Impact of random fabrication errors on backward-wave small-signal gain in traveling wave tubes with finite space charge electron beams

A one-dimensional small-signal theory for the backward-wave mode in a traveling-wave tube (TWT) is developed, which includes the effects of random fabrication errors. This is of interest since the backward-wave mode is the spatial harmonic typically responsible for instability in a TWT. The described model examines how gain and instantaneous 1-dB bandwidth of the backward-wave mode is affected by random fabrication errors, which are modeled as random perturbations of the phase velocity, interaction impedance, and loss along the TWT's length. Random variation of the phase velocity is found to have the largest effect on both the backward-wave gain and the bandwidth while having only a minor effect on fundamental, forward-wave mode behavior.