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An Introduction to Particle Accelerators$
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Edmund Wilson

Print publication date: 2001

Print ISBN-13: 9780198508298

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198508298.001.0001

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Imperfections and multipoles

Imperfections and multipoles

(p.74) 6 Imperfections and multipoles
An Introduction to Particle Accelerators

E. J. N. Wilson

Oxford University Press

This chapter discusses the effect of imperfections in magnetic field, gradient, and alignment using a circle diagram in which divergence, weighted by the local value of beta, is plotted against displacement. Plotting the closed orbit when distorted by a field error in this diagram leads to a relation between the amplitude and error. Random errors are discussed, as are their main sources. Azimuthal error patterns contain many Fourier components, the ones closest to the Q value are most important. Closed orbit bumps may be corrected by applying a chain of overlapping triad bumps to a series of correcting magnets around the ring. The corrections are calculated from beam position measurement at each quadrupole. The chapter also treats gradient errors and how these can stimulate resonances in the working diagram of Q(vertical) versus Q (horizontal). Chromaticity—the momentum dependence of focusing—is discussed: its theory, measurement, and correction with sextupoles.

Keywords:   circle diagram, orbit distortion, Fourier components, correction, triad bumps, beam position, gradient errors, resonances

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