Wang CX. Formulas for tune shift and beta beat due to perturbations in circular accelerators.
PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005;
71:036502. [PMID:
15903597 DOI:
10.1103/physreve.71.036502]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/23/2004] [Indexed: 05/02/2023]
Abstract
Rigorous formulas for nonlinear tune shift and beta -function distortion due to perturbations in the focusing forces are presented, which complement the well-known tune-shift formula for quadrupole errors. Using these formulas, the calculation of nonlinear chromaticity given by Takao [Phys. Rev. E 70, 016501 (2004)] can be greatly simplified and extended to higher order. In addition, an expression for the nonlinear chromatic beta -function distortion is given.
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