Behavior of Traveling-Wave Tubes Near Circuit Cutoff

A theory is developed which explains the operation of a traveling wave tube when operated near the cutoff frequency of the slow wave circuit, including the effect of two circuit waves instead of the usual one. The theory is normalized in a manner analogous to that used in more conventional analyses, making a relatively small number of curves applicable to a large number of cases. The relationship between this theory and the three-wave theory usually used in traveling-wave tube analysis is shown, and they are in agreement when the system is operated far from the cutoff frequency. Numerical results are given for a range of parameters which might be useful in traveling wave tube design, and an excellent agreement with published experimental results is shown.