Eur. Phys. J. D 20, 45-54 (2002)
https://doi.org/10.1140/epjd/e2002-00122-3

Dynamics of a single ion in a perturbed Penning trap. Sextupolar perturbation

¹ Area de Física Aplicada, Universidad de La Rioja, Edificio Científico Tecnológico, C/Madre de Dios 51, 26006 Logroño, Spain
² Departamento de Matemáticas y Computación, Universidad de La Rioja, C/Luis de Ulloa s/n, 26004 Logroño, Spain

Corresponding author: ^a josepablo.salas@dq.unirioja.es

Received: 6 September 2001
Revised: 19 March 2002
Published online: 28 June 2002

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 configuration 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 – which is a constant of the motion because the perturbation we assume is axial-symmetric –, the parameter δ 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 . 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 δ. The escape is also explained on the basis of the shape of the potential energy surface as well as of the phase space structure.