Introduction to the Nonlinear Dynamics Arising from Magnetic Multipoles

摘要

A Hamiltonian is derived describing transverse particle motion in a storage ring. After a transformation to ''action-angle'' variables we show how to apply Green's function techniques to do Lie transform perturbation theory on this Hamiltonian. Two examples are worked out to second order: (1) normal and skew quadrupole field errors; and (2) normal sextupoles. A brief discussion of the single resonance term Hamiltonian includes derivations of the two invariants and calculation of the resonance width for one degree of freedom systems. Finally, we generalize Courant's treatment of modulational diffusion as an illustrative application of Chirikov's criterion to a multi-resonance problem. 29 refs., 3 figs. (ERA citation 11:030412)