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 horizontalvertical coupling study [D. Sagan and D. Rubin, Phys. Rev. ST Accel. Beams 2, 074001 (1999)PRABFM1098440210.1103/PhysRevSTAB.2.074001], 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 CourantSnyder functions. The closedorbit changes due to finite energy gains at rf cavities and radiation energy losses were studied by the 5×5 extended transfer matrix with the fifth column describing kicks in the 4dimension phase space.
 Publication:

Physical Review Accelerators and Beams
 Pub Date:
 January 2007
 DOI:
 10.1103/PhysRevSTAB.10.014002
 arXiv:
 arXiv:physics/0610015
 Bibcode:
 2007PhRvS..10a4002H
 Keywords:

 29.27.Bd;
 29.20.Dh;
 29.20.Lq;
 Beam dynamics;
 collective effects and instabilities;
 Storage rings;
 Synchrotrons;
 Physics  Atomic and Molecular Clusters;
 Physics  Accelerator Physics
 EPrint:
 25 pages, 6 figures