Nonlinear dynamics with sextupoles in low-emittance light source storage rings

Abstract

Abstract An analysis is made of the nonlinear particle motions arising from sextupoles in low-emittance light source rings. By employing the single-resonance approximation to the Hamiltonian expanded into harmonics, boundaries of the stable motion brought about by 1st- and 3rd-order resonances are calculated analytically. These are used together with the second-order tune shifts with amplitude as guidelines of the analysis and of the optimization of sextupoles to improve the dynamic aperture. The application is made to two typical lattices of the light source rings, the Chasman-Green and the triple-bend achromat lattice, to pursue the lattice dependence of the nonlinear characteristics. Apart from the cases where the stability is determined by the lowest-order resonances, studies using particle tracking indicate that the motion is very often driven by higher-order resonances for which further considerations are required. Two approaches are discussed in this context. One is to interpret the phenomena as a combined effect of the lowest-order resonances, which is verified numerically by a fictitious tracking. Another is the perturbative method. The theory developed by Poincare and von Zeipel is used to analyze the horizontal dynamics, which is worked up to 4th order in amplitude. Examples that satisfactorily reproduce the phase-space structure are shown, although it is also found that perturbations of many of the sextupoles required for these low-emittance rings are even higher than 4th order.