Theoretical studies on the beam position measurement with button-type pickups in APS

The response of electrostatic button-type pickups for the measurement of the transverse position of charged particle beams was investigated and analytical formulas were obtained for the signal as a function of time and the coordinates of the beam and the electrodes. The study was done for beam pipes, for rectangular and non-rectangular electrodes, and for several cases of longitudinal beam profiles. The numerical results show good agreement with the analytical results, except that the presence of the photon beam channel and the antechamber causes finite offset ( approximately 20 mu m) of the electrical center in the horizontal direction. Time domain analysis indicates that the error in the measurement of the beam position using circular electrodes as compared to rectangular ones was found to be less than 100 mu m per 1 cm of beam excursion from the center of the beam pipe for the case of the Advanced Photon Source (APS) storage ring vacuum chamber.<>