Matrix Formalism of Synchrobetatron Coupling

Journal Article · Fri Oct 06 04:00:00 EDT 2006 · Physics Review Special Topics - Accelerator and Beams

OSTI ID:892960

Huang, Xiaobiao

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.

• Research Organization: Stanford Linear Accelerator Center (SLAC)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC02-76SF00515
• OSTI ID: 892960
• Report Number(s): SLAC-PUB-12136
• Journal Information: Physics Review Special Topics - Accelerator and Beams, Journal Name: Physics Review Special Topics - Accelerator and Beams
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
Accelerators
ACCPHY
BETATRONS
CAVITIES
ENERGY LOSSES
PHASE SPACE
RADIATIONS
SYNCHROTRONS
TRANSFORMATIONS