Nonlinear Analytic Solution of Eulerian Beam-Wave Interaction Theory Considering Harmonic Interaction of Traveling-Wave Tube Amplifiers

• Published in: IEEE transactions on microwave theory and techniques Vol. 67; no. 1; pp. 16 - 27
• Main Authors: Qiu, Hai-Jian, Hu, Yu-Lu, Hu, Quan, Zhu, Xiao-Fang, Li, Bin
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.01.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Analytic solution; Analytical models; beam-wave interaction (BWI); C band; Computer simulation; Electric fields; Electron tubes; Eulerian analysis; Exact solutions; Frequency conversion; Frequency modulation; harmonic; Harmonic analysis; Mathematical model; nonlinear; Nonlinear analysis; Numerical models; Traveling wave tubes; traveling-wave tubes (TWTs); Wave interaction
• ISSN: 0018-9480; 1557-9670
• DOI: 10.1109/TMTT.2018.2875120

In this paper, a novel Eulerian nonlinear beam-wave interaction (BWI) theory considering harmonic interaction of a helix traveling-wave tube (TWT) is developed. Derived from this Eulerian model, the novel Eulerian nonlinear analytic solutions (the fourth-order analytic solution of fundamental and the second-order analytic solution of harmonic) are first obtained by the method of successive approximation. The analytic relationships between electric fields of fundamental/harmonic frequencies and electron phases are also found. Then, the Eulerian nonlinear analytic solutions and Eulerian nonlinear BWI theory are compared to a Lagrangian theory. C-band and Ku-band helix TWTs based on a single pitch section are included in the simulation. It is found that the Eulerian nonlinear analytic solutions and Eulerian nonlinear BWI theory agree well with the Lagrangian theory at 1-dB gain compression point. Interestingly, the saturation effects caused by electron overtaking cannot be found by the traditional Eulerian analysis but can be described by the Eulerian nonlinear analytic solutions and Eulerian nonlinear BWI theory. Moreover, Eulerian nonlinear analytic solutions are simpler and more accurately than existing approaches and, thus, allow analytical progress. This paper confirms that the Eulerian nonlinear analytic solutions can outperform the previous proposals.