Nonlinear theory considering harmonic interaction using Eulerian hydrodynamic analysis
Authors: Qiu Hai-Jian  , Hu Yu-Lu  , Hu Quan  , Zhu Xiao-Fang  , Li Bin  ,   National Key Laboratory of Science and Technology on Vacuum Electronics, University of Electronic Science and Technology of China, Chengdu 610054, China
Published: December 2020

Traveling wave tube amplifiers are one of the most widely used vacuum electronic devices which are employed in various applications, in the areas of such as radar, wireless communication and electronic countermeasures system. Among traveling wave tubes, space-borne helix traveling wave tubes which are of high power, high efficiency, high reliability, long life and radiation hardened, are extensively used in satellite transmitter, data communication system and global positioning system. With the rapid development of the multiphase digital modulation schemes, communication systems are placing greater demands on the output power, electronic efficiency and nonlinear distortion characteristics of space-borne helix traveling wave tubes. However, the nonlinear beam-wave interaction will lead to the generation of harmonics, and thus reduces the output power and electronic efficiency. The harmonics can also act to create beats with the fundamental wave, and thus generate these beat frequencies which are commonly known as intermodulation products. As a result, the bit-error-rate will be increased and the system performance will be compromised. Therefore, the generation of harmonics is of significant current interest in space-borne helix traveling wave tubes. Understanding this effect provides a strong motivation for nonlinear analysis of a helix traveling wave tube. In this paper, a continuous electron phase distribution is obtained by treating the discrete electron beam as a charge fluid based on the Lagrangian theory. Then, to obtain a nonlinear Eulerian theory considering harmonic interaction, the electron phases in Lagrangian theory have been expanded into a series of harmonic components. Considering the 0th component and 1st component of the electron phases only and integrating over the initial phase distribution with the help of the relation of Bessel function, the nonlinear Eulerian theory considering harmonic interaction is established. The nonlinear Eulerian theory considering harmonic interaction is compared to a Lagrangian theory on a set of traveling wave tube parameters which are based on a single section of L-and C-bands traveling wave tubes. It is found that the nonlinear Eulerian theory considering harmonic interaction agrees accords well with the Lagrangian theory before the saturation effect occurs. But, it begins to make a difference near saturation point where the electron overtaking happens. The maximum error in gain between the nonlinear Eulerian theory considering harmonic interaction and the Lagrangian theory is less than 4% at 1 dB gain compression point. So the present nonlinear Eulerian theory considering harmonic interaction can effectively describe harmonic generation at 1 dB gain compression point. The simulation results validate the correctness and effectiveness of our nonlinear Eulerian theory considering harmonic interaction. In futuristic future efforts, it is hoped that the present nonlinear Eulerian theory considering harmonic interaction may provide insights into the behavioral mechanisms of nonlinear effects in space-borne helix traveling wave tubes.