The Spatial Harmonics Method has been used to study TE modes in a coaxial corrugated cavity. A numerical code has been developed to calculate eigenvalues, fields and ohmic losses on the walls. Numerical results are presented to clarify the influence of the higher-order spatial harmonics to these calculations.

Using the numerical code Fishbone, developed to study the parasitic oscillations in gyrotron beam tunnels, a parametric study is performed on the effect of the dielectric material as well as of the slot geometry on the growth rate of the excited parasitic modes.

We present the mathematical formulation and numerical results for the beam-wave interaction in a coaxial waveguide with rectangular slots filled with a lossy dielectric material. The formalism is based on a full-wave analysis and the linearized Vlasov equation. Numerical results are given for all kinds of modes in simplified gyrotron beam tunnels, and the effect of the losses to the parasitic oscillations is examined and discussed.