A two-wave theory of traveling-wave tubes and backward-wave oscillations

Starting from Pierce's small-signal traveling-wave tube (TWT) equations, a two-wave theory for complicated TWTs and backward-wave oscillations (BWOs) is developed. Explicit gain expressions for TWTs with severs and velocity tapers are given. A detailed treatment is given of a backward-wave amplification structure with a single-step velocity taper in the center. The BWO start oscillation current is calculated as a function of the taper strength. The efficiency of a step velocity taper as a remedy for backward-wave oscillations in the higher passbands of a TWT is then analyzed. It is shown that a suitable taper can increase the start oscillation current by more than a factor of 10 without adverse effects on the TWT performance if the backward wave coupling impedance is low. A tube with a weak linear taper is analyzed by a perturbation technique and it is found that there is no significant difference between the start oscillation currents for tubes with weak linear or abrupt tapers of comparable strengths.