Analysis of the beam position measurement with button-type pickups in APS

Abstract

The response of electrostatic button-type pickups for the measurement of the transverse position of charged particle beams was investigated and analytic formulae were obtained for the signal as a function of time t. 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. In particular, the error in the measurement of the beam position using circular electrodes as compared to rectangular ones was found to be less than 100 urn per 1 cm of beam excursion from the center of the beam pipe for the case of APS. INTRODUCTIONFor capacitive pickup devices, the position of the charged beam is measured through the difference between the electric potentials which develop on the electrodes. For slow, nonrelativistic beams, the image charge induced by the bunch of charged particles has considerably larger longitudinal dimension than the bunch itself. However, for highly relativistic beams, the image charge has the same longitudinal distribution as the beam, due to the Lorentz contraction of the longitudinal component of the electric field.In this article, we will derive the response of the electrode as a function of time and the transverse position of the beam, assuming that both the angular and the longitudinal sizes of the electrodes are finite. The analytical model assumes a simple elliptic geometry for the beam chamber. The results are compared with those obtained numerically for the actual APS beam chamber, and they will be shown to agree quite well. This justifies the use of the analytical model rather than the timeconsuming numerical methods to find the optimal position and size of the electrodes and to analyze how the shape of the electrodes affect the beam position measurement. MONITOR RESPONSEIn order to get the signal from each electrode, we must first obtain the electric field inside the beam chamber. Consider an infinitely narrow beam moving along the longitudinal direction with the constant velocity OHTRIBUT1ON OF TH,S DOCUMENT J DISCLAIMER