Frequency perturbation in nonlinear Paul traps:a simulation study of the effect of geometric aberration,space charge, dipolar excitation, and damping on ion axial secular frequency

This article develops an expression that relates perturbation in ion axial secular frequency to geometric aberration, space charge, dipolar excitation, and collisional damping in nonlinear Paul trap mass spectrometers. A multipole superposition model incorporating hexapole and octopole superposition has been adopted to represent field inhomogeneities. A uniform charge density distribution has been assumed for characterizing space charge. Dipolar excitation has been represented as a forcing term weighted by dipole superposition, and damping is represented in terms of reduced collision frequency in the equation of ion motion. The perturbed secular frequency of the ion has been obtained by using a modified Lindstedt–Poincare´ perturbation technique. The expression for perturbed frequency adequately reflects the reported experimental and simulation results.Perturbation is sign sensitive for octopole superposition and sign insensitive for hexapole superposition. Larger shifts occur with octopole aberrations. Perturbation of secular frequency based on the number of ions is mass dependent. Lower masses show larger negative frequency shifts with an increase in the number of ions within the trap. Dipolar excitation potential shifts the secular frequency in the positive direction and is larger for lower masses than for higher masses. Damping plays a minor role in shifting the secular frequencies. The shift increases as we increase the pressure of the bath gas. The shift in ion secular frequency with the axial distance from the center of the trap shows quadratic variation. (Int J Mass Spectrom 197 (2000) 263–278

A simulation study of coupled secular oscillations in nonlinear Paul trap mass spectrometers

This paper presents the results of a simulation study to understand coupling of axial and radial secular motion in nonlinear Paul trap mass spectrometers having hexapole and octopole superposition in the presence of an external excitation. The equations of motion has the form of a inhomogeneous coupled Duffing oscillators with quadratic and cubic nonlinearities with an periodic forcing function in the axial direction with a frequency corresponding to the ideal axial secular frequency. The study relies on using both numerical as well as analytical techniques to study the role of field inhomogeniety and external excitation in the appearance of coupled frequencies in axial and radial directions. It has been seen that the strength of coupling can be characterized by the magnitude of the coefficient of the cross terms in the equations of motion and the appearance of coupled frequencies in each direction is a function of this coupling strength. Hexapole superposition plays a role only in the axial direction and its influence in coupled oscillations is minimal. Octopole superposition plays the predominant role in determining the appearance of coupled frequencies in both directions. It was further seen that in the presence of an external excitation the axial secular motion was amplitude and phase modulated and resulted in a beat frequency corresponding to the difference between the perturbed axial frequency and the applied excitation frequency. Increasing the amplitude of external excitation results in appearance of an increased number of sidebands in the frequency spectrum in both directions

Transition curves and iso-beta(u) lines in nonlinear Paul traps

This paper has the motivation to understand the role of field inhomogeneties in altering stability boundaries in nonlinear Paul traps mass spectrometers. With the inclusion of higher order terms in the equation of motion, the governing equation takes the form of a nonlinear Mathieu equation. The harmonic balance technique has been used to obtain periodic solutions which represents the transition curves, beta(u) = 0 and beta(u) = 1. A continuous fraction expression, similar in form to the linear case, has also been derived to plot iso-beta(u) lines within the stability region. The expression qualitatively reflects experimental observations in literature related to ion stabilities in nonlinear traps. The role of hexapole and octopole superposition in shifting the stable region as well as ion secular frequencies in nonlinear Paul traps has been discussed using the analytical expression derived in this paper

Design considerations for linear Paul trap mass spectrometer under development

This brief note presents design considerations for a linear ion trap mass spectrometer in our laboratory. The motivation for this effort was to investigate the increased sensitivity that could be obtained in such a configuration in contrast to the conventional three-dimensional Paul trap mass analyzers. This technical report discusses the equation of ion motion and then the conditions for stability in the presence of a dc trapping field in the axial direction, we also present the influence of the trapping voltage, rod length and rf frequency on mass range

Field imperfection induced axial secular frequency shifts in nonlinear ion traps

This article develops a simple analytical expression that relates ion axial secular frequency to field aberration in ion trap mass spectrometers. Hexapole and octopole aberrations have been considered in the present computations. The equation of motion of the ions in a pseudopotential well with these superpositions has the form of a Duffing-like equation and a perturbation method has been used to obtain the expression for ion secular frequency as a function of field imperfections. The expression indicates that the frequency shift is sensitive to the sign of the octopole superposition and insensitive to the sign of the hexapole superposition. Further, for weak multipole superposition of the same magnitude, octopole superposition causes a larger frequency shift in comparison to hexapole superposition

Paul Trap Mass Spectometer Developed in the Mass Spectometry Laboratory

The motivation of this technical report is to describe the design and provide fabrication details of the Paul trap mass spectrometer that has been built in our laboratory. This technical report gives both the theory of ion trapping in Paul trap mass spectrometers and the technical specifications of mechanical assembly, vacuum chamber and other electronic subsystems associated with our laboratory’s Paul trap mass spectrometer. Section 2 gives the theory of the ion trap mass spectrometry including development of equations of ion motion and the conditions required for the ions to have stable trajectories inside the trap. Section 3 provides the technical specifications of our trap electrodes, electronic subsystems including constant current source, gating power supply, extraction power supply, high voltage dc power supply, RF signal generator as well as the vacuum system and graphical user interface are presented. Section 4 presents a few mass spectra to demonstrate the performance our mass spectrometer. Appendix 1 gives the detailed orcad layouts of all the electronic circuits associated with the Paul trap mass spectrometer and the technical data related to the National Instruments data acquisition device PCI-MIO-16-E-1 is given in Appendix 2. At the end of the report a few important and pertinent references are provided

Paul Trap Mass Spectometer Developed in the Mass Spectometry Laboratory

The motivation of this technical report is to describe the design and provide fabrication details of the Paul trap mass spectrometer that has been built in our laboratory. This technical report gives both the theory of ion trapping in Paul trap mass spectrometers and the technical specifications of mechanical assembly, vacuum chamber and other electronic subsystems associated with our laboratory’s Paul trap mass spectrometer. Section 2 gives the theory of the ion trap mass spectrometry including development of equations of ion motion and the conditions required for the ions to have stable trajectories inside the trap. Section 3 provides the technical specifications of our trap electrodes, electronic subsystems including constant current source, gating power supply, extraction power supply, high voltage dc power supply, RF signal generator as well as the vacuum system and graphical user interface are presented. Section 4 presents a few mass spectra to demonstrate the performance our mass spectrometer. Appendix 1 gives the detailed orcad layouts of all the electronic circuits associated with the Paul trap mass spectrometer and the technical data related to the National Instruments data acquisition device PCI-MIO-16-E-1 is given in Appendix 2. At the end of the report a few important and pertinent references are provided