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 th at 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 foun d to be less encumbered, and took less computer time than Lagrangian a pproach as the former avoided a large-scale numerical integration and gave closed-form solutions. Interestingly; it also demonstrated satura tion effects when the third-order nonlinearity was included in the ana lysis, In order to explore the validity of the present Eulerian approa ch to the problem of nonlinear TWT's, it was compared with more accura te Lagrangian approach. Hence, the range of validity of the present no nlinear Eulerian approach was found with respect to the interaction le ngth of the device and the input RF power drive vis-g-vis the saturati on 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 o f nonlinear effects like harmonic generation in TWT's, to be taken up in a subsequent paper.