Analytic Exploration of the Accuracy of Pierce’s Three-Wave Beam-Wave Interaction Theory of Traveling-Wave Tubes

As it is well known that the simplified classical Pierce's three-wave theory can provide scaling insights into traveling-wave tube (TWT) operation for its close-form solutions, and thus becomes a useful guide for TWT design. However, the classical Pierce's three-wave theory shows poor agreement with Lagrangian theory, so determining how to achieve a more accurately Pierce's three-wave theory from Pierce's four-wave theory becomes an open problem. In this paper, a more accurately revised Pierce's three-wave dispersion relation is deduced by using an approximate treatment on the nonlinear term of the dispersion relation of Pierce's four-wave beam-wave interaction theory. Meanwhile, the boundary conditions of classical Pierce's three-wave theory are revised by theoretical analysis. Thus, the revised Pierce's three-wave theory is established. The Pierce small-signal theories are compared to each other and Lagrangian theory on a set of TWT parameters which are based on a single pitch section of C- and Ku- bands TWTs. It is found that the revised Pierce's three-wave theory agrees extremely well with Lagrangian theory and gains more accuracy than the classical Pierce's three-wave theory in the small-signal beam-wave interaction region. Finally, the phase difference between Pierce's four-wave theory and revised Pierce's three-wave theory is discussed.