Second-Order Nonlinear Eulerian Analysis of a Travelling-Wave Tube Amplifier

Abstract

A solution of the nonlinear Eulerian fluid-dynamical equation of a helix traveling-wave tube was developed by the method of successive approximation. The nonlinearity was restricted to the second order that could account for the second harmonic generation in the device and could estimate the sensitivity of the second harmonic to the beam and circuit parameters. The second harmonic RF output power relative to the fundamental was found to be controlled by the beam voltage and current; was less for a negative than for a positive dispersion helical slow-wave structure of the device; and could be minimized by optimizing the distributed loss put along the structure. Unlike the Lagrangian approach, the present Eulerian approach gives a closed-form solution, avoiding a large-scale numerical integration of the problem. Hence the present approach is less encumbered and takes less computertime than the Lagrangian approach. Also, the present analysis, though it is exemplified in this paper with particular reference to the second-order nonlinearity for second harmonic generation, is rather general. One can easily extend the analysis to a higher-order nonlinearity, say, to the third order for the study of third harmonic generation, intermodulation distortion etc. The method however has the limitation in that it cannot account for the saturation that is caused by the defocussing of the electron bunch from the RF phase. However, it can be extended to account for the saturation of the fundamental that is caused by the third-order nonlinearity.