Clarifying Analytically Calculated Dispersion Relations of Finite-Length Overmoded Corrugated Cylindrical Azimuthally Symmetric Slow Wave Structures Using Numerical Simulations

We numerically calculate using the 2-D electromagnetic solver SUPERFISH the dispersion relation for electromagnetic modes supported by finite-length, overmoded, corrugated, cylindrical slow wave structures (SWSs) with azimuthal symmetry by first enforcing electric, and thereafter magnetic boundary conditions on both the left and right boundaries of the SWS. We construct the dispersion relation as a set of dispersion curves related to azimuthally symmetric TM0n modes of the finite-length SWS and compare it with the analytically calculated dispersion relation. It is shown as a result of the numerical calculations that the analytically calculated dispersion curves of higher order TM0n modes of the infinite-length SWS are not the dispersion curves defining each single TM0n mode, but rather are combinations of dispersion curves defining those high-order TM0n modes with some parts of dispersion curves defining lower order TM0(n-k) modes, where k = 1 ... (n - 1).

Automated summary

In this study, numerical calculations were performed to investigate the dispersion relation of electromagnetic modes supported by finite-length, overmoded, corrugated, cylindrical slow wave structures, and compared with analytically calculated results. The results showed that analytically calculated dispersion curves of higher order TM0n modes are combinations of dispersion curves defining those high-order modes and some parts of dispersion curves defining lower order TM0(n-k) modes.