Phys. Rev. E 71, 036502 (2005) [3 pages]Formulas for tune shift and β beat due to perturbations in circular acceleratorsReceived 23 September 2004; published 28 March 2005 Rigorous formulas for nonlinear tune shift and β-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 et al. Phys. Rev. E 70 016501 (2004) can be greatly simplified and extended to higher order. In addition, an expression for the nonlinear chromatic β-function distortion is given. © 2005 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.71.036502
DOI:
10.1103/PhysRevE.71.036502
PACS:
41.85.−p, 29.27.Bd
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