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

Y. Chung

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Conference Record of the 1991 IEEE Particle Accelerator Conference
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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 nonrectangular electrodes, and for several cases of longitudinal beam profiles. The numerical results show good agreement with the
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... ment 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. where the linear dispersion relation w = kV was assumed. The integration variable k cxtcnds from -00 to +m. Then the induced current Ip can be expressed as I. INTR~IXJCTI~N For capacitive pickup deviccs[l-31, the position of the charged beam is measured through the difference between the electric potentials which develop on the electrodes. 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 analyze the response of the button electrodes in both the frequency and the time domains as a function of the transverse position of the beam, taking into account the finite size of the electrodes. The analytical model assumes a simple elliptic geometry for the beam chamber. The results arc compared with those obtained numerically for the actual APS beam chamber, and they will be shown to agree quite well. This justifies the USC of the analytical model rather than the time-consuming 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. The integration is done over the arca of the electrode surface, and zl is the z-coordinate of a reference point, e.g., the center of the electrode zp. n is the direction normal to the electrode surface. If the electrode is connected by a coaxial line of characteristic impedance ZO and if the capacitance between the electrode and the beam chamber is C" then the overall impedance q(k) for the electrode will be If there is frcqucncy filtering represented by F(k), the measured voltage VP(k) will be II. MONITOR RESPONSE Consider an infinitely narrow beam moving along the longitudinal direction with the constant velocity V. Following the procedure by CupCrus[4], instead of solving the full electromagnetic problem directly in the lab frame (unprimed), we will transform to the reference frame (primed) where the beam is at rest, obtain the field and then transform Fig.

doi:10.1109/pac.1991.164553
fatcat:5eags2ga65bstbroxlgc4jxoqu