Measurement of the beam's trajectory using the higher order modes it generates in a superconducting accelerating cavity

It is well known that an electron beam excites higher order modes (HOMs) as it passes through an accelerating cavity. The properties of the excited signal depend not only on the cavity geometry, but on the charge and trajectory of the beam. It is, therefore, possible to use these signals as a monitor of the beam's position. Electronics were installed on all forty cavities present in the FLASH linac in DESY. These electronics filter out a mode known to have a strong dependence on the beam's position, and mix this down to a frequency suitable for digitisation. An analysis technique based on singular value decomposition (SVD) was developed to calculate the beam's trajectory from the output of the electronics. The entire system has been integrated into the FLASH control system.