitic backward-wave oscillation conditions compared to the case when the beam rotation is not considered. Accounting for this phenomenon allows for further improvement of TWT stability to the parasitic backward-wave oscillation. In this paper, we examine the typical super-broad bandwidth TWT that has an anisotropically-loaded circuit-e.g., a helical structure supported by dielectric rods in a metal shell provided with metal longitudinal vanes projecting radial inward. The 2D small-signal model is developed that takes into account the effects of the beam's rotation and focusing magnetic field parameters under Brillouin flow on backward-wave oscillation conditions in TWT. The theory permits an investigation of the effects of amplitude and axial periodicity of permanent periodic magnetic (PPM) focusing magnetic flux density and of Pierce's relative electron velocity parameter on the start oscillation length. Physical and numerical analyses are presented for a TWT's stability to backward-wave oscillation under permanent magnetic focusing, which is longitudinally periodic and homogeneous across the beam, for the case when the backward-wave consists of two nonazimuthally symmetric harmonics. A particular numerical example reveals the dependence of start oscillation length of a TWT on the PPM focusing parameters as well, as Pierce's relative electron velocity parameter. The theory predicts that by tailoring of the magnetic field period it is possible to increase the start-oscillation length by a factor of 1.25 and the power output by the factor 2.6 compared to the case when the beam rotation is not taken into account. The 2D model developed in this paper provides sufficient data for more correct and precise choice between signal amplification and backward-wave oscillation suppression in the anisotropically-loaded helix TWT than the existing 1D theories.