Effects of random circuit fabrication errors on small signal gain in a traveling wave tube

Summary form only given. Random fabrication errors due to fabrication tolerances in the manufacture of slow wave circuits may have detrimental effects on the performance of traveling-wave tubes (TWTs) of all types. Such errors will pose an increasingly serious problem as TWTs are designed and built to operate in the sub-millimeter wavelength regime and beyond. In this paper we present analytical and numerical results on the expected degradation of the small signal gain of a TWT when small random, axially varying perturbations are present in the circuit phase velocity. A new scaling law for the reduction in the ensemble-average gain is derived from the third order ordinary differential equation with randomly varying coefficients that governs the beam-wave interaction in a TWT in the presence of small errors. Analytical results for the average gain reduction compare favorably over a broad range of Pierce parameter values with results from numerical integrations of the differential equation. The effects of random errors on the output phase will also be discussed in our presentation.