Fermilab, Batavia, Illinois, USA
The superconducting radio frequency (SRF) technology is progressing rapidly over last decades toward high accelerating gradients and low surface resistance making feasible the particle accelerators operation with high beam currents and long duty factors. However, the coherent RF losses due to high order modes (HOMs) excitation becomes a limiting factor for these regimes. In spite of the operating mode, which is tuned separately, the parameters of HOMs vary from one cavity to another due to finite mechanical tolerances during cavities fabrication. It is vital to know in advance the spread of HOM parameters in order to predict unexpected cryogenic losses, overheating of beam line components and to keep stable beam dynamics. In this paper we present the method of generating the unique cavity geometry with imperfections while preserving operating mode frequency and field flatness. Based on the eigenmode spectrum calculation of series of randomly generated cavities we can accumulate the data for the evaluation the HOM statistics. Finally, we describe the procedure for the estimation of the probability of the resonant HOM losses in the SRF resonators. The study of these effects leads to specifications of SC cavity and cryomodule and can significantly impact on the efficiency and reliability of the machine operation
