Nonlinear Beam Behaviour Study Using Lie Transforms

The particle motion in sextupole fields of a storage ring is studied analytically. The invariants of mo-tion are constructed up to high orders in the per-turbation parameters for a harmonic-expanded Hamiltonian using Lie transforms implemented in the REDUCE program. The phase space patterns of the motion are drawn up in resonant and non-resonant cases. A technique for estimating a dy-namic aperture (DA) is described. The results are compared with numerical tracking.