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.