Trapped modes in TESLA cavities

In the TESLA linear collider scheme the existence of trapped modes within a TESLA cavity could be a severe problem to be overcome. Damping of trapped modes seems impossible due to their localization within the cavity, which prevents a coupling to the HOM dampers mounted to both ends of the beam pipes. As a consequence the energy of a trapped mode can achieve considerable values after several bunch passings, even in the case of a low shunt impedance of such a mode. This effect gives an additional heat load for the cooling system that has to be taken into account. In this paper we propose a method to prove the existence of these modes in a 9-cell copper TESLA cavity. RF-measurements with beam pipes and numerical simulations with MAFIA have been done. Longitudinal and transversal shunt impedances of the trapped modes within a frequency range up to 10 GHz were calculated.