Perturbed ion traps:: A generalization of the three-dimensional Henon-Heiles problem

This paper presents an analytical study of an axially symmetric perturbation of the Penning trap. This system is modeled as a generalization of the three-dimensional (3D) Henon-Heiles potential. Thus, the same techniques which succeeded in the study of the 3D Henon-Heiles system apply here. The departure Hamiltonian is three dimensional, although it possesses an axial symmetry. This property, together with an averaging process, is used to reduce the original system to an integrable one. We study the flow of the reduced Hamiltonian: equilibria, bifurcations, and stability, extracting thereafter the relevant information about the dynamics of the original problem. (C) 2002 American Institute of Physics.