The theory of the computer calculation of the stability of ion motion in periodic quadrupole fields is considered. A matrix approach for the numerical solution of the Hill equation and examples of calculations of stability diagrams are described. The advantage of this method is that it can be used for any periodic waveform. The stability diagrams with periodic rectangular waveform voltages are calculated with this approach. Calculations of the conventional stability diagram of the 3-D ion trap and the first six regions of stability of a mass filter with this method are presented. The stability of the ion motion for the case of a trapping voltage with two or more frequencies is also discussed. It is shown that quadrupole excitation with the rational angular frequency ϭ N⍀/P (where N, P are integers and ⍀ is the angular frequency of the trapping field) leads to splitting of the stability diagram along iso-␤ lines. Each stable region of the unperturbed diagram splits into P stable bands. The widths of the unstable resonance lines depend on the amplitude of the auxiliary voltage and the frequency. With a low auxiliary frequency splitting of the stability diagram is greater near the boundaries of the unperturbed diagram. It is also shown that amplitude modulation of the trapping RF voltage by an auxiliary signal is equivalent to quadrupole excitation with three frequencies. The effect of modulation by a rational frequency is similar to the case of quadrupole excitation, although splitting of the stability diagram differs to some extent. The methods and results of these calculations will be useful for studies of higher stability regions, resonant excitation, and non-sinusoidal trapping voltages. (J Am Soc Mass Spectrom 2002, 13, 597-613)

In a digital ion trap (DIT), the quadrupole trapping and excitation waveforms are generated by the rapid switching between discrete d.c. voltage levels. As the timing of the switch can be controlled precisely by digital circuitry, the approach provides an opportunity to generate mass spectra by means of a frequency scan in contrast to the conventional voltage scan, thus providing a wider mass range of analysis. An instrument has been constructed which employs a 'non-stretched' ion trap and the field fault around the aperture of the end-cap electrode can be corrected electronically using a field-adjusting electrode. The ion trap was coupled with electrospray ionization (ESI) and atmospheric pressure matrix-assisted laser desorption/ionization (AP-MALDI) sources to demonstrate the capability of the digital method. AP-MALDI mass spectra of singly charged ions with mass-to-charge ratios upto 17 000 Th were generated using a trapping voltage of only 1000 V. Forward and reverse mass scans at resolutions up to 19 000 and precursor ion isolation at resolutions up to 3500 with subsequent tandem mass spectrometric analysis were demonstrated. The method of generating the digital waveforms and period scan is described. Discussion of the issues of mass range, scan speed, ion trapping efficiency and collision-induced dissociation efficiency are also provided.

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Resonant quadrupole excitation of ions confined in a radio frequency quadrupole field with angular frequency omega by an excitation signal with angular frequency omega has been investigated theoretically. It is shown that the spectrum of excitation frequencies has considerable structure which corresponds to different orders of excitation. The resonance condition for orders K = 1,2,3,... in the general case has been obtained as omega n(K) = (omega/K) magnitude of n + beta, -infinity < n < infinity, where K is the order of the resonance and beta and n determine the unperturbed oscillation frequencies. Resonance curves for ion oscillations with different stability parameters beta = 0.1, 0.5, and 0.9 have been constructed by means of direct numerical solution of the equations of motion. The trajectories of ion motion under resonant excitation of different orders have been investigated. For orders K of two and higher, the ion motion shows a beat character with an overall increase of amplitude with time. The stability diagram for ion motion in a mass filter in the presence of quadrupole excitation has been constructed.