Theoretical Analysis of the Dispersion Characteristics for the Coaxial/Cylindrical Slow Wave Structure With Arbitrary Boundary Based on the Operator Theory

A general dispersion function of the coaxial/cylindrical slow wave structure (SWS) with arbitrary boundary is derived based on the operator theory. Owing to the introduction of operators, the proposed theoretical model can be expressed in a simple form, where the boundary functions are no longer restricted to even functions, and both symmetric and asymmetric modes are considered. In order to verify the validity of the proposed theoretical model, the dispersion functions of a coaxial complicated combined periodic SWS (CP-SWS) and a cylindrical one are calculated. Moreover, the theoretical results are compared with the simulation results calculated by HFSS and CST, and the corresponding relative errors are within 2%. In addition, the bandgap, pseudo-modes, and dispersion characteristics of the complicated CP-SWS with multiparts are also analyzed and discussed.