Experimental Characterization of Secular Frequency Scanning in Ion Trap Mass Spectrometers

  • Dalton T. Snyder
  • Christopher J. Pulliam
  • Joshua S. Wiley
  • Jason Duncan
  • R. Graham Cooks
Research Article


Secular frequency scanning is implemented and characterized using both a benchtop linear ion trap and a miniature rectilinear ion trap mass spectrometer. Separation of tetraalkylammonium ions and those from a mass calibration mixture and from a pesticide mixture is demonstrated with peak widths approaching unit resolution for optimized conditions using the benchtop ion trap. The effects on the spectra of ion trap operating parameters, including waveform amplitude, scan direction, scan rate, and pressure are explored, and peaks at black holes corresponding to nonlinear (higher-order field) resonance points are investigated. Reverse frequency sweeps (increasing mass) on the Mini 12 are shown to result in significantly higher ion ejection efficiency and superior resolution than forward frequency sweeps that decrement mass. This result is accounted for by the asymmetry in ion energy absorption profiles as a function of AC frequency and the shift in ion secular frequency at higher amplitudes in the trap due to higher order fields. We also found that use of higher AC amplitudes in forward frequency sweeps biases ions toward ejection at points of higher order parametric resonance, despite using only dipolar excitation. Higher AC amplitudes also increase peak width and decrease sensitivity in both forward and reverse frequency sweeps. Higher sensitivity and resolution were obtained at higher trap pressures in the secular frequency scan, in contrast to conventional resonance ejection scans, which showed the opposite trend in resolution on the Mini 12. Mass range is shown to be naturally extended in secular frequency scanning when ejecting ions by sweeping the AC waveform through low frequencies, a method which is similar, but arguably superior, to the more usual method of mass range extension using low q resonance ejection.

Graphical Abstract


Ion motion Simulations Miniature mass spectrometer Tandem mass spectrometry Higher order fields Collision-induced dissociation Ion ejection 


Quadrupole and linear ion traps are common mass analyzers because of their excellent sensitivity, relatively high operating pressures (mTorr) compared to other analyzers, tolerance for imperfect electric fields, and capabilities for single analyzer collision-induced dissociation (CID) [1, 2]. Methods of scanning quadrupole-based analyzers can be deduced from the Mathieu parameters au and qu, which describe the stability of ions in a quadrupolar field [3, 4]:
$$ {\mathrm{a}}_{\mathrm{u}}=8\mathrm{z}e\mathrm{U}\ /{\varOmega}^2{{\mathrm{r}}_0}^2\mathrm{m} $$
$$ {\mathrm{q}}_{\mathrm{u}}=4\mathrm{z}e\mathrm{V}/{\varOmega}^2{{\mathrm{r}}_0}^2\mathrm{m} $$
where z is the integral charge on the ion, u is the respective dimension (x, y, r, or z), e is the unit elementary charge, U is the amplitude of the DC potential applied between the rods, V is the amplitude of the radio frequency (rf) potential applied to the rods, Ω = 2πf is the angular frequency of the rf potential (f = frequency of the rf), r0 is the characteristic size of the quadrupole or trap (typically the half distance between the rods), and m is the mass of the ion. Assuming the field is purely quadrupolar and solving these parameters for m/z with the understanding that z is now the charge of the ion in coulombs, we obtain
$$ m/z = 8\mathrm{U}/\mathrm{a}{\varOmega}^2{{\mathrm{r}}_0}^2 $$
$$ m/z=4\mathrm{V}\ /\mathrm{q}{\varOmega}^2{{\mathrm{r}}_0}^2. $$

The four experimental parameters that determine the stability of an ion in a quadrupolar field are thus (1) the amplitude of the dc potential, (2) the frequency of the applied fundamental rf waveform, (3) the radius of the device, and (4) the rf amplitude.

In a quadrupole mass filter [5], ions are selected for detection by mass selective stability [6], wherein the amplitudes of the rf and DC are increased while either keeping their ratio constant (constant resolution) or changing their ratio slightly to increase resolving power with mass and maintain unit resolution. With this method, ions of consecutive masses are successively brought to the apex of the Mathieu stability diagram, causing all other ions to become unstable. If the ramp of the rf and DC components is linear, time domain current or voltage data are linearly related to m/z. That is, m/z is directly proportional to the rf/DC amplitude.

By contrast, quadrupole ion traps operate on the basis of mass selective instability [7]. In this technique, typically no DC component is used (U = au = 0), placing all ions on the q axis of the Mathieu stability diagram. The rf amplitude is ramped linearly as a function of time, causing ejection of ions of increasing m/z as they are brought successively to the ejection point (q = 0.908). The ions detected are thus those that are unstable, whereas only stable ions are detected in a conventional quadrupole mass filter. Since m/z is directly proportional to the rf amplitude, the time domain data correspond directly to the mass spectrum. Resonance ejection is a similar scan mode in which a “hole” is created on the q axis of the stability diagram by also applying a small supplementary dipolar AC voltage to eject ions whose secular frequencies match the frequency of the applied AC signal [8]. As before, the rf is ramped, causing ions’ secular frequencies to change; when ions of particular m/z come into resonance with the frequency of the applied AC, these ions are mass-selectively ejected.

Alternative methods of scanning quadrupoles and ion traps exist but are uncommon. Scanning the frequency of the fundamental rf is a variant on the mass-selective instability scan that has been performed by only a few groups. The first report of rf frequency scanning demonstrated advantages for analysis of high mass ions [9], and subsequent reports demonstrated frequency scanning in a quadrupole mass filter with ions ranging in size from mass 176 Da [10] to microparticles [11]. Frequency scanning has also been reported in specially designed digital ion traps, which do not have rf amplitude scan capabilities but which have demonstrated exceptionally fast scan rates while maintaining reasonable resolution (unit resolution for a 100 Hz scan rate, peak widths FWHM ~2.0 Th for a 1000 Hz scan rate) [12, 13, 14]. These scan methods simplify the electronics, but there remain problems of nonlinearity in mass calibration (save for the linear calibration described in ref. [14]), unexpected peaks, and poor mass resolution [15]. As a result, traditional rf amplitude sweeps have remained the favored method of ion trap operation. It is also theoretically possible to sweep the size of the device (r0), but this is impossible in practice [16].

An interesting alternative to sweeping either the rf amplitude or frequency is to instead sweep the frequency of a supplementary AC waveform (Figure S1), that is, to perform secular frequency scanning using an applied dipolar signal. Each ion then has a set of induced frequencies, ⍵u,n, dependent upon trap parameters and m/z [17, 18, 19, 20, 21], which can described by
$$ {\upomega}_{\mathrm{u},\mathrm{n}}=\left(2\mathrm{n}+{\upbeta}_{\mathrm{u}}\right)\varOmega /2\kern2.25em -\infty <\mathrm{n}<\infty $$
where n is an integer, u is the axis of interest (x, y, or z) and a new parameter βu (0 ≤ βu ≤ 1), which is m/z-dependent under fixed operating conditions, has been introduced. Parametric (quadrupolar) resonances can also be excited in certain circumstances, with the main resonance (n = 0, K = 1) occurring at twice the secular frequency. Higher order quadrupolar resonances are predicted to occur when
$$ {\upomega}_{\mathrm{u},\mathrm{n}}=\left|\mathrm{n}+{\upbeta}_{\mathrm{u}}\right|\varOmega /\ \mathrm{K}-\infty <\mathrm{n}<\infty; \mathrm{K}=1,2, \dots, $$
where K is the order of the resonance [22, 23]. They have been described by Collings et al. [22, 23], who used parametric (quadrupolar) excitation to observe these signals. These resonances would appear to require parametric excitation although we show below that they can be accessed using dipolar excitation. The parametric excitation experiment is performed by applying AC signals to the ring and endcap electrodes (in a 3D ion trap), with the ring and endcap excitation signals 180° out of phase. Importantly, in order to eject ions using quadrupolar excitation, the excitation force threshold, fex, must be exceeded [21]. This threshold is given by
$$ {\mathrm{f}}_{\mathrm{ex}}=\alpha {\uplambda}^{1/\mathrm{K}} $$
where alpha is a constant and lambda is a damping constant. That is, in order to excite/eject ions at higher order quadrupolar resonances, a higher waveform amplitude is required. Equivalent higher order dipolar resonances have not been reported, but we will show that— remarkably—dipolar excitation can eject ions at the higher order quadrupolar resonances due to the coupling of motion in r and z (or x and y) in imperfect ion traps with large higher order field contributions.
When n = 0 in Equation 5, we have the ion’s fundamental secular frequency:
$$ {\upomega}_{\mathrm{u},0}={\upbeta}_{\mathrm{u}}\varOmega /2. $$
This is the frequency that is interrogated by resonance excitation/ejection in ion trap instruments operated under dipolar resonance conditions, where, in a 3D ion trap, AC waveforms 180° out of phase with respect to each other are applied to the endcap electrodes. For small au (au < 0.2) and qu (qu < 0.4),
$$ {\upbeta}_{\mathrm{u}}={\left({\mathrm{a}}_{\mathrm{u}} + {{\mathrm{q}}_{\mathrm{u}}}^2/2\right)}^{1/2}. $$
Note that the full definition of βu can be found in ref. [20]. If no DC potential is applied, as is typical of ion trap operation, then au = U = 0 and we have
$$ {\upbeta}_{\mathrm{u}}=\left({2}^{1/2}{\mathrm{q}}_{\mathrm{u}}/2\right)={2}^{3/2}\mathrm{z}\mathrm{V}\ /{\varOmega}^2{{\mathrm{r}}_0}^2\mathrm{m} $$
so that
$$ {\upomega}_{\mathrm{u},0} = {2}^{1/2}\mathrm{z}\mathrm{V}\ /\varOmega {{\mathrm{r}}_0}^2\mathrm{m}. $$

Thus we see that an ion’s secular frequency, for low au and qu, is inversely proportional to m/z. This is not a strictly accurate relationship throughout a,q-space, but it is a reasonable approximation in the range of values for which Equation 9 applies. This is important because it complicates mass calibration. In order to convert from the time domain to the mass domain, each time point must be converted to an excitation frequency dependent upon the scan parameters and electronic triggers. Each frequency is then converted to a value of beta and subsequently to a qu value using an iterative algorithm because beta is a continuing fraction in terms of qu. The qu value is then used to convert to mass, giving the ejected ion mass as a function of time. Thus, in contrast to the simple linear calibration in rf amplitude scanning, there is no analytical equation available to calibrate mass in secular frequency scanning. Nonetheless, a calibration procedure is demonstrated in ref. [24].

To date, secular frequency scanning has been mentioned in patents [25, 26] and review papers [21] but has only been performed sparingly. Welling and co-workers used this method, which they termed “secular scanning”, to obtain higher resolution mass spectra when compared to q scanning in a linear ion trap (the resonance was quadrupolar over a limited mass range and with slow frequency scanning) [27], Roth and coworkers used secular frequency scanning in a linear trap for mass selective excitation [28], and the Austin group at Brigham Young University used it to scan ions out of the halo ion trap [29, 30, 31]. Note that in the case of the halo trap, the geometry of the device necessitated the use of AC frequency scanning because simulations indicated that a conventional rf amplitude ramp would cause ions to collide with the electrodes and ceramic holders instead of being ejected out the apertures in the electrodes. However, AC scanning has yet to be systematically characterized despite some clear advantages, particularly the fact that the high amplitude, high frequency rf signal is kept constant, which greatly simplifies the electronics since strictly linear rf ramps, which are difficult to generate, are no longer needed. This feature is particularly appealing for miniature instruments [32, 33]. More importantly, precursor ion scans using a single ion trap [34, 35] can be performed by exciting ions of successive masses as a function of time using a low amplitude dipolar signal while a chosen product ion is ejected by applying a second high amplitude constant frequency AC signal at the product ion’s secular frequency. This capability would appear to mark a significant step forward in ion trap mass spectrometry, bringing single ion trap capabilities closer to those of the widely used triple quadrupole. The performance of a triple quadrupole is much superior but in some applications the small size and simplicity may favor use of an ion trap. These extended ion trap capabilities demand an understanding of the underlying principles, particularly those of secular frequency scanning, in order to improve the performance of precursor scans in single ion traps.

In this paper, we show that secular frequency scans can be carried out using either a miniature rectilinear ion trap mass spectrometer or a commercial linear ion trap. We also characterize the effect of scan direction, scan rate, rf amplitude, rf frequency, AC amplitude, and pressure on the spectra, and demonstrate facile mass range extension compared with conventional rf amplitude sweeps at low q. “Black holes” occurring at nonlinear resonance points are also investigated.



Frequency scanning experiments were performed using the Mini 12 [36] miniature rectilinear ion trap (RIT) [37] mass spectrometer and a benchtop Thermo LTQ XL linear ion trap (Thermo Scientific, San Jose, CA, USA) in the positive ion mode. The former was chosen to assess the effect of higher order fields and higher pressures, whereas the LTQ exhibits higher performance. The rectilinear ion trap uses electrodes with rectangular cross sections, in contrast to the hyperbolic cross sections of the commercial LTQ. The rf is applied to the y electrodes, while the AC and other waveforms are applied in a dipolar fashion to the x electrodes, which have slits for ion ejection.

Secular frequency scans were performed by outputting a swept frequency sinusoidal waveform of 0.5–10 Vp-p (peak to peak) over a range of 10–500 kHz in a scan lasting 300–800 ms, unless otherwise specified, from a Sony Tektronix AFG320 arbitrary function generator (Beaverton, OH, USA). In the case of the Mini 12, two channels were used to produce a dipolar (180° out of phase) waveform that was applied to the x electrodes after passage through a low pass frequency filter with a cutoff frequency of 500 kHz. Data were recorded using the data system of the Mini 12 [36]. The function generator was triggered on a high frequency kilohertz AC waveform of ~7 Vp-p output from the Mini AC waveform board in a 1 ms segment just prior to the mass scan. Unless otherwise specified, all scans were performed using a constant rf amplitude of 6000 digital-to-analog converter (DAC) units (~195 V0-p) and 0.999 MHz frequency, corresponding to a lower mass/charge cutoff of ~98 Thomson (Th). Note that DAC units and rf and AC amplitudes are directly proportional.

Using the LTQ, secular frequency scans were performed by replacing the resonance ejection waveform generated from the analog board with the same swept frequency waveform as just described. The function generator was triggered at the start of the mass scan using the triggers included in the LTQ Tune diagnostics menu. The rf frequency was tuned to 1.1995 MHz, and the change in rf amplitude built into the Thermo system was minimized by performing “Ultrazoom” scans over the period of the AC frequency scan. Ultrazoom scans occur at a rate of 27 Da/s. This small change in rf amplitude slightly changes resolution, depending on scan direction, but otherwise has a minimal effect on the spectra. The lower mass cutoff (lmco or LMCO) was typically set at 100–200 Th at the beginning of the scan. The LTQ’s data system was used to collect data (~2700 points per s). Unless otherwise specified, all AC scans were linear forward frequency sweeps from low to high frequency (high mass to low mass).


Ions studied in both traps were generated by nanoelectrospray ionization (nESI) at ~2000 V. In the case of the Mini 12, ions were gated into the mass analyzer for ~12 ms, followed by a ~500 ms ion cooling period. The standard Ultrazoom scan function was used in the LTQ.


Simulations were performed in ITSIM 6.0 [38] using a 2010 MacBook Pro (2.4 GHz Core i5, 3 GB usable RAM, 32-bit Windows 10). One hundred ions of each m/z were generated at the start of the simulations with a Gaussian distribution of positions about the center of the trap but zero velocity in x, y, and z. The frequency, but not amplitude, of the supplementary AC waveform applied to the simulated rectilinear trap was ramped linearly (in a forward or reverse direction) versus time while the main trapping rf amplitude and frequency were kept constant. Simulated scan times were shortened to ~3 ms in order to decrease computational time. In order to compensate for the shorter scan time, higher AC amplitudes were used. Collisions were simulated using a hard-sphere collision model at 4 mTorr helium.


Didodecyldimethylammonium bromide and EPA 508.1 herbicide mix (a mixture of alachlor, butachlor, simazine, atrazine, metolachlor, and hexachlorocyclopentadiene) were purchased from Sigma Aldrich (St. Louis, MO, USA, and Bellefonte, PA, USA, respectively). Hexadecyltrimethylammonium bromide was purchased from Tokyo Chemical Industry Co. (Tokyo, Japan). Benzylhexadecyldimethylammonium chloride was purchased from JT Baker Chemical Co. (Phillipsburg, NJ, USA). Ultramark calibration solution (4.5 ppm caffeine, 2 ppm MRFA, and 0.0005% Ultramark 1621 in ACN:MeOH:H2O 2:1:1 with 0.5% acetic acid) was purchased from Thermo Fisher (Rockford, IL, USA). All reagents were initially dissolved in either HPLC grade methanol (MeOH) or deionized water and then diluted in 50:50 MeOH:H2O with 0.1% formic acid to obtain their final concentrations, which were generally 1–10 ppm.

Results and Discussion

The secular frequency scans over a frequency range of 10–500 kHz, swept from low to high frequency with an amplitude of 3 Vp-p (Mini 12) and 1 Vp-p (LTQ), are shown in Figure S3 for a sample of three tetraalkylammonium ions (2–6 ppm) along with the equivalent resonant ejection spectra using the Mini 12 (simulated results shown in (b) and the LTQ (d)-(f). Peak widths are quite broad (~2 ms FWHM) in the RIT, likely due to the low pressure in the trap and the presence of higher order fields, whereas the LTQ shows much sharper peaks (~1 ms FWHM). The spectrum obtained from the LTQ when converted to the mass domain (Figure S3e), indicated peak widths of ~2–3 Da. Preliminary experiments using an approximately linear mass scan on a cylindrical ion trap showed the ability to resolve bromine isotopic peaks, despite the imperfect geometry (Figure S4). Under more optimal conditions where the rf amplitude is increased (LMCO = 200 Th), peak widths approaching unit width can be obtained using the LTQ, as discussed later. Resolution decreases with increasing mass due to the nonlinear spacing of ion secular frequencies in terms of mass.

Experimental results illustrating the effect of scan direction on the spectra are shown in Figure 1. The effect on peak height and width is very pronounced on the Mini 12, where higher order fields are present in large proportions since the fields are only 65% quadrupolar [37]. In this experiment, it was critical to alter the rf amplitude on the Mini 12 so that the ions of interest were ejected at approximately the same time because, as we will show later, secular frequency scans are highly sensitive to pressure. Since the Mini 12 uses a discontinuous atmospheric pressure interface, the pressure in the trap is variable as a function of time, which will affect resolution and sensitivity (see Figure S5 for forward versus reverse sweeps with ion ejection at different pressures).
Figure 1

Effect of scan direction on the secular frequency scan mass spectra of tetraalkylammonium salts: (a) Mini 12, and (b) LTQ. Scan time was 300 ms from 10 to 500 kHz (or vice versa) with an AC amplitude of 1 Vp-p. The rf amplitude was 14,000 DAC units (a lower mass cutoff of ~200 Th) for (a). Cooling time on the Mini 12 was 210 ms; (b) was performed during an Ultrazoom scan from 200 to 227 Th. Labels show m/z, FWHM peak temporal width, and area under the curve. Red boxes indicate peaks showing ejection at higher order parametric resonances

In general, reverse frequency sweeps (forward mass scans) result in up to 50% higher signal compared with forward frequency sweeps on the Mini 12, and resolution in the reverse sweep is also significantly better.

The same effect of scan direction on mass spectra is observed in conventional rf scans with resonance ejection [39]. Owing to nonlinear fields, ion frequencies shift upward toward the ejection point in a forward resonance ejection scan (low mass to high mass), resulting in an increase in sensitivity and resolution; the opposite effect is observed for the reverse rf amplitude sweep since the secular frequency shifts away from the working point [40]. See Figure S6 for reproduced resonance absorption curves of n-butylbenzene, which show the increase of ion secular frequency at higher AC amplitudes (i.e., in regions with more prominent higher order fields). The effect is much less pronounced on the LTQ since its rods are hyperbolic rather than rectangular [41].

Note that nonlinear fields cause absorption spectra to shift to higher frequencies only for a positive octopole or other even higher order contribution, as is present in the Mini 12 [37]. A positive octopole increases field strength, particularly near the electrodes, which causes ion frequencies of motion to increase correspondingly. The opposite occurs for a negative octopole component. For traps with a negative octopole component, higher resolution and sensitivity would be obtained in the forward frequency sweep.

A rather minor but interesting and unexpected effect of scan direction is illustrated by the red boxes in Figure 1. The relative spacing between the indicated peaks is identical to the spacing between the main peaks in the spectrum, which indicates that the same ions are being ejected at different frequencies. As we will show later, these frequencies correspond to higher order parametric resonances, which are observed despite using dipolar excitation. In the forward sweep, these resonances, of which there are many as given by Equation 6, are encountered before the secular frequency. This could have both a detrimental and favorable effect on resolution and sensitivity. In the forward sweep, the ions would increase their amplitude as they encounter these higher order resonances, which may increase the rate of ejection when their secular frequencies match the AC frequency at a later point in time. However, this effect appears to be very small, likely due to collisional cooling during the long mass scan, so that resolution and sensitivity in forward frequency sweeps are always worse than in reverse sweeps. The parametric resonances are significantly weaker on the LTQ than on the Mini, which indicates that higher order fields play a role. Curiously, the parametric resonances also appear in reverse frequency sweeps, even though they are encountered after the secular frequency. However, secular frequency scanning, particularly with low AC amplitudes, is a relatively weak method of ejection, so a small population of ions is left over after their secular frequencies have already been matched. Thus, these ions are ejected at their parametric resonance frequencies instead.

The effect of scan rate on the spectra is shown in Figure S7. The scan rate was changed by altering the scan time on the function generator while keeping the scan range constant. The scan rate here is nonlinear since the AC frequency is swept linearly while ion secular frequencies follow an approximately inverse relationship (Equation 11). Nonetheless, decreasing the scan rate increases peak separation in time, which is an expected result since ions experience more rf cycles at or near resonance and since their resonance conditions are further separated in time, but it decreases signal intensity. A similar result is obtained in conventional rf amplitude scans; decreasing the scan rate increases resolution but also decreases S/N, the latter partly due to charge transfer to neutral gas molecules [39].

The amplitude of the supplementary signal has a significant effect on the appearance of the spectrum, as shown in Figure 2. Ion intensity decreases, peak width increases, and ion ejection time decreases with increasing AC amplitude for both forward and reverse frequency scans, in agreement with theory [42]. Generally, signals of ~1 Vp-p or less are enough to generate spectra with high sensitivity and good resolution on the LTQ. If the AC amplitude is too low, however, ions do not gain enough energy to escape the trap, especially in the Mini 12, and at high AC amplitudes some ions are ejected prematurely or even at higher order resonances, particularly when the rf amplitude is also high as discussed later. Sensitivity for ions of different masses is dissimilar due to differences in pseudo-potential well depth, which increases with V and q, and scan rate, which increases with m/z. More rapid ejection at higher AC amplitudes implies that mass calibrations are valid only for one AC amplitude, but fortunately this relationship is approximately linear [24]. Although forward and reverse sweeps both show increasing peak width with increasing AC amplitude, they have different optimal AC amplitudes. The forward sweep on the LTQ exhibits the best sensitivity at ~1 Vp-p, whereas the reverse sweep shows the highest ion intensity at ~4 Vp-p. This is likely caused by ion frequency shifts at higher AC amplitudes, which will tend to degrade performance in forward sweeps.
Figure 2

Effect of AC amplitude on the secular frequency scan of three quaternary ammonium ions, m/z values labeled. Inset voltages are peak-to-peak voltages of the supplementary AC frequency ramp. The rf amplitude was kept at 6000 DAC units (LMCO = 100 Th on the LTQ) and the frequency of the supplementary AC was swept from 10 to 500 kHz over 800 ms. Shown are (a) a forward frequency scan on the Mini 12, and (b) forward and (c) reverse frequency scans on the LTQ

The amplitude of the rf waveform has perhaps the most noticeable effect on spectral resolution, as shown in Figure 3 where carbon isotope peaks are resolved with an Ultrazoom scan starting at 200 Th on the LTQ (Figure 3b, inset). Since each ion’s secular frequency is directly proportional to the applied rf voltage (for q < 0.4), increasing the rf amplitude causes ions to be ejected later in the scan. This results in increased resolution because their secular frequencies are further apart. Since secular frequency and mass-to-charge are inversely proportional, high mass ions have secular frequencies that are close to each other, whereas the secular frequencies of low mass ions are better separated in time, which causes resolution to decrease with mass in a linear frequency sweep. However, increasing the rf amplitude also increases each ion’s potential well depth (Dx,y = qVrf/4) [20, 21], resulting in less efficient ejection and a loss in sensitivity. Figure S7 shows a similar effect of rf frequency on the spectra; however, in this case the expected inverse relationship between secular frequency and rf frequency is observed.
Figure 3

Effect of rf amplitude on the secular frequency scan of three quaternary ammonium ions, m/z values labeled: (a) Mini 12, and (b) LTQ. Scan parameters were AC amplitude 2 Vp-p, 10 to 500 kHz, over 800 ms. Inset in (b) shows resolved carbon isotope peaks. Inset legends indicate the rf amplitude either in DAC units or LMCO

Pressure variations are well known to cause substantial changes in mass resolution [7]. Approximately 1 mTorr of a light bath gas such as helium greatly increases resolution and sensitivity in quadrupole ion traps because of collisional cooling, which causes the ion cloud to collapse to the center of the trap where higher order fields are less prominent. However, if the pressure is too high, collisions during the mass scan can cause ions to be ejected at the wrong time, degrading mass resolution. Secular frequency scanning appears to be more tolerant of higher-pressure operation than resonance ejection scans but significantly more affected by low pressure operation (Figure 4). The pressure in the rectilinear ion trap was altered by varying the amount of time between the opening of the discontinuous atmospheric pressure interface (DAPI) valve [43] and the beginning of the mass scan. In resonance ejection scans, resolution on the Mini 12 is optimum at the lowest pressures achieved, that is, for the scans with collisional cooling times longer than ~600 ms. Sensitivity is largely the same for every resonance ejection scan beyond ~300 ms of cooling. The initial drop in peak intensity can be attributed to collisional ion losses at higher pressure and charge transfer to the background gas [39], but beyond this no significant difference in ion intensity is observed. This is not the case for secular frequency scans, which appear to be highly pressure sensitive as illustrated in the forward frequency scans in (c) and (d) and reverse scans in (e) and (f). Parts (c) and (e) indicate that the highest resolution is obtained at the higher pressures, particularly for the reverse frequency scan, which shows superior performance in peak width and ion intensities. As the collisional cooling time is increased beyond ~500 ms, the peak width increases dramatically. Sensitivity correspondingly decreases to the point where little to no ion intensity is observed beyond ~500 ms of collisional cooling in (d) and (f).
Figure 4

Effect of pressure on the signal intensity of m/z 284, 360, and 382: (a) and (b) resonance ejection, (c) and (d) experimental forward frequency scan, (e) and (f) experimental reverse frequency scan. All experiments were performed on the Mini 12. The resonance ejection scan was 300 ms with a resonance waveform of 345 kHz, 35,000 DAC units. Secular frequency scans were 300 ms, 1 Vp-p, 10–500 kHz or vice versa, with a lower mass cutoff of ~200 Th. Peak area was calculated by summing the intensities across the peak, which could result in a negative value

As mentioned previously, higher order parametric resonances are particularly evident in forward frequency scans since low frequencies and, thus, many higher order resonances, are scanned through before the secular frequency. Peaks corresponding to these higher order resonances were observed in several experiments (see Figure 1), despite the fact that only dipolar excitation was applied. This is further demonstrated and quantified using the Mini 12 with a mixture of five pesticides analyzed by resonance ejection and secular frequency scanning (Figure 5). The main peaks in the spectrum are protonated herbicides simazine (m/z 203), atrazine (m/z 217), metolachlor (m/z 285), and derivatives of atrazine (m/z 174 and 250), confirmed as derivatives or metabolites by MS/MS. In the secular frequency scan experiment, both the amplitude of the AC and the rf signals were varied (rf = 6000 corresponds to ~195 V0-p and rf = 12,000 corresponds to ~386 V0-p). The rf amplitude was increased only during the mass scan and not before ion injection. At the lower rf amplitude higher order parametric resonances were not observed (Figure 5b). However, when the rf and AC amplitudes were increased, parametric resonances corresponding to K = 4 were observed. Further increase of the AC amplitude to ~3 Vp-p resulted in appearance of K = 6 and 8 resonances, and K = 10 resonances were subsequently observed when the AC amplitude was >7 Vp-p. Note that there is some overlap in the K = 6 and 8 resonances, as shown in Table 1.
Figure 5

Higher order parametric resonances in forward frequency scans. Mass spectra of a mixture of five protonated pesticides, m/z values labeled, recorded by (a) resonance ejection using the Mini 12, and (b), (c) secular frequency sweeps for different combinations of rf amplitudes (arb. units) and AC amplitudes. Resonance ejection was performed over 300 ms at 345 kHz. The secular frequency sweep was performed over 800 ms from 50 to 500 kHz. The values of K in (c) indicate ejection frequencies that correspond to higher order parametric resonances of K = 2, 4, 6, 8, and 10. See Table 1 for calculations. Note that rf = 6000 corresponds to ~195 V0-p and rf = 12,000 corresponds to ~386 V0-p

Table 1

Experimental Ejection Frequencies for Ions in Figure 5, Indicating Ejection of Ions at Higher Order Parametric Resonances Despite Application of Only Dipolar Excitation

Calibration parameters


Experimental ejection time (ms)

Experimental ejection frequency (kHz)

Calculated βx

Calculated qx

Parametric frequency / experimental frequency

Parametric order

Time (ms)

AC frequency (kHz)







K = 2 or dipolar









K = 2 or dipolar









K = 2 or dipolar








K = 4








K = 4








K = 4








K = 6








K = 6


250, 203





5.86, 7.86

K = 6, 8








K = 8








K = 10








K = 10

Experimental ejection frequencies were calculated using the linear calibration data on the left. The parametric frequency was assumed to be twice the K = 2.00 frequency. The parametric order is the K value of the resonance, which corresponds to Equation 6. Note that βx values are calculated from the experimental ejection frequencies. This is not meant to indicate the βx value at which the ions reside (except for the K = 2 case), but rather the βx values to which the frequencies correspond; qx values are calculated from βx only for the K = 2 case since this is where the ions reside on the q axis of the Mathieu stability diagram. 

Although higher order dipolar resonances have not previously been reported, it is feasible that higher order parametric resonances are being excited due to the coupling of motion in the x and y dimensions, which is a direct result of higher order field components (e.g., hexapole and octopole) introduced by electrode imperfections, electrode truncation, non-ideal geometries, and misalignment. The calculated frequencies of ejection at the higher AC amplitudes corresponded to approximately one-half, one-third, one-fourth, and one-fifth of the secular frequency (Table 1), or equivalently one-fourth, one-sixth, one-eighth, and one-tenth of the parametric resonance frequency, which is indicative of higher order quadrupolar resonances (K > 1 in Equation 6). These resonances were not limited to the Mini 12; spectra on the LTQ also suffered from these added peaks if the amplitudes of the AC and rf were high enough (see Figure S9 and Table S1). Since the LTQ has hyperbolic rods compared with the rectangular cross sections in the RIT, the resonances were more difficult to observe, presumably because of weaker coupling of ion motion in x and y. For example, only with a very high LMCO of ~1000 Da were the parametric resonances observed on the benchtop instrument. Furthermore, the K = 4 resonances were the only ones observed in this case, which is further evidence for x,y-coupled motion as the cause.

In general, higher resonances can only be accessed with higher excitation amplitudes as illustrated in Figure S10, which is reproduced from Collings et al. This shows regions of the Mathieu stability diagram in which the higher order parametric resonances may be accessed. Since the parameter Q is directly proportional to the excitation amplitude and because K increases with Q, higher amplitudes are required for excitation at K > 1 resonances.

An alternative explanation for these findings is possible: electronic coupling between the AC and rf waveforms could accidentally introduce a small supplementary quadrupole field. The need for higher AC and rf amplitudes corroborates this explanation as well. However, though the rf and AC are coupled together electronically on the LTQ (i.e., the rf is applied to all four rods and the AC is applied only to one pair), this is not the case on the Mini 12. In the latter case, the rf is applied to one rod pair and the AC is applied to the other pair, so there ought to be no coupling between the two. Small perturbations in the sinusoidal excitation could also promote excitation at parametric resonances because of the introduction of higher harmonics. Nonetheless, the more likely cause is the higher order field components because of (1) the difference in the accessibility of these resonances on the two different instruments, (2) the observation of parametric resonances on both instruments with two different sets of electronics, and (3) the AC amplitude dependence observed on the Mini 12, which agrees with previous reports (Figure S10).

In any case, sensitivity and peak width appeared to be improved over that of the fundamental resonance, which has been reported previously [22, 23]. Higher resolution at higher order resonances may present an interesting alternative to mass spectral acquisition compared with the fundamental resonances. Furthermore, if the secular frequency scan were used for fragmentation, it may benefit from the higher order fields since ions will gain kinetic energy at several points during the mass scan (the secular frequency and the higher order parametric resonances), promoting more efficient collision-induced dissociation. The fragmentation would be fairly mass-selective in time, but different ions of the same mass would presumably fragment at several different times, leading to some overlap in the spectral intensities.

An advantage of secular frequency scanning over conventional rf scanning is mass range extension at low rf amplitudes. Mass range extension can also be accomplished in an ion trap by resonance ejection at a low q value, that is, at a low AC frequency, or by lowering the rf frequency [9]. Figure S11 shows the secular frequency scan mass spectrum of a calibration solution of caffeine (m/z 195), the peptide MRFA (m/z 525), and Ultramark 1621 (m/z 1022–1922, every 100 Th). For reference, resonance ejection at an optimal q value was performed as well (Figure S12). As shown, the high mass Ultramark calibration ions can be detected at low rf amplitudes by using a relatively low amplitude AC waveform scanned through low frequencies using an appropriate scan time. Despite the closeness of their secular frequencies, the fast frequency scanning, and the large mass range, the Ultramark peaks are resolved in a linear frequency sweep, and their higher order resonances can even be observed using the Mini 12 with a 4 Vp-p AC amplitude (not shown). The same experiment on the LTQ is shown in Figure S11c and S11d. Ion intensity in the secular frequency scan with a LMCO of 1000 Th is double that in the resonance ejection scan with a LMCO of 50, though the latter is a shorter scan in terms of time and the scan rate is uniform, which contrasts with the secular frequency scan in which the scan rate increases with mass. When converted to the mass domain (not shown), the approximate resolution is ~2 Da FWHM (m/z 1422) for the secular frequency scan, but again resolution degrades with increasing mass. Mass range extension in this method is arguably superior to resonance ejection at low q for several reasons: in the latter case (1) ions are also ejected at q = 0.908, convoluting the mass spectrum, (2) higher rf amplitudes are required, (3) a linear rf amplitude ramp is needed, and (4) the entire mass spectrum is difficult to obtain because of the low mass cutoff imposed by the supplementary AC [this assumes ions below that cutoff are ejected from the trap prior to the mass scan, due to reason (1)].

One of the main concerns about secular frequency scanning is the presence of “black holes” in the Mathieu stability diagram [44, 45]. These occur on iso-β lines where nonlinear higher order resonances corresponding to, for example, hexapole resonances or octopole resonances occur. The RIT is not expected to have hexapole multipole coefficients due to symmetry in the electrodes and electric field [37]. However, the octopolar coefficient in the RIT is ~7.9% of the quadrupolar coefficient and, thus, contributes substantially to the electric field. Thus, we chose to investigate the nonlinear octopolar resonance at β = 1/2 [46, 47]. Figure 6 shows forward and reverse frequency sweeps when m/z 284 is placed just below (i.e., β < 1/2), on (β = 1/2), or just above (β > 1/2) the nonlinear resonance point. In the forward frequency sweep, no signal is observed for peaks at the black hole, regardless of AC amplitude and other relevant parameters. In the reverse frequency sweep, peak splitting is observed at lower AC amplitudes, but use of higher amplitudes (inset in Figure 6b) diminishes the splitting. Peak splitting has been reported previously in double resonance ejection experiments [18] (i.e., applying a resonance waveform with frequency corresponding to a higher order hexapole or octopole resonance), but the complete lack of peak intensity in the forward frequency sweep is striking. The difference here is that when the resonance point is scanned from low to high frequency, multiple resonances for each ion are encountered before the secular frequency, as shown in Figure 5. These preliminary excitations cause ions to become translationally excited and to occupy regions closer to the electrodes. Such ions are more susceptible to the higher order resonance points, resulting in a flat intensity profile at the nonlinear resonance point.
Figure 6

Black holes in secular frequency scanning. Shown are secular frequency scan mass spectra of three quaternary ammonium ions m/z 284, 360, and 382, where m/z 284 was placed below, on, or above the nonlinear octopolar resonance at β = 1/2. (a) Forward frequency sweep, and (b) reverse frequency sweep. Red boxes indicate the peak at the nonlinear resonance point. Scans were performed on the Mini 12 with parameters 10–500 kHz (or vice-versa), 1 Vp-p AC amplitude, 300 ms in duration, and a rf amplitude such that m/z 284 was just below, on, or above the nonlinear resonance point at β = 1/2. Inset in (b) shows disappearance of peak splitting at higher AC amplitudes


Secular frequency scanning is an electronically simple alternative to conventional rf amplitude or frequency ramping, which has advantages in terms of access to ions of high mass. Initial results show poorer resolution, but this can be optimized by tuning the AC amplitude, rf amplitude (or rf frequency), and pressure, or by scanning at a constant rate. Higher order fields and non-optimal pressure also appear to contribute to peak broadening. Imperfect ion traps with large higher order field contributions, such as the Mini 12, through coupling of x- and y-motion of ions excited by a dipolar signal allow parametric excitation with observation of signals at a set of higher order parametric resonances. In normal dipolar secular frequency scan conditions, these processes do not make a large contribution to the mass spectra, but it is important to recognize their origin.



The authors thank Zane Baird and Adam Hollerbach for help with electronics and data collection, and Wolfgang Plass for the improved version of ITSIM 6.0. The authors also acknowledge discussions with Jae Schwartz (Thermo Fisher Scientific). This work was supported by NASA (grant IP 11033366).

Supplementary material

13361_2016_1377_MOESM1_ESM.docx (1.9 mb)
ESM 1 (DOCX 1984 kb)


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Copyright information

© American Society for Mass Spectrometry 2016

Authors and Affiliations

  • Dalton T. Snyder
    • 1
  • Christopher J. Pulliam
    • 1
  • Joshua S. Wiley
    • 1
  • Jason Duncan
    • 1
  • R. Graham Cooks
    • 1
  1. 1.Department of Chemistry and Center for Analytical Instrumentation DevelopmentPurdue UniversityWest LafayetteUSA

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