Nonlinear Analyses of the Parasitic Backward-Wave Oscillation Power in the Magnetically Focused Pulsed Helix Traveling-Wave Tube Amplifier in the Absence of the Amplified Signal

This paper analyzes parasitic backward-wave oscillation power as a function of interaction length and focusing magnetic field parameters in a generic helix traveling-wave tube (TWT) amplifier in the absence of amplified signal. The permanent periodic magnetic (PPM) focusing of the electron beam, the relatively narrowband (less than one octave) TWT, the electron gun with no control grid, the pulsed full beam current cutoff operating mode of the TWT, and the accelerating voltage pulse wider than the amplified RF pulse are considered. Under such conditions, the parasitic backward-wave oscillation can build up at the leading and trailing edge and at the top of the accelerating pulse before and after the input RF signal is applied when the instantaneous accelerating voltage provides for the synchronism condition. The parasitic backward-wave oscillation, although nondesirable in general, can be tolerated if its power does not exceed some allowable level. In this paper, the nonlinear (large-signal) theory of beam-wave interaction in the TWT in the specified case is developed. The theory accounts for the interaction of the multiple harmonics of the backward wave of the slow-wave circuit with the electron beam that alternatively changes the direction of its rotation on each half period of the focusing magnetic field. A system of equations, which makes accessible the start oscillation length and the starting Pierce relative velocity parameter as a function of the electrical parameters of the TWT, the PPM focusing field period, and the magnetic flux density distribution in the large-signal regime, is obtained. A particular numerical example reveals the relation between interaction length, PPM focusing field period, and parasitic backward-wave oscillation power. The approach permits one to design a TWT having the maximum possible interaction length under the allowable parasitic backward-wave oscillation power. Also, the results demonstrate that the focusing magnetic field param- - eters have a significant effect on the interaction of the rotating electron beam with the backward wave in the nonlinear regime, as they have in the linear regime