Insights from one-dimensional linearized Pierce theory about wideband traveling-wave tubes with high space charge

One-dimensional (1-D) linearized Pierce theory is examined for high space charge wideband traveling-wave tubes (TWTs). The more exact quartic equation is shown to provide reasonable predictions for the frequency-dependent small signal gain function, provided one has an accurate knowledge of the cold circuit phase velocity and space-charge reduction factor. Accurate knowledge of these parameters is particularly critical for predicting the high-frequency end of the positive gain region. The common simplified cubic equation is shown to underestimate the gain. On the other hand, quantitative comparisons show that the cubic solution remains acceptably accurate for first-trial design procedures where it offers advantages of scaling insights and incorporation into closed-form "optimized design" expressions. Guidelines are provided for approximating the growing wave's wavenumber in calculating the space-charge reduction factor. These guidelines are needed for all 1-D TWT models and simulations. Calculations illustrate that positive gain always involves the beam velocity exceeding the "hot" phase velocity of the wave.