Eulerian analysis for harmonic generation and its control in a helix travelling-wave tube

Nonlinear Eulerian hydrodynamical equations of a helix travelling-wave tube were formulated and their solutions obtained by the method of successive approximation. The method was applied to the problem of second harmonic generation in the device and its conditioning. The present Eulerian approach, unlike the Lagrangian one, did not give a picture of electron overtaking and that of the position of electron bunch relative to the RF phase, nor did it account for saturation effects caused by the defocusing of the RF wave from the electron bunch. Nevertheless, the approach was found to be less encumbered and it took less computer time than Lagrangian approach as it avoided large-scale numerical integration and gave dosed-form solutions. It also exhibited saturation effects by the inclusion of the third-order nonlinearity in the analysis. Second harmonic generation in the device was correlated with the dispersion and interaction impedance characteristics of the slow-wave structure as well as with Pierce's velocity synchronisation parameter. The reduction of the second harmonic content of the device by the use of a negative dispersion slow-wave structure as well as by a distributed loss put on it was demonstrated. Furthermore, the analysis was used to study the role of second harmonic injection in reducing the second harmonic content of the device. The optimum values of the relative amplitude and phase of two harmonically related signal inputs were predicted for reduced second harmonic and enhanced fundamental RF signal outputs.