Improving the numerical efficiency and accuracy of the modal expansion inside gyrotron cavities

In the theoretical investigation of gyrotrons an accurate representation of the electromagnetic field inside the beam - field interaction cavity is required. In this contribution, two improvements of the modal expansion inside cavities with coupling apertures are suggested which significantly increase the accuracy and the numerical efficiency of this method. Expanding the electromagnetic field in terms of the eigenfunctions of the corresponding completely shielded cavity leads to a non-uniform convergence of some field series at the apertures which makes the modal analysis inaccurate and numerically inefficient. It is demonstrated how the non-uniform convergence is removed by means of convergence acceleration. Furthermore, it is shown how the asymptotic values for some slowly converging series related to the modal analysis can be estimated and hence a moderate number of cavity eigenfunctions need to be considered which also leads to a considerable improvement of the performance of this method. The effectiveness of both improvements is demonstrated for various examples.