Successive Resonances for Ion Ejection at Arbitrary Frequencies in an Ion Trap
The use of successive resonances for ion ejection is demonstrated here as a method of scanning quadrupole ion traps with improvement in both resolution and sensitivity compared with single frequency resonance ejection. The conventional single frequency resonance ejection waveform is replaced with a dual-frequency waveform. The two included frequencies are spaced very closely and their relative amplitudes are adjusted so that the first frequency that ions encounter excites them to higher amplitudes where space charge effects are less prominent, thereby giving faster and more efficient ejection when the ions come into resonance with the second frequency. The method is applicable at any arbitrary frequency, unlike double and triple resonance methods. However, like double and triple resonance ejection, ejection using successive resonances requires the rf and AC waveforms to be phase-locked in order to retain mass accuracy and mass precision. The improved performance is seen in mass spectra acquired by rf amplitude scans (resonance ejection) as well as by secular frequency scans.
KeywordsQuadrupole ion trap Scan modes Successive resonance ejection Double resonance ejection Arbitrary frequency Mass resolution
Since the quadrupole ion trap was first proposed in the early fifties by German physicist and later Nobel Laureate Wolfgang Paul , many methods of mass spectral acquisition using ion traps have been demonstrated. A key development was the mass selective instability scan . With this technique, a mass spectrum can be obtained by scanning ions sequentially out of the trap in order of increasing m/z (mass/charge ratio, also Thomson, Th) by ramping the amplitude of the driving radiofrequency (rf) waveform. The rf ramp causes ion trajectories to become unstable in one or more dimensions as the ions are brought to the working point (e.g., qz = 0.908) where qz is the classic Mathieu parameter for the z axis, and the z-instability allows the ions to be detected externally .
Later, an alternative method of ion trap scan out was demonstrated. The method, which was termed “resonance ejection” [4, 5, 6, 7], uses a small supplementary AC signal to impose a second working point or “hole” on the q axis (more precisely, on an iso-β line) of the Mathieu stability diagram. The ions can then be scanned through the operating point and ejected in order of increasing m/z as the rf amplitude is increased, which generally results in increased resolution compared with boundary ejection. Alternatively, the “hole” can be scanned through all possible q values by ramping the frequency of the supplementary AC at fixed rf amplitude in what has been termed a “secular frequency scan” [8, 9, 10, 11, 12].
Franzen showed that ion ejection at a nonlinear resonance point greatly increases mass resolution, and this capability was incorporated into the commercial Bruker Corporation Esquire series of ion trap instruments. The scan was termed a “double resonance ejection” because of the co-occurrence of the dipolar excitation and the hexapolar (or octopolar) nonlinear resonance . The effect of the hexapolar or octopolar resonance is to make the rate of ion ejection faster than the normal linear growth in amplitude with time, thus resulting in better resolution . The effect has also been demonstrated in a micro-ion trap by the Ramsey group [22, 23]. A similar triple resonance scan mode has been patented by Varian [24, 25]. The method is procedurally similar to double resonance ejection, where double resonance is achieved by parametric excitation at the hexapole resonance, and the triple resonance is realized by simultaneously applying a dipolar waveform at the lower sideband (Ω - ⍵u) corresponding to the hexapolar resonance, again at βu = 2/3. Other sidebands, which generally occur at nΩ ± m⍵u, n and m being positive integers, may also be interrogated, but their magnitudes diminish with increasing n and m.
Multiple resonances may also be imposed on different regions of the Mathieu stability diagram. For example, in compressive resonance ejection , multiple resonance waveforms are used to impose several “holes” of instability on the q axis. The rf amplitude is ramped, causing multiple populations of ions to be ejected at each time point. The mass spectrum can then be mathematically calculated by using an algorithm to decompress the data. Rhombic ion ejection can also be performed by exciting ions simultaneously in orthogonal directions . Because the ions being ejected travel around the rest of the ion cloud rather than through it, space charge effects are decreased and resolution is improved.
Here, successive excitation and ejection is described and demonstrated for the resonance ejection rf amplitude scan method [4, 5, 6, 7]. It is later shown for the secular frequency scan method of recording mass spectra [8, 9, 10, 11, 12, 28]. The successive resonance variant improves performance in both cases. In the successive resonance scan, a first supplementary AC frequency is given a low amplitude in order to excite ions to higher orbits in the ion trap, and a second, slightly higher frequency is given a higher amplitude in order to swiftly eject the excited ions. The sum of these two frequencies is applied to the ion trap in a dipolar fashion. While the spacing between the successive resonances needs to be fixed in order to obtain good results, the set of frequencies can be placed at any location on the q axis of the Mathieu stability diagram. The method retains the increase in resolution that has been previously demonstrated in resonance ejection variants but is more versatile because it does not require higher order field contributions, as do double and triple resonance ejection.
Ions were generated by nanoelectrospray ionization (nESI) at ~2 kV. Typical spray tip diameters were ~5 μm.
Didodecyldimethylammonium bromide was purchased from Sigma Aldrich (St. Louis, Missouri, USA), hexadecyltrimethylammonium bromide was purchased from Tokyo Chemical Industry Co. (Tokyo, Japan), and benzylhexadecyldimethylammonium chloride was purchased from J.T. Baker Chemical Co (Phillipsburg, New Jersey, USA). Reagents were dissolved in HPLC grade methanol and then diluted in 50:50 MeOH:H2O with 0.1% formic acid to final concentrations of ~5 ppm. Pierce ESI LTQ calibration solution was obtained from Thermo Fisher (Rockford, IL, USA).
All experiments were performed using a Thermo LTQ XL linear ion trap mass spectrometer interfaced to an Orbitrap (San Jose, CA, USA). The rf frequency was tuned to 1175 kHz. For resonance ejection with a fixed excitation frequency and an rf scan, the built-in scan function was used but, unless otherwise specified, the resonance ejection signal was replaced with an AC waveform of specified frequencies and amplitudes. The waveform was supplied by a Keysight 33612A arbitrary waveform generator (Newark, SC, USA). For successive resonance ejection, two channels on the generator were set to different frequencies and summed into a single channel. One frequency was less than half the driving rf frequency (i.e., a secular frequency) and the other was set to a frequency less than ~15 kHz from the first frequency (or the corresponding lower sideband Ω - ⍵, where ⍵ represents the secular frequency). General frequencies were 490 and 501 kHz, with the former having a smaller amplitude (~1 Vpp versus ~4 Vpp). With a resonance frequency of ~490 kHz, the scan rate of the instrument was ~16,666 Da/s.
Successive resonance secular frequency scanning was similarly performed in the secular frequency scan mode with the rf amplitude held sensibly constant. This was achieved over a period of 1 s using the Ultrazoom scan mode instead of the desired fixed rf amplitude because the LTQ instrument will only record data during an rf scan and the choice of the Ultrazoom scan minimizes the change in rf amplitude, thus limiting the (undesired) change in ion secular frequency. The same waveforms were applied in the successive resonance secular frequency scans but their frequencies were ramped linearly with time from high to low frequency (low to high mass). All auxiliary waveforms were triggered at the beginning of the mass scan with the trigger tools in the LTQ Tune diagnostics menu and were phase-locked to the rf frequency.
Mass calibration was performed by visually comparing the results of the successive resonance experiment with those obtained by analyzing each solution with the built-in resonance ejection scan (which was mass calibrated with Pierce ESI LTQ calibration solution using the built-in automatic calibration procedure). Resolution is reported as m/Δm, where Δm is the full width at half maximum (FWHM).
Results and Discussion
Successive resonance ejection at arbitrary frequencies can be accomplished by synthesizing a single dipolar waveform with two frequency components. The first frequency is set to any arbitrary frequency, in contrast to previous reports of double  and triple  resonance, which were performed only at nonlinear resonance points. The second frequency is set on a frequency that corresponds to a Mathieu q value that is close to the first frequency (in our case, ~10 kHz higher than the first frequency). As an example, with a driving rf frequency of 1.2 MHz, the two frequency components would be an arbitrarily chosen frequency of 490 kHz with an amplitude of ~1 Vpp and a second frequency at 501 kHz with an amplitude of ~5 Vpp. Alternatively, a lower rf sideband frequency of 1200 - 501 = ~699 kHz (Ω - ⍵) may be used. Note that the optimal difference between the two frequencies will vary with pressure, AC amplitude, and rf amplitude scan rate.
The first resonance that ions encounter during the rf ramp is used to excite ions to higher amplitudes. The amplitude of this particular frequency component is deliberately kept low to excite ions but prevent ion ejection, which would result in ghost peaks. The second frequency is set ~10 kHz higher and has a higher amplitude so that the excited ions are swiftly ejected from the trap. The frequency difference increases approximately linearly with scan rate and also varies slightly with the relative AC amplitudes. The result of the successive resonance phenomenon is improved sensitivity and resolution. As we will discuss later, this appears to be, at least in part, due to a mitigation of space charge effects.
Now we take a moment to discuss the mechanism by which resolution is improved. In double and triple resonance ejection, resolution is improved when setting the resonance ejection frequency at a nonlinear resonance point, as discussed before. The co-occurrence of the excitation frequency and nonlinear resonance causes the ions to experience a rate of change of amplitude in the trap (that is, how far the ion is from the quadrupole center) that is faster than linear (see Refs. [18, 24, 29]), which is the rate of change that is usually observed when resonantly exciting ions. The mechanism of successive resonances, however, differs because nonlinear field resonances are not used and therefore not necessary. Instead, the ions are excited just before they are ejected. Because they are excited, (1) they are closer to the edge of the trap and therefore ejected faster than they would be if they occupied the center of the ion trap, (2) space charge is largely mitigated because the ion’s trajectory has time to recover from space charge effects that are very prominent at the trap center, where the rest of the ion cloud resides, and (3) the effects of non-linear fields are increased, assisting in ion ejection.
The major contribution of mechanism (2) is indicated by the resolution improvement with respect to m/z throughout most of the spectra presented here. If mitigation of space charge effects is a primary driver of resolution improvement, we expect the resolution improvement to decrease with m/z since the ions are being ejected in order of increasing m/z. That is, lower mass ions experience the greatest space charge effects since (1) they are ejected first when the ion cloud is dense, and (2) they unfortunately occupy the center of the ion cloud  and must be ejected through the distribution of higher m/z ions. Looking at Figure 1, we see that the resolution for m/z 284, the first ion ejected in the scan and, thus, the one subjected to the most space charge, is increased by approximately a factor of 4. The second ion ejected, m/z 360, experiences a factor of 3 increase in resolution, and the last m/z ejected, m/z 382, shows an increase in resolution of a factor of 1.5. Rhombic ion ejection, in which the ions are excited in both x and y, also reduces space charge effects because the ions being ejected circle the rest of the ion cloud .
A further note should be added regarding the isotopic distributions observed in the successive resonance scan. The distribution in the two scans differs slightly, which we attribute to the different phase relationship between the rf and two excitation waveforms. However, further studies will need to be performed in order to understand the effect of phase on isotope distributions.
Successive Resonances for Ion Ejection at Secular and Sideband Frequencies more than Doubles Mass Resolution Achieved Using a Benchtop Thermo LTQ Linear Ion Trap
When performing successive resonance ejection, the resonance waveforms must be carefully matched experimentally, both in terms of amplitude and frequency. We noticed peak splitting and “ghost” peaks with many different combinations of scan rate, AC amplitudes, and frequencies. Careful tuning of each parameter must be performed in order to obtain good peak shape and avoid ghost peaks.
Variants of Successive Resonance Ejection Utilized in This Study
Sum frequency successive resonance
Two frequencies with small frequency difference, summed together
Sum of two frequencies: 490 kHz sine + 501 kHz sine
Successive resonance by amplitude modulation
One frequency amplitude modulated to give sideband frequencies
490 kHz sine amplitude modulated by 10 kHz, giving sidebands at 480 and 500 kHz
Successive resonance secular frequency scan
Secular frequency scan
Two close ac frequencies, both ramped, summed together
Sum of two scanned frequencies: 200–100 kHz sine + 200.04–100.04 kHz sine
Successive resonances can similarly be used to improve the resolution in secular frequency scanning, which we have previously characterized as a simple and interesting alternative to ramping the rf amplitude [10, 12, 28]. In the secular scan method, the frequency of the auxiliary AC signal is ramped to eject ions when their static secular frequencies match the varying AC frequency. In other words, the “hole” on the Mathieu stability diagram imposed by the supplementary AC is scanned, while the rf amplitude is constant, whereas in resonance ejection ions are scanned through the hole by ramping the rf amplitude, which increases ion secular frequencies until they match the AC frequency at which point the ions are ejected. Generally, the resolution of the former method is poorer, which is discussed in depth in a previous paper on secular frequency scan mass calibration .
Although it is not shown here, successive resonances may be most applicable to improving the performance of miniature mass spectrometers, which tend to suffer from lower resolution and higher space charge effects than benchtop instruments [32, 33].
The resolution of a benchtop ion trap is more than tripled using successive resonance ejection at arbitrarily chosen static and dynamic frequencies. The resolution improvement is attributed largely to decreased space charge effects during ejection when the ions are first excited to amplitudes beyond the rest of the ion cloud. Because the mechanism does not depend on higher order fields for resolution improvement, additional hexapole and octopole resonances are not needed in this method. Isotope ratios in the successive resonance scans can differ from those obtained by single frequency resonance ejection, likely due to the different phase relationships between the rf and AC waveforms as each ion is ejected. In addition, beat frequencies that develop from the sum of two sinusoids may play a role in the resolution improvement.
This paper is complemented by parallel work in ion isolation using dual frequencies with high amplitudes  and broadband ion activation using a fixed AC amplitude and scanning the rf amplitude in the reverse direction . This emerging set of techniques makes up a unique package that addresses every step of the MS/MS experiment.
The researched presented herein was supported by NASA (Award NNX16AJ25G).
- 1.Paul, W., Steinwedel, H.: A new mass spectrometer without a magnetic field. Z. Naturforsch Sect. A 8, 448–450 (1953)Google Scholar
- 9.Austin, D.E., Wang, M., Tolley, S.E., Maas, J.D., Hawkins, A.R., Rockwood, A.L., Tolley, H.D., Lee, E.D., Lee, M.L.: Halo ion trap mass spectrometer. Anal. Chem. 79, 2927–2932 (2007)Google Scholar
- 13.March, R.E., Todd, J.F.J.: Quadrupole ion trap mass spectrometry. John Wiley and Sons: Hoboken, NJ (2005)Google Scholar
- 16.Wang, Y., Franzen, J., Wanczek, K.P.: The non-linear resonance ion trap. Part 2. A general theoretical analysis. Int. J. Mass Spectrom. Ion Processes 124, 125–144 (1993)Google Scholar
- 17.Franzen, J.: The non-linear ion trap. Part 4. Mass selective instability scan with multipole superposition. Int. J. Mass Spectrom. Ion Processes 125, 165–170 (1993)Google Scholar
- 18.Franzen, J.: The non-linear ion trap. Part 5. Nature of non-linear resonances and resonant ion ejection. Int. J. Mass Spectrom. Ion Processes 130, 15–40 (1994)Google Scholar
- 19.Wang, Y., Franzen, J.: The non-linear resonance QUISTOR. Part 1. Potential distribution in hyperboloidal QUISTORs. Int. J. Mass Spectrom. Ion Processes 112, 167–178 (1992)Google Scholar
- 20.Wang, Y., Huang, Z., Jiang, Y., Xiong, X., Deng, Y., Fang, X., Xu, W.: The coupling effects of hexapole and octopole fields in quadrupole ion traps: a theoretical study. J. Mass Spectrom. 48, 937–944 (2013)Google Scholar
- 25.Wells, G.J., Wang, M., Marquette, E.G.: Mass scanning method using an ion trap mass spectrometer U.S. Patent 5,714,755 (1998)Google Scholar
- 27.Zhang, X., Wang, Y., Hu, L., Guo, D., Fang, X., Zhou, M., Xu, W.: Reducing space charge effects in a linear ion trap by rhombic ion excitation and ejection. J. Am. Soc. Mass Spectrom. 27, 1256–1262 (2016)Google Scholar
- 28.Snyder, D.T., Pulliam, C.J., Cooks, R.G.: Linear mass scans in quadrupole ion traps using the inverse Mathieu q scan. Rapid Commun. Mass Spectrom. doi:10.1002/rcm.7710
- 34.Snyder, D.T., Cooks, R.G.: Ion isolation in a linear ion trap using dual resonance frequencies. J. Am. Soc. Mass Spectrom. doi: 10.1007/s13361-016-1494.
- 35.Snyder, D.T., Cooks, R.G.: Multigenerational broadband collision-induced dissociation of precursor ions in a linear quadrupole ion trap. J. Am. Soc. Mass Spectrom. doi: 10.1007/s13361-016-1493.