A perturbative formulation of nonlinear dispersion for particle motion in storage rings

We provide a perturbative formulation of nonlinear dispersion for particle motion in storage rings without linearizing the kinematic term and give recursion expressions for higher-order terms up to the fourth order. As an example, the nonlinear dispersion function of the SPring-8 storage ring is numerically calculated. The numerical calculation shows that the higher-order terms up to third order are not significantly modulated by magnetic error if the dispersion of the linear optics is sufficiently small. An experimental study of the nonlinear dispersion was also carried out and it was found that the agreement between the theory and the measurement was fairly good up to second order.