ION OSCILLATION FREQUENCIES IN A COMBINED TRAP

A combined trap is a quadrupole trap to which the fields of both the Paul and the Penning traps are applied. In this paper, equations of motion for ions confined in a combined trap are derived from first principles. The equations of motion are shown to give well-understood solutions for the Paul and Penning traps in the appropriate cases before they are solved to yield the axial and radial oscillation frequencies for ions in a combined trap. The dependence of these oscillation frequencies on the applied fields is investigated. The theoretical predictions were tested in an ion trap at Imperial College using very small numbers of ions, in some cases single ions. The single-ion cases were identified by the observation of quantum jumps in the fluorescence, which is characteristic of a single ion under these conditions. The agreement between the theory and experiment is good.