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By M. Minty, F. Zimmerman

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37. J. Turner, private communication (1998). 38. V. Ziemann, “Corrector Ironing”, SLAC internal report Single-Pass Collider Note CN-393 (1992). 39. W. 9, Cambridge University Press, Cambridge (1986). 40. The MathWorks, Inc. (1994). 41. J. Corbett, F. Fong, M. Lee, V. Ziemann, “Optimum Steering of Photon Beam Lines in SPEAR”, Proc. of 1993 IEEE PAC Washington, p. 1483 (1983). 42. M. Minty, C. J. Hendrickson, R. Sass, T. Slaton, M. Woodley, “Feedback Performance at the Stanford Linear Collider”, Proc.

Quadrupole Excitation If the beam is not centered in a quadrupole magnet, and the strength of this quadrupole is varied, the beam receives a kick. This causes a change in the beam trajectory, for single-turn measurements, or a change in the closed orbit, for measurements on a stored beam. For a single-pass measurement, the dipole kick can easily be inferred by fitting the difference trajectory to a betatron oscillation including one additional kick at the location of the quadrupole. 11) If beam-based alignment is performed on a stored beam, the additional kick of the closed orbit induced by the change in quadrupole strength is given by the sum of two components, the change in field strength and the change in the closed-orbit offset at the quadrupole.

12: Response of the orbit and energy feedback in the ring-to-linac transfer line of the SLC to a fast step change in energy 24 : (left) before and (right) after additional BPMs were included in the feedback loop. 1. Design of an orbit feedback loop Write an algorithm for orbit correction in one plane assuming uncoupled, linear transport in a transport line. Let the beam position be detected using two BPMs and use two fast corrector dipoles for implementing the desired deflections. Introduce (assumed known) relative phase advances and beta functions as needed to take into account phase differences between the correctors, between the BPMs, and between the correctors and BPMs.

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