PMID: 15244955Jul 13, 2004Paper

Finding a nonlinear lattice with improved integrability using Lie transform perturbation theory

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Kiran G Sonnad, John R Cary

Abstract

A condition for improved dynamic aperture for nonlinear, alternating gradient transport systems is derived using Lie transform perturbation theory. The Lie transform perturbation method is used here to perform averaging over fast oscillations by canonically transforming to slowly oscillating variables. This is first demonstrated for a linear sinusoidal focusing system. This method is then employed to average the dynamics over a lattice period for a nonlinear focusing system, provided by the use of higher order poles such as sextupoles and octupoles along with alternate gradient quadrupoles. Unlike the traditional approach, the higher order focusing is not treated as a perturbation. The Lie transform method is particularly advantageous for such a system where the form of the Hamiltonian is complex. This is because the method exploits the property of canonical invariance of Poisson brackets so that the change of variables is accomplished by just replacing the old ones with the new. The analysis shows the existence of a condition in which the system is azimuthally symmetric in the transformed, slowly oscillating frame. Such a symmetry in the time averaged frame renders the system nearly integrable in the laboratory frame. This con...Continue Reading

References

May 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·Y K Batygin
Oct 9, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·L F WangK Oide

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