Simplified Approach to the Nonlinear Analysis in Helix Slow-Wave-Structure for a Traveling Wave Tube

Abstract

A stationary 1-D nonlinear code based on Lagrangian disk model is developed on the basis of a simple set of analytical expressions to study nonlinear dynamics in the helix slow-wave structure used in a traveling wave tube. The loss profiles such as triangular and Gaussian types are modeled as stairsteps and a simple formula is developed to found the loss at a plane for such loss profile. In contrast to the earlier works in nonlinear theory, at present, no numerical method is used at any stage. The method, introduced in this work, is general in nature because it can handle (a) multi-section structure with sever, (b) different loss profiles, namely, center (Gaussian) and tip (triangular: increasing or decreasing), (c) space charge effect on the electrons, (d) backward waves arising due to reflections, etc. Accuracy of the theory and code is verified with comparison of the computed present results with the results from simulation code MAGIC and published elsewhere and found to be in good agreement. The generation and suppression of the harmonic power are studied for a typical structure. It is found that the introduction of resynchronization section of the reduced pitch enhances the fundamental power with the reduction of the second harmonic power. In addition, the method can be used for any helix slow-wave-structure consisting of homogeneous/inhomogeneous dielectric support rods in isotropic/anisotropic overall metallic enclosure, because the axial propagation constant and interaction impedance obtained for any structure and model such as sheath and tape helix approximations or from any simulation codes can be used as the input in the program to make the code more general.