Determination of Ion Frequencies in a Quadrupole Ion Trap By Using a Fast Direct Current Pulse as Pump and a Laser Probe

A new technique has been developed which allows the direct measurement of frequencies of ions trapped in a quadrupole ion trap mass spectrometer. This pump/probe method employs a fast direct current (DC) pulse (pump) to displace a kinetically cooled ion population from the center of the trap, and a laser (probe) which recognizes when ions reappear at the center of the trap by the formation of photodissociation fragments. The translationally excited ions undergo periodic motion within the confines of the ion trap, and this periodic motion can be followed by recording the intensity of the photodissociation fragment as a function of the delay time between the DC pump and the laser probe. The DC pulse has a rise time of 15 ns; data are taken 1 ms after its application to allow stable ion motion to be sampled. Sampling of the ion cloud is done at 50 ns intervals, and fast Fourier transformation of the time-based data yields the ion frequencies and their relative magnitudes. Data are reported for ions derived from acetophenone (m/z 105) and 1,4-cyclohexadiene (m/z 80) under various trapping conditions corresponding to different Mathieu q_z values. The measured fundamental secular frequencies, f_z and f_r, are found to agree well with those predicted. The presence of higher order multipole contributions to the trapping field is evident from such ion frequencies as the drive frequency, f_RF,. The ability to measure ion frequencies under operating conditions provides a new tool for comparing simulated and experimental data. Simulation data from the program ITSIM, modified to account for the effects of collisions, are shown to predict the major frequency components observed in the experimental data.     

Sensitivity and amplitude calibration of a Fourier transform 3D quadrupole ion trap mass spectrometer

With a three-dimensional (3D) quadrupole ion trap running in a Fourier transform operating mode, the detected signal is an image of the collective motion of the confined ions. Consequently, it is assumed that the image signal is the sum of the axial trajectories of the simultaneously confined ions. The resulting frequency spectrum after Fourier transformation comprises frequency peaks at the axial secular frequencies of the confined species according to their mass/charge ratio. With a singly confined species, the maximal amplitude of the image signal is proportional to the amplitude of the secular axial frequency peak. The matrix method is employed to express the axial trajectory sampled at the confinement field period. In that case, the expression of the image signal, as well as its maximal amplitude, is calculated as a function of the trap operating conditions and initial axial positions and axial velocities of the ions. The initial position and velocity distributions are connected to the injection mode. With the steady ion flow injection mode (SIFIM) and an initial phase of the confinement field equal to kπ, the maximal amplitude of the image signal is proportional to either the sum of the initial axial positions or the number of confined ions and the mean value of the initial axial positions. By simulation, amplitude fluctuation of the frequency peak is then calculated for a number of ions ranging between some tens to some thousands of ions injected by SIFIM. The peak amplitude fluctuations induced by the fluctuations of the number of ions are seven times greater than those induced by the fluctuations of the distribution of the initial axial positions.     

Determination of Positions,Velocities, and Kinetic Energies of Resonantly Excited Ions in the Quadrupole Ion Trap Mass Spectrometer by Laser Photodissociation

The effects on ion motion caused by the application of a resonance AC dipole voltage to the end-cap electrodes of the quadrupole ion trap are described. An excimer laser is used to photodissociate benzoyl ions, and its triggering is phase locked to the AC voltage to follow the motion of the ion cloud as a function of the phase angle of the AC signal. Resonantly excited ions maintain a coherent motion in the presence of He buffer gas, which dissipates energy from the ions via collisions. Maximum ion displacements, which depend upon the potential well depth (q _z value), occur twice each AC cycle. Axial components of ion velocities are determined by differentiating the displacements of the distributions with respect to time. The experimental data show that these velocities are maximized when the ion cloud passes through zero axial displacement, and they compare favorably with results calculated using a simple harmonic oscillator model. Axial components of ion kinetic energies are low (<5 eV) under the chosen experimental conditions. At low values of q2 (≈ 0.2), the width of the ion distribution increases as the ion cloud approaches the center of the trap and decreases as it approaches the end-cap electrodes. This effect is created by compaction of the ion trajectories when ion velocities are decreased,     

Characterization of an Electron Ionization Source Trap Operating in the Presence of a Magnetic Field Through Computer Simulation

We explore the feasibility of conducting electron ionization (EI) in a radio-frequency (rf) ion source trap for mass spectrometry applications. Electrons are radially injected into a compact linear ion trap in the presence of a magnetic field used essentially to lengthen the path of the electrons in the trap. The device can either be used as a stand-alone mass spectrometer or can be coupled to a mass analyzer. The applied parallel magnetic field and the oscillating rf electric field produced by the trap give rise to a set of coupled Mathieu equations of motion. Via numerical simulations, electron trajectories are studied under varying intensities of the magnetic field in order to determine the conditions that enhance ion production. Likewise, the dynamic behavior of the ions are investigated in the proposed EI source trap and the fast Fourier transform FFT formalism is used to obtain the frequency spectrum from the numerical simulations to study the motional frequencies of the ions which include combinations of the low-frequency secular and the high-frequency micromotion with magnetron and cyclotron frequencies. The dependence of these motional frequencies on the trapping conditions is examined and particularly, the limits of applying a radial magnetic field to the EI ion trap are characterized.

Reduction of axial kinetic energy induced perturbations on observed cyclotron frequency

With Fourier transform ion cyclotron resonance (FTICR) mass spectrometry one determines the mass-to-charge ratio of an ion by measuring its cyclotron frequency. However, the need to confine ions to the trapping region of the ion cyclotron resonance (ICR) cell with electric fields induces deviations from the unperturbed cyclotron frequency. Additional perturbations to the observed cyclotron frequency are often attributed to changes in space charge conditions. This study presents a detailed investigation of the observed ion cyclotron frequency as a function of ion z-axis kinetic energy. In a perfect three-dimensional quadrupolar field, cyclotron frequency is independent of position within the trap. However, in most ICR cell designs, this ideality is approximated only near the trap center and deviations arise from this ideal quadrupolar field as the ion moves both radially and axially from the center of the trap. To allow differentiation between deviations in observed cyclotron frequency caused from changes in space charge conditions or differences in oscillation amplitude, ions with identical molecular weights but different axial kinetic energy, and thus amplitude of z-axis motion, were simultaneously trapped within the ICR cell. This allows one to attribute deviations in observed cyclotron frequency to differences in the average force from the radial electric field experienced by ions of different axial amplitude. Experimentally derived magnetron frequency is compared with the magnetron frequency calculated using SIMION 7.0 for ions of different axial amplitude. Electron promoted ion coherence, or EPIC, is used to reduce the differences in radial electric fields at different axial positions. Thus with the application of EPIC, the differences in observed cyclotron frequencies are minimized for ions of different axial oscillation amplitudes.     

Direct observation of trapping motion in elongated fourier-transform mass spectrometry trapped ion cells

Measurements by Fourier-transform mass spectrometry (FTMS) have been used to measure trapping oscillation profiles in elongated trapped ion cells of length 10–43 cm. Trapping periods extracted from these profiles are found to vary linearly with cell length for elongated cells. This is in contrast with the prediction based on a quadrupolar approximation of the electric field that trapping period should increase exponentially with increased cell length. An alternate analytical expression for trapping motion is derived that better accounts for the motion of ions with sufficient energy to approach the trap plates. Calculated trapping frequencies are within a few percent of values determined from ion trajectory simulations for any combination of cell length, trap potential, ion mass, and ion kinetic energy. The new expression also explains the experimentally determined trapping data obtained in elongated cells. This expression predicts an average axial energy near 0.6 eV for the ions that are preferentially detected by FTMS with the specific pulse sequence employed. Department of Chemistry,     

Theoretical investigation on confinement of ions in a cube‐shaped ion trap

The confinement of ions in a cube‐shaped ion trap and the mathematical formalism governing the behavior of ions in the trap is investigated theoretically. Afterwards, the stability regions are computed using the fourth‐order Rung–Kutta method. Consequently, the influence of the direction of ions, injected into the trap from its center on the stability region, is numerically discussed. Moreover, the maximum angle of injection with respect to the vertical axis of the cube for which the ions could be confined in the trap without invoking any direct current component of voltage (henceforth referred to as limiting angle) was calculated. Strong linear correlation between the angle of injection and the ratio of the stability region areas is confirmed. A nonlinear feature of a cube‐shaped ion trap is demonstrated with a focus on the equations of motion for an ion confined into the trap. It is worthwhile to note that the stability region of our cubic ion trap, which has its own boundary conditions and electrodynamics, has been theoretically investigated for the first time. Besides, the limiting angle as well as the aforementioned strong linear correlation has not been reported in the literature previously. Copyright © 2015 John Wiley & Sons, Ltd.     

Quadrupole excitation of ions in linear quadrupole ion traps with added octopole fields

Modeling and experimental studies of quadrupole excitation of ions in linear quadrupole traps with added octopole fields are described. An approximate solution to the equations of motion of ions trapped in a quadrupole with added octopole and dodecapole fields, with quadrupole excitation and damping is given. The solutions give the steady-state or stationary amplitudes of oscillation with different excitation frequencies. Trajectory calculations of the oscillation amplitudes are also presented. The calculations show that there can be large changes in the amplitude of ion oscillation with small changes in excitation frequency, on both the low and high-frequency sides of a resonance. Results of experiments with quadrupole excitation of reserpine ions in linear quadrupole traps with 2.0%, 2.6%, and 4.0% added octopole fields are given. It is found that as the excitation frequency is changed, two resonances are generally observed, which are attributed to the motion in the x and y directions. The two resonances can have quite different intensities. Sudden jumps or sharp sided resonances are not observed, although in some cases asymmetric resonances are seen. The calculated frequency differences between the two resonances are in approximate agreement with the experiments.     

Ion trajectory simulation for electrode configurations with arbitrary geometries

A multi-particle ion trajectory simulation program ITSIM 6.0 is described, which is capable of ion trajectory simulations for electrode configurations with arbitrary geometries. The electrode structures are input from a 3D drawing program AutoCAD and the electric field is calculated using a 3D field solver COMSOL. The program CreatePot acts as interface between the field solver and ITSIM 6.0. It converts the calculated electric field into a field array file readable by ITSIM 6.0 and ion trajectories are calculated by solving Newton's equation using Runge-Kutta integration methods. The accuracy of the field calculation is discussed for the ideal quadrupole ion trap in terms of applied mesh density. Electric fields of several different types of devices with 3D geometry are simulated, including ion transport through an ion optical system as a function of pressure. Ion spatial distributions, including the storage of positively charged ions only and simultaneous storage of positively/negatively charged ions in commercial linear ion traps with various geometries, are investigated using different trapping modes. Inelastic collisions and collision induced dissociation modeled using RRKM theory are studied, with emphasis on the fragmentation of n-butylbenzene inside an ideal quadrupole ion trap. The mass spectrum of 1,3-dichlorobenzene is simulated for the rectilinear ion trap device and good agreement is observed between the simulated and the experimental mass spectra. Collisional cooling using helium at different pressures is found to affect mass resolution in the rectilinear ion trap.     

Surface-induced dissociation of molecular ions in a quadrupole ion trap mass spectrometer

A method is reported by which surface-induced dissociation is used to activate ions stored in a quadrupole ion trap mass spectrometer. The method employs a short (< 5 μs), fast-rising (< 20-ns rise time), high voltage direct current (dc) pulse, which is applied to the endcaps of a standard Paul-type quadrupole ion trap. This is in contrast to the application of an alternating current (ac) signal normally used to resonantly excite and dissociate ions in the trap. The effect of the dc pulse is to cause the ions rapidly to become unstable in the radial direction and subsequently to collide with the ring electrode. Sufficient internal energy is acquired in this collision to cause high energy fragmentations of relatively intractable molecular ions such as pyrene and benzene. The dissociations of limonene are used to demonstrate that high energy demand processes increase in relative importance in the dc pulse experiment compared with the usual resonance excitation method used to cause activation. The fragments are scanned out of the ion trap using the conventional mass-selective instability scan mode. Simulations of ion motion in the trap provide evidence that surface collisions occur at kinetic energies in the range of tens to several hundred electronvolts. The experiments also demonstrate that production of fragment ions is sensitive to the phase of the main radiofrequency drive voltage at the point when the dc is initiated.     

A modified homotopy perturbation method and the axial secular frequencies of a non-linear ion trap

In this paper, a modified version of the homotopy perturbation method, which has been applied to non-linear oscillations by V. Marinca, is used for calculation of axial secular frequencies of a non-linear ion trap with hexapole and octopole superpositions. The axial equation of ion motion in a rapidly oscillating field of an ion trap can be transformed to a Duffing-like equation. With only octopole superposition the resulted non-linear equation is symmetric; however, in the presence of hexapole and octopole superpositions, it is asymmetric. This modified homotopy perturbation method is used for solving the resulting non-linear equations. As a result, the ion secular frequencies as a function of non-linear field parameters are obtained. The calculated secular frequencies are compared with the results of the homotopy perturbation method and the exact results. With only hexapole superposition, the results of this paper and the homotopy perturbation method are the same and with hexapole and octopole superpositions, the results of this paper are much more closer to the exact results compared with the results of the homotopy perturbation method.     

Matrix methods for the calculation of stability diagrams in quadrupole mass spectrometry

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 omega = Nomega/P (where N, P are integers and omega is the angular frequency of the trapping field) leads to splitting of the stability diagram along iso-beta 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.     

Dipole excitation of ions in linear radio frequency quadrupole ion traps with added multipole fields

Ion motion with auxiliary dipole excitation and collisional damping in a linear radiofrequency quadrupole ion trap incorporating small amounts of even higher order multipoles is studied analytically. The ion motion is modeled in a pseudopotential that is mostly quadratic with small amounts of higher spatial harmonics. Ion motion along x and y axes is characterized by two uncoupled forced and damped anharmonic oscillator equations. A multiple time scales method is used to solve the equations of motion of ions with a first order perturbation correction. Analytical relations between the oscillation amplitudes at steady state (the stationary amplitudes) and excitation frequency are calculated. The frequency response curves show that in some cases bistable behavior might be obtained, i.e., there are two stable stationary amplitudes for a given excitation frequency.     

Dynamic collision-induced dissociation (DCID) in a quadrupole ion trap using a two-frequency excitation waveform: II. Effects of frequency spacing and scan rate

Dynamic CID of selected precursor ions is achieved by the application of a two-frequency excitation waveform to the end-cap electrodes during the mass instability scan of a quadrupole ion trap (QIT) mass spectrometer. This new method permits a shorter scanning time when compared with conventional on-resonance CID. When the excitation waveform consists of two closely-spaced frequencies, the relative phase-relationship of the two frequencies plays a critical role in the fragmentation dynamics. However, at wider frequency spacings (>10 kHz), these phase effects are diminished, while maintaining the efficacy of closely-spaced excitation frequencies. The fragmentation efficiencies and energetics of n-butylbenzene and tetra-alanine are studied under different experimental conditions and the results are compared at various scan rate parameters between 0.1 and 1.0 ms/Th. Although faster scan rates reduce the analysis time, the maximum observed fragmentation efficiencies rarely exceed 30%, compared with values in excess of 50% achieved at slower scan rates. The internal energies calculated from the simulations of n-butylbenzene at fast scan rates are approximately 4 eV for most experimental conditions, while at slow scan rates, internal energies above 5.5 eV are observed for a wide range of conditions. Extensive ITSIM simulations support the observation that slowing the scan rate has a similar effect on fragmentation as widening the frequency spacing between the two excitation frequencies. Both approaches generally enhance CID efficiencies and make fragmentation less dependent upon the relative phase angle between the excitation waveform and the ion motion.     

Kinetic energy effects in an ion ensemble subjected to mass-selective isolation and resonance excitation: A simulation study

A simulation study is described of the behaviour of ions confined in a quadrupole ion trap during each of two separate operations of a tandem mass spectrometric experiment. The two operations are those of mass-selective ion isolation and mass-selective resonance excitation to the point of ion ejection from the ion trap. The method of mass-selective ion isolation simulated is that of consecutive ion isolation. Simulation data indicate that the collisional history of the ions prior to the isolation process can greatly influence the degree to which ions survive this process. Simulation data for mass-selective resonance ejection are compared with experimental data obtained with a Finnigan-MAT ion trap mass spectrometer. In each operation, the facility with which ions absorb energy from the field within the ion trap, whether this field is derived from the R.F. drive potential or a supplementary potential, can determine the extent to which ions are retained within the ion trap during the two mass-selective operations described.     

Model for ion injection into a quadrupole ion trap to assess the distribution of initial conditions of confinement

A pulsed ion-injection mode for a quadrupole ion trap is described. Switched direct current (d.c.) potentials are applied to the source and trap electrodes to inject the ions into the trap and slow them down. The injection time is sufficient to ensure a steady distribution of the injected ions at the beginning of the confinement.An elementary uni-dimensional model is detailed giving the axial positions and velocities of the ions injected into the trap. The ion distribution in phase space, the number of injected ions and the number of injected ions that will be trapped are also given. These expressions depend on ion position and velocity at the creation, applied potentials and spatial location of the source and trap electrodes.This model is validated by comparing simulation and experimental results. For this purpose the number of confined ions is plotted versus the slowing-down potentials applied on the ring and the upper end-cap of the trap. The size of the area of removable ions in the source is deduced from these results.     

Theoretical Study of Dual-Direction Dipolar Excitation of Ions in Linear Ion Traps

The ion enhanced activation and collision-induced dissociation (CID) by simultaneous dipolar excitation of ions in the two radial directions of linear ion trap (LIT) have been recently developed and tested by experiment. In this work, its detailed properties were further studied by theoretical simulation. The effects of some experimental parameters such as the buffer gas pressure, the dipolar excitation signal phases, power amplitudes, and frequencies on the ion trajectory and energy were carefully investigated. The results show that the ion activation energy can be significantly increased by dual-direction excitation using two identical dipolar excitation signals because of the addition of an excitation dimension and the fact that the ion motion radius related to ion kinetic energy can be greater than the field radius. The effects of higher-order field components, such as dodecapole field on the performance of this method are also revealed. They mainly cause ion motion frequency shift as ion motion amplitude increases. Because of the frequency shift, there are different optimized excitation frequencies in different LITs. At the optimized frequency, ion average energy is improved significantly with relatively few ions lost. The results show that this method can be used in different kinds of LITs such as LIT with 4-fold symmetric stretch, linear quadrupole ion trap, and standard hyperbolic LIT, which can significantly increase the ion activation energy and CID efficiency, compared with the conventional method.

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Action spectroscopy and temperature diagnostics of H+ 3 by chemical probing

Infrared absorption spectroscopy of few hundred H+(3) ions trapped in a 22-pole ion trap is presented using chemical probing as a sensitive detection technique down to the single ion level. By exciting selected overtone transitions of the (v(1)=0,v(2) (l)=3(1))<--(0,0(0)) vibrational band using an external cavity diode laser an accurate diagnostics measurement of the effective translational and rotational temperatures of the trapped ions was performed. The absolute accuracy of the measured transition frequencies was improved by a factor of four compared to previous plasma spectroscopy measurements using velocity modulation [Ventrudo et al., J. Chem. Phys. 100, 6263 (1994)]. The observed buffer gas cooling conditions in the ion trap indicate how to cool trapped H+(3) ions into the lowest ortho and para rotational states. Future experiments will utilize such an internally cold ion ensemble for state-selected dissociative recombination experiments at the heavy ion storage ring Test Storage Ring (TSR).     

Proposal for radio-frequency spectroscopy of molecular ions

A method is proposed for the detection of low-frequency spectroscopic transition in gaseous molecular ions by monitoring the motion induced by inhomogeneous fields at the sum frequency of harmonic motion in an ion trap and the transition frequency. Numerical examples are given.     

Ion motion in the rectangular wave quadrupole field and digital operation mode of a quadrupole ion trap mass spectrometer

A quadrupolar electric field driven by a rectangular wave voltage can be used for mass-selective storage and analysis. The ion motion in such an electric field is derived, and the stability of ions is presented in the a-q diagram that is commonly used for sinusoidal wave quadrupole mass spectrometry in association with the solution of the Mathieu equation. The pseudo-potential well is discussed in an approximation that leads to the relation of secular frequency to operating parameters. A scheme for a digital ion trap mass spectrometer is described, based on this theory. An ion optics simulation was performed to check the theory of resonant ejection, and to prove the feasibility of the mass scan method for a practical ion trap of such geometry.