DOI: 10.1140/epjd/e2002-00122-3 THE EUROPEAN PHYSICAL JOURNAL D Dynamics of a single ion in a perturbed Penning trap.

Abstract. In the frame work of classical mechanics, we study the nonlinear dynamics of a single ion trapped in a Penning trap perturbed by an electrostatic sextupolar perturbation. The perturbation is caused by a deformation in the conguration of the electrodes. By using a Hamiltonian formulation, we obtain that the system is governed by three parameters: the z-component of the canonical angular momentum P { which is a constant of the motion because the perturbation we assume is axial-symmetric {, the parameter that determines the ratio between the axial and the cyclotron frequencies, and the parameter a which indicates how far from the ideal design the electrodes are. We study the case P = 0. By means of surfaces of section, we show that the phase space structure is made of three fundamental families of orbits: arch, loop and box orbits. The coexistence of these kinds of orbits depends on the parameter . The escape is also explained on the basis of the shape of the potential energy surface as well as of the phase space structure. PACS. 05.45.-a Nonlinear dynamics and nonlinear dynamical systems { 39.10.+j Atomic and molecular beam sources and techniques { 52.25.Gj Fluctuation and chaos phenomena