2005
DOI: 10.1103/physrevstab.8.094001
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Dependence of average path length betatron motion in a storage ring

Abstract: The dependence of path length on betatron motion in a storage ring is analytically calculated from equations of motion using curvilinear coordinates. It is demonstrated that the change of average path length for one revolution is expressed by a sum of the products of invariant of betatron motion and chromaticity in both the horizontal and vertical directions. Because of this effect, a quasi-isochronous electron storage ring should have a considerable momentum spread when the chromaticities are large.

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Cited by 17 publications
(12 citation statements)
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“…The betatron oscillation also changes the averaged path length for a revolution [3,4]. Then, after a single deflection, the particle would start synchrotron oscillation.…”
Section: B Path-length Shift and Energy Displacementmentioning
confidence: 99%
“…The betatron oscillation also changes the averaged path length for a revolution [3,4]. Then, after a single deflection, the particle would start synchrotron oscillation.…”
Section: B Path-length Shift and Energy Displacementmentioning
confidence: 99%
“…To avoid additional amplitude dependent orbit lengthening effects, the transverse chromaticity has to be set to small values [27][28][29]. Alpha is considered as a function of only and expanded into a power series, using the notation [30,31] …”
Section: A the Low-opticsmentioning
confidence: 99%
“…In the electron ring experiments, an extension of a comparison of electron and positron magnetic moments [15,16], adjustment of the sextupole fields yielded an IPP lifetime of about 0.8 s. It has been argued that the simultaneous appearance of zero chromaticity and long IPP lifetime should occur in general [17]. Shoji has explained the connection between increased pathlength and chromaticity [18]. At Q x ∼ Q y ∼ 3.6, the nearest spin resonances are too far away to matter [19].…”
mentioning
confidence: 99%