Calculating trapped modes in TESLA cavities with time and frequency domain methods

We report the development of different algorithms for the calculation of quality factors of trapped eigenmodes in accelerating cavities, which have resonance frequencies above the cutoff frequency of the beam tubes. The analysis is based on a discretization of such cavity structures by the Finite Integration Technique (FIT), and the radiation at the open boundaries is systematically taken into account by different approaches in time and frequency domain. Comparison with the conventional method of analyzing closed cavities and identifying modes with little change in frequency as function of boundary condition show qualitative differences. Some modes from the closed cavity model do not exist in the open structure and thus would be misinterpreted as trapped modes when only a closed cavity analysis is employed. Results indicate that even single cell cavities of the TESLA type show Q-values above 10 ³. And for the TESLA. 9-cell cavity trapped modes with Q-values in excess of 10⁶ are found, which correspond to recent measurement results from the TESLA Test Facility at DESY