ABSTRACT
Ions are conned within an electrodynamic three-dimensional quadrupole eld of rotational symmetry when their trajectories are bounded in the radial (r) and axial (z) directions. The ion motion in the trapping eld is pseudo-harmonic. In a pure quadrupolar trapping eld the ion motions in both the radial and axial directions are independent of each other. The equations of motion for a single ion in the trapping eld can be resolved into a pure axial motion and a pure radial motion, which have identical mathematical forms described by the Mathieu equation [1]. The Mathieu equation for the axial motion contains two parameters, az and qz, which characterize the solutions in the axial direction. Similar parameters, ar and qr, exist for the radial motions. These parameters dene a two-dimensional region in (ai, qi) space for the coordinate (i = r or z), in which the ion motions are bounded and therefore stable. For small values of qi, the pseudo-harmonic motion of an ion can be characterized by the dominant fundamental frequency for motion in the (i) coordinate [1]. A point in (ai, qi) space denes the operating, or ‘working,’ point for the ion. The amplitude of the ion motion in the radial or axial direction can be increased by the application of a supplementary alternating eld having a symmetry and a frequency that are in resonance with one of the frequencies of the ion motion. If the amplitude of the ion motion is increased sufciently, the ion will be driven to the surface of an electrode. When a hole exists in the electrode to which the ion is directed, the ion will escape the trapping eld altogether and exit the trap whereupon it can be detected. This manipulation of the ion motion forms the basis for mass scanning in ion trap mass spectrometers.
