Nonlinear Eulerian hydrodynamical analysis of helix traveling-wave tubes

Nonlinear Eulerian hydrodynamical equations of a helix traveling-wave tube (TWT) were formulated and their solutions obtained by the method of successive approximation. The present Eulerian approach, unlike the Lagrangian one, does not give a picture of electron overtaking and that of the position of electron bunch relative to the RF phase-nor does it account for saturation effects caused by the defocusing of the RF wave from the electron bunch. Nevertheless, Eulerian approach was found to be less encumbered, and took less computer time than Lagrangian approach as the former avoided a large-scale numerical integration and gave closed-form solutions. Interestingly, it also demonstrated saturation effects when the third-order nonlinearity was included in the analysis. In order to explore the validity of the present Eulerian approach to the problem of nonlinear TWTs, it was compared with more accurate Lagrangian approach. Hence, the range of validity of the present nonlinear Eulerian approach was found with respect to the interaction length of the device and the input RF power drive vis-a-vis the saturation behavior of the device. It is hoped that, in the regime of validity thus found, one can use the present Eulerian approach for the study of nonlinear effects like harmonic generation in TWTs, to be taken up in a subsequent paper.