Trapped modes in tapered vacuum chambers for a mini-gap undulator magnet

Consideration of transverse wakefields and impedances due to the tapered vacuum chambers for superconducting mini-gap undulators revealed the existence of trapped modes. To investigate this phenomenon, a series of analytical and numerical calculations were performed for both elliptical and rectangular chambers. A rectangular prototype was built and measured and the experimental results were found to be in very good agreement with theory. Knowledge about the impedance of tapered vacuum chambers is important for the evaluation of transverse instabilities in high-energy accelerators.