Octupolar perturbation of a single ion in a Penning trap

We investigate the classical dynamics of a single ion trapped in a Penning trap perturbed by a octupolar electrostatic perturbation that introduces nonlinearities in the motion. We show that the dynamics is controlled by a single external parameter that combines the influence of the electric and magnetic fields. Through the variation of this parameter, we explore the evolution of the phase space structure of the system by the numerical continuation of the families of periodic orbits.