Phase-space structure of the Penning trap with octupole perturbation

Abstract

A Lie transformation is developed to study the structure of classical phase space for a perturbed Penning trap. In general, perturbations may result from imperfections or may be deliberately introduced into the system by the application of fields. We study the lowest order non-trivial perturbation in the trap, which is octupolar, using classical perturbation methods. The original three-degree-offreedom problem is reduced to a single degree of freedom by (i) symmetry arguments, (ii) generation of apt action-angle variables, and (iii) computation of the classical normal form. The phase space structure of the resulting normalized Hamiltonian, in the 1:1 resonance, is then analyzed. In the process we discover a saddle-node bifurcation. This approach provides for a global view of the reduced phase space, and, thereby, allows for a systematic study of the impact of several simultaneously applied perturbations.

Production of trans-Neptunian binaries through chaos-assisted capture

“…It is interesting to note that chaos in the Hill sphere is similar to the situation in several problems of current interest in atomic and molecular physics; these include the creation of non‐dispersive electronic Trojan wave packets in Rydberg atoms (Bialynicki‐Birula, Kalinski & Eberly 1995; Farrelly & Uzer 1995; Lee, Brunello & Farrelly 1995, 1997; Lee et al 2000; Kalinski, Hansen & Farrelly 2005) in Rydberg atoms; the dynamics and ionization of Rydberg atoms and molecules in external microwave (Griffiths & Farrelly 1992; Farrelly 1994; Farrelly & Uzer 1995; Farrelly, Lee & Uzer 1995; Deprit et al 1996; Brunello et al 1997; Bellomo et al 1997) or magnetic fields (Johnson, Farrelly & Scheibner 1983, Saini & Farrelly 1987; Uzer et al 1991) and the dynamics of ions in ion traps (Howard & Farrelly 1993; Elipe, Farrelly & Wytrzyszczak 2002).…”