ION DYNAMICS IN PERTURBED QUADRUPOLE ION TRAPS

We use the results of a Lagrangian formulation of the dynamics of ions in a Penning trap to calculate the motional frequencies of the ions a s a function of the trapping parameters. We then add realistic perturb ations to the ideal trapping fields in the formalism and deduce the ef fects of these perturbations on the ion motion. For an ideal trap ther e exist values of the applied trapping fields that result in a degener acy in the ion oscillation frequencies associated with different types of motion. We show that this motional frequency degeneracy is lifted by the inclusion of the effect of a tilt of the trap axis with respect to the axis of the applied magnetic field, leading to an ''avoided cr ossing'' between the oscillation frequencies. We calculate typical ion orbits for trap parameters that give oscillation frequencies near the avoided crossing between the axial and modified cyclotron frequencies . We generalize the analysis to include the motion of ions in a combin ed (Penning-Paul) trap and perform an experiment to test the predictio ns of the theory for a degeneracy between the modified cyclotron frequ ency and the axial frequency for Mg+ ions held in a tilted combined tr ap. The oscillation frequencies are measured for a range of tilt angle s using a photon-photon correlation technique. There is good agreement between the experimental results and the theoretical predictions. The method we describe may prove to be a useful means by which trap imper fections can be identified and subsequently removed.