Loss of precision in resonant beam position monitors due to finite Q

The performance of resonant beam position monitors is limited in part by the presence of a symmetrical (common mode) excitation of the cavity. Due to finite Q, a centred beam will give a non-zero output at the observation frequency. This interference is analysed and general expressions are given for the electrical and magnetic spectral densities, split into the wanted resonant term and the “broad-band” unwanted signal, for a cavity with arbitrary shape. This analysis is particularly relevant to beam position monitor studies for the CERN linear collider (CLIC), where very precise measurement of transverse beam position is required. It is shown that a common mode position error of under 1 μm is obtainable from a high Q 33GHz pill-box, even prior to the use of any external difference-taking elements