Ion dynamics in perturbed quadrupole ion traps

Abstract

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 as a function of the trapping parameters. We then add realistic perturbations to the ideal trapping fields in the formalism and deduce the effects of these perturbations on the ion motion. For an ideal trap there exist values of the applied trapping fields that result in a degeneracy 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 crossing'' 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 combined ͑Penning-Paul͒ trap and perform an experiment to test the predictions of the theory for a degeneracy between the modified cyclotron frequency and the axial frequency for Mg ϩ ions held in a tilted combined trap. The oscillation frequencies are measured for a range of tilt angles 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 imperfections can be identified and subsequently removed.

First-order perturbative calculation of the frequency-shifts caused by static cylindrically-symmetric electric and magnetic imperfections of a Penning trap

“…While we have solved the classical equations of motion exactly for the ideal Penning trap, general analytic solutions are not available for the ion dynamics in the case of cylindricallysymmetric imperfections. As remarked by [42], already the low-order anharmonic electric imperfection present enormous difficulties [43,44]. Despite the richness of non-linear phenomena, insofar as they do not cause instability, the main concern for Penning-trap mass spectrometry has always been the frequency-shift that goes along, because measuring frequencies is paramount.…”

Phase-space structure of the Penning trap with octupole perturbation

“…The quadrupole (l = 2) case was analytically solved by Horvath et al [5]. Our goal here is to study the octupole (l = 4) contribution, to obtain information about stability regions and to show the behavior of the phase flow.…”

“…The dominating terms of the nonlinear contribution depend on the actual trap geometry [5]. Thus, for example, in a trap where the ideally hyperbolic electrodes are approximated by electrodes of spherical section, the main nonlinear term is the octupole [29].…”

“…Consequently, it has become one of the most versatile experimental devices in atomic and molecular physics [2][3][4][5]. Applications of the Penning trap are broad and have included tests of fundamental theories, e.g., of QED, and the determination of fundamental physical constants such as the fine structure constant [6][7][8].…”

The ‘hybrid cell’: a new compensated infinity cell for larger radius ion excitation in Fourier transform ion cyclotron resonance mass spectrometry

“…In a spatially uniform direct current (dc), magnetic field, and a three‐dimensional quadrupolar electrostatic trapping potential (e.g. near the center of an ICR ion trap), the ion radial and axial motions are uncoupled in energy and the ion cyclotron, magnetron, and axial frequencies are each independent of ion position 15. Ions can be confined for a long period of time without significant loss (the record is 10 months for a single electron in a Penning trap16).…”