Perturbative Approach to Nonlinear Chromaticity of a Circular Accelerator

The larger a size of a storage ring becomes, the bigger value the chromaticity reaches, which should be corrected by strong sextupole magnets. Hence, for the purpose of precisely controlling the chromaticity, it is necessary to know the nonlinear behavior. In this paper we derive the perturbative expression for the higher order terms of nonlinear chromaticity in terms of the nonlinear dispersion function, whose general formula we have derived before [1]. Calculating the nonlinear chromaticity of the SPring-8 storage ring as an example, we prove the validity of the formula.