Axisymmetric Waves in Re-Entrant Cavities

We employ a well-established method to determine the dispersion properties of transverse magnetic and transverse electric waves in re-entrant cavities. We assume that the waveguide structure consists of a large number of identical cavities in order that the Floquet theorem could be applied to describe the electromagnetic field in an empty cylinder. Furthermore, we describe the electromagnetic field in each cavity region by an eigenfunction expansion for standing waves. Inferring boundary conditions leads to a system of two infinite sets of equations, which is solved numerically by truncation. A numerical code has been developed to calculate the dispersion relation and the electromagnetic field components. Numerical results are presented for several waveguide geometries, including the case of the real gyrotron beam-tunnel geometry. A comparison with already established codes is made.