Evaluation of the beam-coupling impedances of the DAΦNE cavity: numerical and analytical results

Waveguide dampers are going to be widely used in accelerator RF cavities to reduce the beam-coupling impedances at the frequency of the higher order modes, in order to avoid multi-bunch instabilities. The numerical evaluation of the beam-coupling impedances in cavities equipped with waveguide dampers leads to the solution of a 3D field problem, that requires a vast amount of computing time on powerful computers. In this paper we present a simple analytical method, based on the well-known Kirchhoff approximation, that permits an evaluation of the coupling between the cavity and the waveguide modes, thus yielding a first estimate of the Q-factors of the damped modes. We also discuss the evaluation of the damping effect in the case of the DAΦNE RF cavity through the post-processing of the data from a 3D code. The results of the two approaches are compared, and checked against experimental results and other numerical simulations.