A large signal theory of traveling wave amplifiers including the effects of space charge and finite coupling between the beam and the circuit

The non-linear behavior of the traveling-wave amplifier is calculated in this paper by numerically integrating the motion of the electrons in the presence of the circuit and the space charge fields. The calculation extends the earlier work by Nordsieck and the small-C theory by Tien, Walker and Wolontis, to include the space charge repulsion between the electrons and the effect of a finite coupling between the circuit and the electron beam. It however differs from Poulter's and Rowe's works in the methods of calculating the space charge and the effect of the backward wave. The numerical work was done using 701-type I.B.M. equipment. Results of calculation covering QC from 0.1 to 0.4, b from 0.46 to 2.56 and k from 1.25 to 2.50, indicate that the saturation efficiency varies between 23 per cent and 37 per cent for C equal to 0.1 and between 33 per cent and 40 per cent for C equal to 0.15. The voltage and the phase of the circuit wave, the velocity spread of the electrons and the fundamental component of the charge-density modulation are either tabulated or presented in curves. A method of calculating the backward wave is provided and its effect fully discussed.