Sextupole correction and dynamic aperture: numerical and analytical tools

The authors discuss analytical and numerical tools for dealing with nonlinearities arising from the chromatic perturbations and sextupoles in circular accelerators. Chromatic effects are described and the usual methods of correction are discussed. The Hamiltonian formalism as a tool for dealing with the effect of nonlinearities in the transverse coordinates is described. Different approaches for the nonlinear betatron motion are obtained, and the distortion of nonlinear invariant curves is calculated. An approximate analytical expression for the nonlinear invariant curves in phase space is derived. In addition, a semianalytic tool is introduced for estimating the dynamic aperture without use of a tracking program. (author)