Formulas for tune shift and beta beat due to perturbations in circular accelerators.
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.
Wang
Chun-xi
CX
Argonne National Laboratory, Illinois 60439, USA. wangcx@aps.anl.gov