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We present a new modelling approach for the dielectric loaded gyrotron beam tunnel. We treat the problem realistically as a finite sized structure by considering for the first time open boundary conditions. Matching the field of discrete spectrum in the rings, with the field of continuous spectrum in the hollow region, produces Fourier integrals that are evaluated by use of contour integration and residue theory. The final linear system of equations for the mode coefficients is numerically solved. The method can be extended for finding the complex eigenfrequencies of the structure as well as for modelling more advanced concepts of beam tunnels

Electromagnetic modelling of dielectric loaded aperiodic gyrotron beam tunnels