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Title: Matrix Formalism of Synchrobetatron Coupling

Abstract

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 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 x 5 extended transfer matrix with the fifth column describing kicks in the 4-dimension phase space.

Authors:
;
Publication Date:
Research Org.:
Stanford Linear Accelerator Center (SLAC)
Sponsoring Org.:
USDOE
OSTI Identifier:
892960
Report Number(s):
SLAC-PUB-12136
TRN: US200625%%221
DOE Contract Number:  
AC02-76SF00515
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics Review Special Topics - Accelerator and Beams
Country of Publication:
United States
Language:
English
Subject:
43 PARTICLE ACCELERATORS; BETATRONS; CAVITIES; ENERGY LOSSES; PHASE SPACE; RADIATIONS; SYNCHROTRONS; TRANSFORMATIONS; Accelerators,ACCPHY

Citation Formats

Huang, Xiaobiao, and /SLAC. Matrix Formalism of Synchrobetatron Coupling. United States: N. p., 2006. Web.
Huang, Xiaobiao, & /SLAC. Matrix Formalism of Synchrobetatron Coupling. United States.
Huang, Xiaobiao, and /SLAC. Fri . "Matrix Formalism of Synchrobetatron Coupling". United States. https://www.osti.gov/servlets/purl/892960.
@article{osti_892960,
title = {Matrix Formalism of Synchrobetatron Coupling},
author = {Huang, Xiaobiao and /SLAC},
abstractNote = {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 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 x 5 extended transfer matrix with the fifth column describing kicks in the 4-dimension phase space.},
doi = {},
journal = {Physics Review Special Topics - Accelerator and Beams},
number = ,
volume = ,
place = {United States},
year = {Fri Oct 06 00:00:00 EDT 2006},
month = {Fri Oct 06 00:00:00 EDT 2006}
}