Rigorous computation of time-dependent electromagnetic fields in gyrotron cavities excited by internal sources

Computation in frequency, as well as in time domain of the electromagnetic field in aperture-coupled cavities which are excited by electron beams, requires an accurate representation of the field. Furthermore, a fast tool for simulation of beam-field interaction in electron tubes is desirable. Application of the modal expansion method, which utilizes both the solenoidal and the irrotational eigenfunctions of the equivalent short-circuited cavity, is generally rigorous but numerically inefficient. In this contribution, three main steps towards a more accurate and simultaneously more efficient analysis are presented. First, it is shown how the irrotational magnetic eigenfunctions can be eliminated from the analysis. Furthermore, some poorly convergent series in the frequency domain analysis as well as in the time-domain analysis are replaced by analytic expressions. Finally, the modal analysis is directly formulated in time domain using rigorous boundary conditions. Numerical results are presented for idealized structures with impressed current density and for self-consistent calculations which are compared to analytical or to numerical results, respectively. Thus, excellent accuracy of the developed method is proved and significant simplifications are justified. For weakly inhomogeneous cavities, the influence of mode conversion on field profile and on numerical aspects is also discussed.