Ion excitation in a linear quadrupole ion trap with an added octopole field

Modeling of ion motion and experimental investigations of ion excitation in a linear quadrupole trap with a 4% added octopole field are described. The results are compared with those obtained with a conventional round rod set. Motion in the effective potential of the rod set can explain many of the observed phenomena. The frequencies of ion oscillation in the x and y directions shift with amplitude in opposite directions as the amplitudes of oscillation increase. Excitation profiles for ion fragmentation become asymmetric and in some cases show bistable behavior where the amplitude of oscillation suddenly jumps between high and low values with very small changes in excitation frequency. Experiments show these effects. Ions are injected into a linear trap, stored, isolated, excited for MS/MS, and then mass analyzed in a time-of-flight mass analyzer. Frequency shifts between the x and y motions are observed, and in some cases asymmetric excitation profiles and bistable behavior are observed. Higher MS/MS efficiencies are expected when an octopole field is added. MS/MS efficiencies (N(2) collision gas) have been measured for a conventional quadrupole rod set and a linear ion trap with a 4% added octopole field. Efficiencies are chemical compound dependent, but when an octopole field is added, efficiencies can be substantially higher than with a conventional rod set, particularly at pressures of 1.4 x 10(-4) torr or less.     

Mass selective axial ion ejection from linear quadrupoles with added octopole fields

Mass selective axial ejection of ions from linear quadrupoles with added octopole fields is described. Quadrupoles with 2.0% and 2.6% added octopole fields have been tested and compared with a conventional quadrupole. The effects of trapping ions at different q values, excitation voltage, scan direction, balanced and unbalanced rf voltages on the rods, and dc applied between the rods have been investigated. The highest scan speeds and best resolution are obtained with resonant excitation and ejection at high q (q = 0.8). With axial ejection, the quadrupole with a 2.0% added octopole field provides mass resolution and ejection efficiencies similar to a conventional rod set. Quadrupole, dipole, and simultaneous dipole-dipole excitation between the x and y rod pairs were compared, and no advantage was found with quadrupole or dipole-dipole excitation. The effects of scan speed were investigated and a resolution at half height of about 1600 is possible at scans speed up to 5000 Th/s.     

Linear quadrupoles with added hexapole fields

Linear quadrupoles with added hexapole fields are described. The shifts in ion oscillation frequency caused by the addition of a hexapole field are calculated within the effective potential model. Methods to construct linear quadrupoles with added hexapole fields with exact electrode geometries and with round rods are discussed. A quadrupole with added hexapole field can be constructed with round rods by rotating two rods (say the y rods) towards an x rod. Computer simulations are used to investigate the possibility of mass analysis with quadrupoles with added hexapole fields. We find that a quadrupole with an added hexapole field in the range 2-12% can provide mass analysis provided the dc is applied with the correct polarity and value. When a rod set is constructed with round rods, other multipoles in the potential degrade the peak shape, resolution and transmission. The largest of these after the quadrupole and hexapole are a dipole and octopole term. With round rod sets, the peak shape can be improved by using different diameters for the x and y rod pairs to minimize the octopole term in the potential and by injecting ions at the field center where the dipole term is zero. Calculations of the boundaries of the stability diagram for this case show the boundaries move out, relative to those of a pure quadrupole field, but remain sharp.     

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.     

Linear quadrupoles with added octopole fields

Two methods of adding relatively small octopole fields to the main quadrupole field of quadrupoles and linear ion traps with cylindrical rods are investigated. The first, 'stretching' the quadrupole by moving two rods out from the axis, produces a combination of higher order fields with similar magnitudes in which the octopole field is not necessarily the greatest. The quadrupole field strength is changed significantly and a large potential appears on the axis. The second method uses rod pairs of different diameters. It adds octopole components of up to several percent while all other higher order fields remain small. An axis potential is also added, but it is only a few percent of the radio-frequency (RF) voltage and approximately equal to the strength of the octopole field. The axis potential can be removed by moving the larger rod pair out from the axis or applying unbalanced RF to the electrodes.     

Quadrupole mass filters with octopole fields

The performance of quadrupole mass filters with added octopole fields in the range 2.0-4.0% has been investigated. The added fields are much greater than those normally added to conventional rod sets by mechanical tolerances or construction errors. Quadrupole rod sets with added octopole fields were constructed with round rods by making one pair of rods greater in diameter than the other pair. For positive ions, resolution at half height of only about 200 is possible if the negative direct current (dc) output of the quadrupole power supply is connected to the smaller rods. If the positive dc output of the quadrupole power supply is connected to the smaller rods, the resolution improves dramatically; a resolution at half height of 5800 has been observed with a rod set with 2.6% added octopole field. For negative ions the best resolution is obtained with the polarity of the dc reversed, i.e. with the negative dc applied to the smaller rods. These findings are unexpected in view of the literature that argues that to obtain high mass resolution with quadrupole mass filters, higher order multipoles must be kept as small as possible. Numerical simulations of peak shapes agree qualitatively with experiments. Simulation of the boundaries of the first stability region for positive ions shows that when the positive dc is applied to the smaller rods, the addition of a 2.0% octopole field causes the boundaries to shift slightly but the boundaries are well defined, and the tip of the stability region remains sharp. When the positive dc is applied to the larger rods, the boundaries of the stability region move out and become diffuse. For instruments that require a rod set that can be used both as a linear trap and a mass filter, these rod sets may offer improved trap performance while still being capable of providing conventional mass analysis.     

Mass analysis in islands of stability with linear quadrupoles with added octopole fields

Mass analysis with linear quadrupole mass filters is possible by forming "islands" in the stability diagram with auxiliary quadrupole excitation. In this work, computer simulations are used to calculate stability boundaries, island positions, and peak shapes and ion transmission for mass analysis with linear quadrupole mass filters that have added octopole fields of about 2 to 4%. Rod sets with exact geometries that have quadrupole and octopole fields only in the potential, and round rod sets, with multipoles up to N = 10 (the twenty pole term) included in the calculations, show the same stability boundaries, island positions, and peak shapes. With the DC voltage applied to the rods so that the Mathieu parameter a < 0, conventional mass analysis is possible without the use of an island. With the DC polarity reversed so that a > 0, the resolution and transmission are poor preventing conventional mass analysis. In principle, mass analysis in an island is possible with operation at either of two tips. Provided the correct island tip is chosen for mass analysis, peak shapes comparable to those with a > 0 and no excitation are possible, both with a > 0 and with a < 0. In the latter case, the use of an island of stability allows mass analysis when the added octopole otherwise prevents conventional mass analysis.     

Space Charge Induced Nonlinear Effects in Quadrupole Ion Traps

A theoretical method was proposed in this work to study space charge effects in quadrupole ion traps, including ion trapping, ion motion frequency shift, and nonlinear effects on ion trajectories. The spatial distributions of ion clouds within quadrupole ion traps were first modeled for both 3D and linear ion traps. It is found that the electric field generated by space charge can be expressed as a summation of even-order fields, such as quadrupole field, octopole field, etc. Ion trajectories were then solved using the harmonic balance method. Similar to high-order field effects, space charge will result in an “ocean wave” shape nonlinear resonance curve for an ion under a dipolar excitation. However, the nonlinear resonance curve will be totally shifted to lower frequencies and bend towards ion secular frequency as ion motion amplitude increases, which is just the opposite effect of any even-order field. Based on theoretical derivations, methods to reduce space charge effects were proposed.

The coupling effects of hexapole and octopole fields in quadrupole ion traps: a theoretical study

A theoretical method, the harmonic balance method, was introduced to study the coupling effects of hexapole and octopole fields on ion motion in a quadrupole ion trap. Ion motion characteristics, such as ion motion center displacement, ion secular frequency shift, nonlinear resonance curve and buffer gas damping effects, have been studied with the presence of both hexapole and octopole fields. It is found that hexapole fields have bigger impacts on ion motion center displacement, while octopole fields dominate ion secular frequency shift. Furthermore, the nonlinear features originated from hexapole and octopole fields could enhance or cancel each other, which provide us more space in a practical ion trap design process. As an example, an ion trap with improved performance was designed using a specific combination of hexapole and octopole fields. In this ion trap, a hexapole field was used to achieve efficient ion directional ejection, while an octopole field was added to correct the chemical mass shift and resolution degradation introduced by the hexapole field. Copyright © 2013 John Wiley & Sons, Ltd.     

Experimental investigation of mass analysis using an island of stability with a quadrupole with 2.0% added octopole field

We describe experimental investigations of mass analysis using an island of stability with a linear quadrupole with a 2.0% added octopole field. The island is formed by auxiliary quadrupole excitation. The experiments confirm the results of previous computer simulations (Konenkov et al., J. Am. Soc. Mass Spectrom. 2007; 18: 826-834). With the resolving direct current (dc) applied to the quadrupole so that the Mathieu parameter a > 0, conventional mass analysis with applied radio-frequency (rf) and dc and no auxiliary excitation is possible. In this case, use of an island of stability yields similar peak shape and resolution. However, with the polarity of the resolving dc reversed, so that a < 0, only very low resolution can be obtained; the added octopole prevents conventional mass analysis. By using a stability island when a < 0, the resolution is substantially improved. In this case the use of an island allows mass analysis under conditions where the added octopole field severely degrades conventional analysis. The experiments also confirm the position of the island predicted by the simulations.     

Characteristics of stability boundary and frequency in nonlinear ion trap mass spectrometer

In this article, the Poincare-Lighthill-Kuo (PLK) method is used to derive an analytical expression on the stability boundary and the ion trajectory. A multipole superposition model mainly including octopole component is adopted to represent the inhomogeneities of the field. In this method, both the motional displacement and secular frequency of ions have been expanded to asymptotic series by the scale of nonlinear term ε, which represents a weak octopole field. By solving the zero and first-order approximate equations, it is found that a frequency shift exists between the ideal and nonlinear conditions. The motional frequency of ions in nonlinear ion trap depends on not only Mathieu parameters, a and q, but also the percentage of the nonlinear field and the initial amplitude of ions. In the same trap, ions have the same mass-to-charge ratio (m/z) but they have different initial amplitudes or velocities. Consequently, they will be ejected at different time through after a mass-selective instability scan. The influences on the mass resolution in quadrupole ion trap, which is coupled with positive or negative octopole fields, have been discussed respectively.     

Relative dissociation energy measurements using ion trap collisional activation

The measured minimum resonance excitation amplitudes for decomposition of polyatomic ions in the quadrupole ion trap collisional activation experiment are shown to correlate with literature critical energies. The present article describes how experiments can be performed to derive threshold resonance excitation amplitudes via the kinetics associated with collision-induced dissociation (i.e., dissociation rate constants) in the quadrupole ion trap. The relationship between these threshold values and critical energies is established empirically by using kinetic data acquired for molecular ions with critical energies measured with other techniques. The experiments are complicated by the change in optimum resonance excitation frequency with amplitude, due presumably to contributions from higher order fields. It is proposed that the threshold resonance excitation amplitude is a measure of the change in temperature of the parent ion population required to achieve a measurable rate of decomposition. The present results indicate that the quadrupole ion trap may see new applications as a quantitative tool for the study of gaseous ion chemistry.     

Increased Fragmentation Efficiency of Ions in a Low Pressure Linear Ion Trap with an Added dc Octopole Field

In-trap fragmentation of ions in a hybrid linear ion trap triple quadrupole mass spectrometer occurs at pressures about 5e-5 torr. At these low pressures, efficient fragmentation of heavy ions (such as the singly charged homogenously substituted triazatriphosphorine of mass 2721.89 Da) can take a long time because of the relatively low collision frequency with the background gas and the high internal energy content required to produce fragmentation. Increasing the amplitude used for dipolar excitation leads to loss of the ion upon the quadrupole rods. In the work presented here, the addition of a dc octopolar field to a linear ion trap is described. The dc octopolar field was created by the addition of four auxiliary electrodes situated between the quadrupole rods at a distance of 10 mm from the axis. The inclusion of the dc octopolar field was shown to cause the ions’ frequency of motion to shift out of phase with the excitation signal at high radial amplitudes. This resulted in beat-like trajectories with periods of excitation and de-excitation as the ions’ frequency of motion shifted in and out of phase with the excitation signal. This led to a reduction in the loss of ions on the quadrupole rods during the excitation process. The result is an increased fragmentation efficiency relative to the fragmentation efficiency obtained when using an LIT constructed of round rods only. The inclusion of the dc octopolar field allowed the ion to be fragmented more efficiently in a relatively short excitation period.     

Nonlinear resonance effects during ion storage in a quadrupole ion trap

Contributions of higher-order fields to the quadrupolar storage field produce nonlinear resonances in the quadrupole ion trap. Storing ions with secular frequencies corresponding to these nonlinear resonances allows adsorption of power from the higher-order fields. This results in increased axial and radial amplitudes which can cause ion ejection and collision-induced dissociation (CID). Experiments employing long storage times and/or high ion populations, such as chemical ionization, ion-molecule reaction studies, and resonance excitation CID, can be particularly susceptible to nonlinear resonance effects. The effects of higher-order fields on stored ions are presented and the influence of instrumental parameters such as radiofrequency and direct current voltage (q_z and a_z values), ion population, and storage time are discussed.     

Potential Distribution and Transmission Characteristics in a Curved Quadrupole Ion Guide

The potential distribution in the curved quadrupole is exactly characterized by the Laplace equation, and an approximate solution to the Laplace equation is calculated. We represent the Laplace equation under the coordinates named minimal rotation frame (MRF) and derive an expression on the hexapole and octopole superposition. Our conclusion is in agreement with the results by the numerical (SIMION) method. Based on the Poincare-Lighthill-Kuo (PLK) method reported in our previous work, the nonlinear effects of ion motion are investigated in detail. The frequency shift of ion motion can be well eliminated by coupling the hexapole component with a positive octopole component, and the transmission efficiency of ions is found to decrease dramatically with the increase of the ionic kinetic energy in the z-direction. Furthermore, the transmission characteristics of ions are discussed with regards to the phase-space theory. The results show that the centrifugally introduced axis shift is mainly responsible for the ion losses. A modified direct current (dc) voltage supply pattern is hence proposed to compensate for this effect.     

Excitation frequencies of ions confined in a quadrupole field with quadrupole excitation

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.     

The non-linear ion trap. Part 5. Nature of non-linear resonances and resonant ion ejection

The superposition of higher order multipole fields on the basic quadrupole field in ion traps generates a non-harmonic oscillator system for the ions. Fourier analyses of simulated secular oscillations in non-linear ion traps, therefore, not only reveal the sideband frequencies, well-known from the Mathieu theory, but additionally a commonwealth of multipole-specific overtones (or higher harmonics), and corresponding sidebands of overtones. Non-linear resonances occur when the overtone frequencies match sideband frequencies. It can be shown that in each of the resonance conditions, not just one overtone matches one sideband, instead, groups of overtones match groups of sidebands.The generation of overtones is studied by Fourier analysis of computed ion oscillations in the direction of thez axis. Even multipoles (octopole, dodecapole, etc.) generate only odd orders of higher harmonics (3, 5, etc.) of the secular frequency, explainable by the symmetry with regard to the planez = 0. In contrast, odd multipoles (hexapole, decapole, etc.) generate all orders of higher harmonics. For all multipoles, the lowest higher harmonics are found to be strongest. With multipoles of higher orders, the strength of the overtones decreases weaker with the order of the harmonics.Forz direction resonances in stationary trapping fields, the function governing the amplitude growth is investigated by computer simulations. The ejection in thez direction, as a function of timet, follows, at least in good approximation, the equation

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wheren is the order of multipole, andC is a constant.This equation is strictly valid for the electrically applied dipole field (n = 1), matching the secular frequency or one of its sidebands, resulting in a linear increase of the amplitude. It is valid also for the basic quadrupole field (n = 2) outside the stability area, giving an exponential increase. It is at least approximately valid for the non-linear resonances by weak superpositions of all higher odd multipoles (n = 3,5,…), showing hyperbolically increasing amplitudes, whereas the even multipoles strongly suppress their ownz direction non-linear resonances. The hyperbolic increase of the amplitude, having a mathematical pole, explains the fast ejection processes possible with non-linear resonances.     

Space-charge effects with mass-selective axial ejection from a linear quadrupole ion trap

Methods to reduce mass shifts caused by space charge with mass‐selective axial ejection from a linear quadrupole ion trap are investigated. For axial ejection, dipole excitation is applied to excite ions at q ≈ 0.85. The trapping radiofrequency (rf) voltage is scanned to bring ions of different m/z values into resonance for excitation. In the fringing field at the quadrupole exit, excited ions gain axial kinetic energy, overcoming the trapping potential, and are ejected from the trap. Space charge causes the frequencies of ion oscillation to decrease. Thus, greater rf voltages are required to bring ions into resonance for excitation and ejection, and the ions shift to higher apparent masses in a mass spectrum. At the same time, the peaks broaden, lowering resolution. The effects of injection q value, ejection q value, excitation amplitude, quadrupole dc voltages applied to the electrodes, applying an rf voltage to the exit lens, and scan speed, on mass shifts have been studied experimentally. Most experiments were done with only ions of protonated reserpine (m/z 609.3 and its isotopic peaks) in the trap. Some experiments were done with ions of protonated reserpine and ions of m/z 622 in the trap. In general, the mass shifts are reduced with higher ejection q values, higher excitation amplitudes, with quadrupole dc applied, and at higher scan speeds. The application of quadrupole dc appears to increase the ion cloud temperature, which lowers mass shifts. Thus, a proper choice of operating conditions can reduce, but not eliminate, mass shifts caused by space charge. Copyright © 2011 John Wiley & Sons, Ltd.     

Resonance shifts in the excitation of the n = 0, K = 1 to 6 quadrupolar resonances for ions confined in a linear ion trap

Experiments examining the excitation of the quadrupolar n = 0, K = 1 to 6 resonances for the ion reserpine in a linear ion trap have been shown to produce resonance shifts that were dependent upon either or both of the excitation amplitude and trap pressure (Collings, B. A.; Douglas, D. J. J. Am,. Soc. Mass Spectrom., 2000, 11, 1016-1022). The extent of this dependency was determined by examining the effects of each parameter using an ion trajectory simulator. The simulations indicated that it is the change in excitation amplitude that is mostly responsible for the resonance shifts with a minor dependency upon the trapping pressure. It was found that the higher excitation amplitudes required to observe the higher order resonances resulted in greater shifts relative to the theoretical resonances predicted for an excitation amplitude of zero volts. The nature of these shifts can be understood by examining the equations of motion for an ion trapped in a quadrupolar potential during the excitation process. Rearrangement of the equations of motion lead to a Mathieu stability diagram in which the coordinate and ordinate variables are dependent upon the excitation frequency and amplitude. In such a diagram the resonances occur in the regions of instability. The calculated resonance shifts showed good correlation with the experimental and simulation results.     

Observation of higher order quadrupole excitation frequencies in a linear ion trap

The resonant frequencies for quadrupole excitation of ions confined with a buffer gas in a linear quadrupole ion trap with Mathieu parameters a = 0 and q ∼ 0.36 have been measured. The resonances are predicted to occur at angular frequencies ω _n ^K given by ω _n ^K = (Ώ/K)|n + β| without the presence of a buffer gas where ϒ is the angular frequency of the trapping radio frequency, K = 1,2,3 … is the order of the resonance calculated with perturbation theory, and n = 0, ±1, ±2, ±3 …. The resonances are measured through fragmentation of protonated reserpine. The observed frequencies agree closely with the theoretical values but there are small differences which vary from +0.6% at K = 2 to −2.7% at K = 6. This is believed to be the result of the dependence of the resonant frequencies upon the buffer gas density and/or the excitation amplitude. The resolution of the resonances (measured from the depletion of precursor and formation of fragment ions) increased by a factor of 2 as K increased from 1 to 6. This increase in resolution warrants further investigation into the use of higher order resonances for isolation and excitation of trapped ions.