Analysis of Helical Slow-Wave Structures for Modeling Helix Thickness Using an Improved Helical-Harmonics Approximation—Part I: Theory

In this two-part paper, an improved helical-harmonics approximation (HHA) is presented, and subsequently validated by applying it to the analysis of cold (beam-absent) helix slow-wave structures (SWSs) with smoothed rods. The first part presents the theory and relevant formulations. By starting from Maxwell´s equations, we obtain an improved form of supporting equations for field components in the so-called helical coordinate system with the help of which the effect of helix pitch angle on the validity of HHA is revealed. By evaluating the error in solutions caused by small changes in the pitch angle across the tape thickness, we show that HHA holds to be valid in a region whose radial thickness is a fraction of actual helix tape thickness. Furthermore, field components of a helix SWS and its dispersion relation are determined using this modified approximation. Moreover, all helical armonics that are necessary for the convergence of the results are incorporated in our analysis. The present improved HHA-based analysis of helical SWS yields a more accurate modeling of the tape thickness than the analysis based on the conventional HHA as well as that by the tape-helix model.