Rigorous tape analysis of inhomogeneously-loaded helical slow-wave structures

The inhomogeneously-loaded helical slow-wave structure is field analyzed by azimuthally smoothing out the discrete supports into a number of continuous dielectric tube regions of appropriate permittivity values. The analysis is made rigorous by removing the usual approximation of considering the radial propagation constant to be the same in the different structure regions; moreover, a tape-helix instead of a simpler sheath-helix model has been used to consider the space-harmonic effects. This renders the present analysis more general, accurate and capable of dealing with a wide range of structure parameters, and particularly makes it valid for large values of helix pitch angle, inhomogeneity and separation between the helix and the metal envelope of the structure. Further, structured expressions amenable to easy computation are presented with the help of the recurrence relations for various structure regions, and methods to use them effectively in an iterative cycle for the desired accuracy are suggested. The developed analytical expressions have also been checked by seeing that they pass on, as special cases, to those obtained earlier by making simplifying assumptions. In this comparison, care has been taken to account for the helix tape thickness by considering a free-space gap equal to the difference between the mean helix radius and the inner radius of the dielectric helix support. The results for the propagation characteristics of an inhomogeneously-loaded helical structure presented here are rather general and can readily be used for the structure design, performance evaluation, and control of any space harmonic of interest in a practical device.