Influence of velocity spread on gain and efficiency of klystrons

This paper presents the calculation of the effect of velocity spread in electron streams on the gain and efficiency in klystrons. Using the density-function method and assuming a half-Maxwellian velocity distribution, a small-signal theory of a klystron tube was developed. The form of the solution is a power series whose coefficients contain even powers of ω q/ω. The effect of losses in the cavity has also been included. The results are presented as plots of the ratios of the ac component of the bunched current with velocity spread vs a dimensionless parameter that is a measure of the velocity spread. The plots contain ωq/ω, the lengths of the drift tube and of the gaps as important design parameters.