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 TM ${}_{{0}{n}}$ 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 TM ${}_{{0}{n}}$ modes of the infinite-length SWS are not the dispersion curves defining each single TM ${}_{{0}{n}}$ mode, but rather are combinations of dispersion curves defining those high-order TM ${}_{{0}{n}}$ modes with some parts of dispersion curves defining lower order TM ${}_{0({n-k})}$ modes, where ${k}={1}\ldots ({n}-{1})$ .