Bunch lengthening by a betatron motion in quasi-isochronous storage rings

In this paper we present a complete linear synchrobetatron coupling formalism by studying the transfer matrix which describes linear horizontal and longitudinal motions. With the technique established in the linear horizontal-vertical coupling study [D. Sagan and D. Rubin, Phys. Rev. ST Accel. Beams {\bf 2}, 074001 (1999)], we found a transformation to block diagonalize the transfer matrix and decouple the betatron motion and the synchrotron motion. By separating the usual dispersion term from the horizontal coordinate first, we were able to obtain analytic expressions of the transformation under reasonable approximations. We also obtained the perturbations to the betatron tune and the Courant-Snyder functions. The closed orbit changes due to finite energy gains at rf cavities and radiation energy losses were also studied by the 5$\times$5 extended transfer matrix with the fifth column describing kicks in the 4-dimension phase space.Comment: 25 pages, 6 figures; The subject-class should be soly "Accelerator Physics"; The comment (the last setence of the 3rd paragraph) in version 1 about the first appearance of the closed orbit formula was wrong. To my best knowledge PRE 72, 056501 was the first paper giving that formula, not SLAC technote PTM-5

Section: Introductionmentioning

confidence: 99%

Matrix formalism of synchrobetatron coupling

Huang

2007

“…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%

Metrology Light Source: The first electron storage ring optimized for generating coherent THz radiation

Feikes

Hartrott

Ries

et al. 2011

The Metrology Light Source is a recently constructed 630 MeV electron storage ring, operating as a synchrotron radiation source for the THz to extreme UV spectral range. It is the first storage ring optimized for generating intense, broadband, coherent THz radiation, based on a bunch shortening mode. Stable (''steady state'') or bursting THz radiation up to an average power of about 60 mW can be obtained. The applied machine operation mode is achieved by manipulating the momentum compaction factor by a novel tuning scheme. The underlying low-scheme is of general interest for operating a storage ring in a short bunch mode and is the main subject of this paper.

“…Here f rf is the rf frequency of the accelerating cavity. This consequence is very much different from that of the linear oscillating term [3]. The linear oscillating term is obtained from Eq.…”

Section: Effect Of the Change Of Path Lengthmentioning

confidence: 85%

“…[3] by the same author. The radial displacement produced by the linear betatron oscillation is written as…”

Section: B Contribution Of Linear Partmentioning

confidence: 96%

“…However, in extreme QI conditions, we must consider many effects that are negligible under normal conditions. One of them is bunch lengthening by a linear betatron motion [3], which is location dependent. In this article we sought to investigate the second order effect, the shift in average path length for one revolution by betatron motion.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dependence of average path length betatron motion in a storage ring

Shoji

2005

Self Cite

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.