Phase-space structure of the Penning trap with octupole perturbation

Details Phase-space structure of the Penning trap with octupole perturbation Phase-space structure of the Penning trap with octupole perturbation

Mar 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002phrva..65c3423e&link_type=abstract

Physical Review A, vol. 65, Issue 3, id. 033423

Statistics

Computation

1

Optical Cooling Of Atoms, Trapping, General Theory Of Classical Mechanics Of Discrete Systems, Multiple Resonances, Celestial Mechanics

Scientific paper

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 nontrivial perturbation in the trap, which is octupolar, using classical perturbation methods. The original three-degree-of-freedom 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.

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