Rigorous analysis of trapped modes in accelerating cavities

We report the development of different algorithms for the calculation of quality factors of 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, and the radiation at the open boundaries is systematically taken into account by different approaches in time and frequency domain. Results indicate that even single cell cavities of the TESLA type show Q values of 10³ and multicell cavities values in excess of 10⁴. Thus these modes may cause considerable beam instabilities. Comparison with the conventional method of analyzing closed cavities and identifying modes with little change in frequency as a function of boundary condition shows 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.