Fast readout algorithm for cylindrical beam position monitors providing good accuracy for particle bunches with large offsets

A simple, analytically correct algorithm is developed for calculating “pencil” relativistic beamcoordinates using the signals from an ideal cylindrical particle beamposition monitor (BPM) with four pickupelectrodes (PUEs) of infinitesimalwidths. The algorithm is then applied to simulations of realistic BPMs with finite width PUEs. Surprisingly small deviations are found. Simple empirically determined correction terms reduce the deviations even further. The algorithm is then tested with simulations for non- relativistic beams. As an example of the data acquisition speed advantage, a Field Programmable Gate Array-based BPM readout implementation of the new algorithm has been developed and characterized. Finally, the algorithm is tested with BPM data from the Cornell Preinjector.