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 formulae were obtained for the signal a a function of time t and the coordinates of the beam and the electrodes. The study was done for beam pipes of circular and elliptic cross sections, 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 (-20 pm) 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 pm per 1 cm of beam excursion from the center of the beam pipe for the case of APS storage ring vacuum chamber. d>‘(x, t) = j dk,ik (z- vt