Trajectory calculations of space‐charge‐induced mass shifts in a linear quadrupole ion trap

Abstract

RATIONALE:If too many ions are stored in a linear quadrupole ion trap, space charge causes the oscillation frequencies to decrease. Ions therefore appear at higher apparent mass-to-charge ratios in a mass spectrum. To further understand this process, we have used trajectory calculations of ions to determine mass shifts. METHODS: Two models of the ion cloud are used. The first assumes that the acceptance of the quadrupole is uniformly filled with ions. The second assumes that the ions have a thermal distribution trapped in the effective potential. Both give analytical descriptions of the field from space charge. Ion trajectories are calculated with and without space charge. Oscillation frequencies are determined with a Fourier transform. Shifts in oscillation frequency with space charge are then used to calculate mass shifts. RESULTS: Both ion cloud models give similar results. More diffuse ion clouds or ion clouds that have higher temperatures produce lower electric fields near the center of the trap and hence lower mass shifts. Space charge produces a nonlinear field. As a result, the discrete resonant frequencies of ions in a pure quadrupole field become distributions of frequencies.Comparisons with experiments show agreement for reasonable values of the parameters of the two ion cloud models. CONCLUSIONS: This relatively simple method for calculating the effects of space charge shows (i) that the spread of oscillation frequencies reduces mass resolution with axial ejection and (ii) that mass shifts are reduced with ion clouds with greater spatial extents or higher ion temperatures. Copyright © 2012 John Wiley & Sons, Ltd.Linear quadrupole ion traps are finding increasing applications in mass spectrometry, either combined with other mass spectrometers such as 3D trap, time-of-flight, or ion cyclotron resonance (ICR) mass analyzers to improve duty cycle, [1] or used as stand-alone mass analyzers. [2,3] In a linear quadrupole ion trap ions are confined radially by a potential given by:where x and y are Cartesian coordinates, r 0 , the field radius, is the distance from the center of the trap to an electrode, U and V rf are the amplitudes of the dc and radio-frequency (rf) voltages, respectively, applied between an electrode and ground, and Ω = 2pf is the angular frequency of the rf voltage. Ions are confined axially by stopping potentials applied to electrodes at the ends of the quadrupole. The motion of an ion is described in terms of the Mathieu parameters:where z is the number of charges on an ion, e is the magnitude of the electron charge, and m is the ion mass. If ions are confined at q ≤ 0.4, ion motion can be described approximately as motion in the effective potential V eff given by:where the well depth D is given by:Ions oscillate in the quadrupole potential with angular frequencies given by:where n = 0, AE1, AE2. . .. and b is a function of the parameters a and q. For mass analysis, ions are excited with an auxiliary dipole voltage at an oscillation frequency corresponding to a high q value. The trappi...

Mass selectivity of dipolar resonant excitation in a linear quadrupole ion trap

“…This means that Eqn. (15) is valid for dipolar excitation and confirms the mechanism of the peak broadening proposed by Fisher. A contour S(q) is calculated for ions of one mass, but having various initial conditions in the quadrupole field.…”

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“…With a damping gas the resolution is no longer described by the simple relation of Eqn. (15). A given resolution at excitation frequency ν À 1 might be achieved with a decreased excitation time.…”

A Short Overview of the Components in Mass Spectrometry Instrumentation for Proteomics Analyses

“…Considering the ion population being injected in a quadrupole analyzer, a selection can be made according to their m/z ratio, making some ions to have a stable trajectory in the analyzer, while a considerable number of other ions will not go all the way through (Figure 2A, arrows). The ion path occurs in the z direction, while the attraction and repulsion are occurring simultaneously in the x and y direction ( Figure 2A) [38,42]. If the oscillations of an ion are stable, the ion will continue to drift down the rod assembly and reach the detector.…”

“…When the voltage is applied to the electrodes in the trap, a "trapping potential" is formed, which keeps the ions inside the trap [38,42]. In a ion trap, the trajectories of trapped ions of consecutive specific m/z rations are affected and become unstable when the field within the trap is changed.…”