On Johnson's backward wave oscillation thresholds in TWT

This work extends Johnson's classical theory [H. R. Johnson, Proc. IRE 43, 684 (1955)] for the threshold of backward wave oscillation (BWO) in a traveling-wave tube (TWT) by including (1) random variations of circuit phase velocity along the tube axis and (2) finite reflections at the two ends of the circuit. We find that the BWO threshold is minimally affected by random variations in circuit phase velocity. We find that the threshold depends on the magnitude and phase of the composite end reflection coefficients. An attempt is made to compare with an experimental helix test TWT.