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, req uires an accurate representation of the held, Furthermore, a fast tool for simulation of beam-field interaction in electron tubes is desirable. Applic ation 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, th ree main steps towards a more accurate and simultaneously more efficient an alysis are presented, First, it is shown how the irrotational magnetic eige nfunctions can be eliminated from the analysis. Furthermore, some poorly co nvergent series in the frequency-domain analysis as well as in the time-dom ain analysis are replaced by analytic expressions, Finally, the modal analy sis is directly formulated in time domain using rigorous boundary condition s. 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 justi fied. For weakly inhomogeneous cavities, the influence of mode conversion o n field profile and on numerical aspects is also discussed.