Effects of Random Circuit Fabrication Errors on the Mean and Standard Deviation of Small Signal Gain and Phase of a Traveling Wave Tube

Random fabrication errors may have detrimental effects on the performance of traveling wave tubes (TWTs) of all types, especially in the sub-millimeter wavelength regime and beyond. Previous studies calculated the standard deviation of the small signal gain and the output phase of a TWT in the presence of small random, axially varying perturbations in the circuit phase velocity, assuming synchronous interaction and zero AC space charge effects. This paper relaxes the latter assumptions. In addition, we calculate the ensemble-average gain and the ensemble-average phase that result from random axial variations in the circuit phase velocity, using two analytic approaches. One is a perturbative approach including all three modes of the coupled beam-circuit equations. The other treats the evolution of only the dominant (exponentially growing) mode. The analytical results on the expected gain and phase compare favorably with results from numerical integrations of the governing equation in the absence of space charge, but are found to deviate from the numerical integrations with the inclusion of space charge effects. The effects of small pitch errors in a 210 GHz folded waveguide TWT are evaluated in an example.