Nonlinear Eulerian hydrodynamical analysis of helix traveling-wave tubes for harmonic generation and its control

Eulerian hydrodynamics was developed to study the nonlinear problem of second harmonic generation in a helix traveling-wave tube (TWT). A closed-form expression for the second-harmonic component of RF output power was obtained. The method required the specification of the dispersion and interaction impedance characteristics of the helical slow-wave structure (SWS) used in the device, obtainable by the field analysis of the SWS. Care was taken however to restrict the present Eulerian theory to the correct regime, which was found in terms of the RF input power drive and the device interaction length, by validating the theory against the more accurate Lagrangian theory. Within this regime, that was below the saturation level of the device, the effect of the dispersion of the SWS on the second harmonic generated in the device was studied. It was found that, irrespective of whether the dispersion of the SWS is positive or negative, the second harmonic content of the device decreased with the amount of the dispersion. Furthermore, though both the fundamental and the second harmonic content of the device decreased with the distributed loss on the SWS, the second harmonic relative to the fundamental showed a minimum at an optimum value of the distributed loss.