Matrix-shimmed ion cyclotron resonance ion trap simultaneously optimized for excitation, detection, quadrupolar axialization, and trapping

A different symmetry is required to optimize each of the three most common Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) electric potentials in a Penning (ICR) ion trap: one-dimensional dipolar ac for excitation (or detection), two-dimensional azimuthal quadrupolar ac excitation for ion axialization, and three-dimensional axial quadrupolar dc potential for ion axial confinement (trapping). Since no single trap shape simultaneously optimizes all three potentials, many trap configurations have been proposed to optimize the tradeoffs between the three requirements for a particular experiment. A more general approach is to divide each electrode into small segments and then apply the appropriate potential to each segment. Here, we extend segmentation to its logical extreme, by constructing a “matrix-shimmed” trap consisting of a cubic trap, with each side divided into a 5 × 5 grid of electrodes for a total of 150 electrodes. Theoretically, only 48 independent voltages need be applied to these 150 electrodes to generate all three desired electric potential fields simultaneously. In practice, it is more convenient to employ 63 independent voltages due to construction constraints. Resistive networks generate the potentials required for optimal quadrupolar trapping and quadrupolar excitation. To avoid resistive loss of excitation amplitude and detected signal, dipolar excitation/detection voltages are generated with a capacitive network. Theoretical Simion 6. 0 simulations confirm the achievement of near-ideal potentials of all three types simultaneously. From a proof-of-principle working model, several experimental benefits are demonstrated, and proposed future improvements are discussed.     

Trapped-ion cell with improved dc potential harmonicity for FT-ICR MS

The trapped-ion cell is a key component critical for optimal performance in Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry (MS). To extend the performance of FT-ICR MS, we have developed a new cell design that is capable of generating a DC trapping potential which closely approaches that of an ideal Penning trap, i.e., a 3D axial quadrupolar potential distribution. The new cell design was built upon an open cylindrical geometry, supplemented with two pairs of cylindrical compensation segments. Electric potential calculations for trial cell geometries were aimed at minimizing spatial variations of the radial electric field divided by radius. The resulting cell proportions and compensation voltages delivered practically constant effective ion cyclotron frequency that was independent of ion radial and axial positions. Our customized 12 tesla FT-ICR instrument was upgraded with the new cell, and the performance was characterized for a range of ion excitation power and ion populations. Operating the compensated cell at increased postexcitation radii, approximately 0.7 of the cell inner radius, resulted in improved mass measurement accuracy together with increased signal intensity. Under these same operating conditions the noncompensated open cell configuration exhibited peak splitting and reduced signal life time. Mass accuracy tests using 11 calibrants covering a wide m/z range reproducibly produced under 0.05 ppm RMS precision of the internal calibration for reduced ion populations and the optimal excitation radius. Conditions of increased ion population resulted in a twofold improvement in mass accuracy compared with the noncompensated cell, due to the larger achievable excitation radii and correspondingly lower space charge related perturbations of the calibration law.     

The 'hybrid cell': a new compensated infinity cell for larger radius ion excitation in Fourier transform ion cyclotron resonance mass spectrometry

A new 'hybrid' ion cyclotron resonance (ICR) trap is proposed and analyzed by computer simulations. The trap is basically a hybrid of a segmented end cap (Infinity) and capacitively coupled cylindrical cell, with additional electrodes placed at the center of each end cap. The new trap produces an on-axis electric field z-profile similar to that of the Infinity cell or capacitively coupled open cylindrical cell during ion excitation. Simion simulations demonstrate that, during detection, appropriate changes of the potentials applied to the two new sets of electrodes produce a radial electric field z-profile that more closely approaches that for an ideal axial three-dimensional quadrupolar potential at high post-excitation ICR orbital radius, for improved signal-to-noise ratio and resolving power, and minimal m/z-discrimination.     

Excitation modes for fourier transform-ion cyclotron resonance mass spectrometry

Various geometric configurations for the excitation of coherent ion motion in Fourier transform-ion cyclotron resonance mass spectrometry (FT-ICR/MS) are analyzed (in some cases for the first time) with unified notation. The instantaneous power absorption, F v, in which v is ion velocity and F the force produced by the applied excitation electric field (harmonic, single frequency, on-resonance, in-phase), is time averaged and then set equal to the time rate of change of ion total (cyclotron + magnetron + trapping) energy, to yield a differential equation that is readily solved for the (time-dependent) amplitude of each of the various ion motions. The standard FT-ICR excitation (namely, radial dipolar) is reviewed. The effects of quadrature and radial quadrupolar excitation on ion radial (cyclotron and magnetron) motions are also reviewed. Frictional damping is shown to decrease the ion cyclotron orbital radius and trapping amplitude but increase the magnetron radius. Feedback excitation (i.e., excitation at the simultaneously detected ion cyclotron orbital frequency of the same ion packet) is introduced and analyzed as a means for exciting ions whose cyclotron frequency changes during excitation (as for relativistically shifted low-mass ions). In contrast to conventional radial dipolar excitation, axial dipolar excitation of the trapping motion leads to a mass-dependent ion motional amplitude. Parametric (i.e., axial quadrupolar) excitation is shown to produce an exponential increase in the ion motional amplitudes (hyperbolic sine and hyperbolic cosine amplitude for cyclotron and magnetron radii, respectively). More detailed consideration of parametric excitation leads to an optimal ion initial radial position in parametric-mode FT-ICRjMS.     

Initial Experimental Characterization of a New Ultra-High Resolution FTICR Cell with Dynamic Harmonization

A new Fourier transform ion cyclotron resonance (FTICR) cell based on completely new principles of formation of the effective electric potential distribution in Penning type traps, Boldin and Nikolaev (Proceedings of the 58th ASMS Conference, 2010), Boldin and Nikolaev (Rapid Commun Mass Spectrom 25:122–126, 2011) is constructed and tested experimentally. Its operation is based on the concept of electric potential space-averaging via charged particle cyclotron motion. Such an averaging process permits an effective electric force distribution in the entire volume of a cylindrical Penning trap to be equal to its distribution in the field created by hyperbolic electrodes in an ideal Penning trap. The excitation and detection electrodes of this new cell are shaped for generating a quadratic dependence on axial coordinates of an averaged (along cyclotron motion orbit) electric potential at any radius of the cyclotron motion. These electrodes together with the trapping segments form a cylindrical surface like in a conventional cylindrical cell. In excitation mode this cell being elongated behaves almost like an open cylindrical cell of the same length. It is more effective in ion motion harmonization at larger cyclotron radii than a Gabrielse et al.-type (Int J Mass Spectrom Ion Processes 88:319–332, 1989) cylindrical cell with four compensation sections. A mass resolving power of more than twenty millions of reserpine (m/z 609) and more than one million of highly charged BSA molecular ions (m/z 1357) has been obtained in a 7T magnetic field.     

Effect of frequency sweep direction on motion of excited ions in fourier transform ion cyclotron resonance cells

Ion motion during frequency sweep excitation was computer simulated to study the effect of the direction of frequency sweep on the z motion of ions in a cylindrical Fourier transform ion cyclotron resonance (FT-ICR) cell. It is shown that the z motion is more forcefully excited by upsweep that by downsweep; thus at large amplitudes ions are more easily ejected to the trapping electrodes by upsweep and larger cyclotron orbits can be achieved by downsweep. This effect was confirmed by experiment and the results are favorably compared with the calculations. From these results it is concluded that downward sweeping is advantageous for ion detection and upward sweeping is preferable for ion ejection. The simulations clearly explain the effect of the direction of frequency sweep by visualizing the directions of the forces that ions experience immediately after the excitation of their cyclotron motion. It was demonstrated by experiment that the z ejection can be reduced by applying a phase-adjusted ac potential to the trapping electrodes.     

Simulated ion trajectory and induced signal in ion cyclotron resonance ion traps

We present a numerical method for computation of electrostatic (trapping) and time-varying (excitation) electric fields and the resulting ion trajectory and detected time-domain-induced voltage signal in a rectangular (or cubic) ion cyclotron resonance (ICR) ion trap. The electric potential is calculated by use of the superposition principle and relaxation method with a large number of grid points (e.g., 100 × 100 × 100 for a cubic trap). Complex ICR experiments and spectra may now be simulated with high accuracy. Ion trajectories may be obtained for any combination of trapping and excitation modes, including quadrupolar or cubic trapping in static or dynamic mode; and dipolar, quadrupolar, or parametric excitation with single-frequency, frequency-sweep (chirp), or stored waveform inverse Fourier transform waveforms. The resulting ion trajectory may be represented either as its three dimensional spatial path or as two-dimensional plots of x-, y-, or z-position, velocity, or kinetic energy versus time in the absence or presence of excitation. Induced current is calculated by use of the reciprocity principle, and simulated ICR mass spectra are generated by Fourier transform of the corresponding time-domain voltage signal.     

Laser-induced fluorescence for ion tomography in a Penning trap

Laser-induced ion fluorescence of laser-desorbed Ba⁺ ions provides a measure of the relative number of ions near the center of the Penning trap of a Fourier transform ion cyclotron resonance mass spectrometer. Here, we report the detection of Penning-trapped ions by ion fluorescence, subject to radially outward ion cloud expansion (because of ion-neutral collisions), radially inward ion cloud compression (because of quadrupolar axialization), and the effects of buffer gas pressure and electrostatic trapping potential on those processes. At high pressure and high trapping voltage, radial ejection is far more rapid than axial ejection; quadrupolar axialization increases the number of ions near the center of the trap as well as the length of time that ions may be trapped; higher pressure results in faster magnetron radial expansion; and the choice of azimuthal quadrupolar excitation waveform significantly affects the efficacy of axialization. Based on these results, we suggest that directly detected laser-induced ion fluorescence provides a general new tool for mapping the ion distribution and its time evolution in response to various excitatory and damping effects.     

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.     

Improved ion extraction from a linear octopole ion trap: SIMION analysis and experimental demonstration

Externally generated ions are accumulated in a linear octopole ion trap before injection into our 9.4 T Fourier transform ion cyclotron resonance (FT-ICR) mass analyzer. Such instrumental configuration has previously been shown to provide improved sensitivity, scan rate, and duty cycle relative to accumulated trapping in the ICR cell. However, inefficient ion ejection from the octopole currently limits both detection limit and scan rate. SIMION 7.0 analysis predicts that a dc axial electric field inside the linear octopole ion trap expedites and synchronizes the efficient extraction of the octopole-accumulated ions. Further SIMION analysis optimizes the ion ejection properties of each of three electrode configurations designed to produce a near-linear axial potential gradient. More efficient extraction and transfer of accumulated ions spanning a wide m/z range promises to reduce detection limit and increase front-end sampling rate (e.g., to increase front-end resolution for separation techniques coupled with FT-ICR mass analysis). Addition of the axial field improves experimental signal-to-noise ratio by more than an order of magnitude.     

Dynamically Harmonized FT-ICR Cell with Specially Shaped Electrodes for Compensation of Inhomogeneity of the Magnetic Field. Computer Simulations of the Electric Field and Ion Motion Dynamics

The recently introduced ion trap for FT-ICR mass spectrometers with dynamic harmonization showed the highest resolving power ever achieved both for ions with moderate masses 500?C1000?Da (peptides) as well as ions with very high masses of up to 200?kDa (proteins). Such results were obtained for superconducting magnets of very high homogeneity of the magnetic field. For magnets with lower homogeneity, the time of transient duration would be smaller. In superconducting magnets used in FT-ICR mass spectrometry the inhomogeneity of the magnetic field in its axial direction prevails over the inhomogeneity in other directions and should be considered as the main factor influencing the synchronic motion of the ion cloud. The inhomogeneity leads to a dependence of the cyclotron frequency from the amplitude of axial oscillation in the potential well of the ion trap. As a consequence, ions in an ion cloud become dephased, which leads to signal attenuation and decrease in the resolving power. Ion cyclotron frequency is also affected by the radial component of the electric field. Hence, by appropriately adjusting the electric field one can compensate the inhomogeneity of the magnetic field and align the cyclotron frequency in the whole range of amplitudes of z-oscillations. A method of magnetic field inhomogeneity compensation in a dynamically harmonized FT-ICR cell is presented, based on adding of extra electrodes into the cell shaped in such a way that the averaged electric field created by these electrodes produces a counter force to the forces caused by the inhomogeneous magnetic field.     

Fourier transform ion cyclotron resonance cell with dynamic harmonization of the electric field in the whole volume by shaping of the excitation and detection electrode assembly

A new principle of formation of the effective electric field distribution in a Penning trap is presented. It is based on the concept of electric potential space averaging via charged particle cyclotron motion. The method of making hyperbolic-type field distribution in the whole volume of a cylindrical Penning trap is developed on the basis of this new principal. The method is based on subdividing the cell cylindrical surface into segments with shapes producing quadratic dependence on axial coordinate of an averaged (along cyclotron motion orbit) electric potential at any radius of cyclotron motion. The cell performance is compared in digital experiments with the performance of a Gabrielse-type cylindrical cell with four compensation electrodes and is shown to be more effective in ion motion harmonization at higher cyclotron radii and axial oscillation amplitude.     

Frequency shifts and modulation effects due to solenoidal magnetic field inhomogeneities in ion cyclotron mass spectrometry

Solenoidal (i.e. axially symmetric) magnetic field inhomogeneities, which in addition have symmetry under the operation z → −z are the most important to Fourier transform-ion cyclotron resonance (FT-ICR) mass spectrometry since they introduce frequency shifts at first-order in perturbation theory. Frequency shifts for all three fundamental modes are derived for the leading second-order and fourth-order solenoidal inhomogeneities without any restrictions on the initial conditions. The analytical frequency shifts agree very well with frequency shifts obtained from numerical trajectory calculations using the exact classical equations of motion. The effect of the inhomogeneity on the ion trajectory is solved analytically. For a strong magnetic bottle field, the cyclotron motion is frequency modulated at twice the z-oscillation frequency resulting in sidebands. However, the amplitude of these sidebands is negligibly small for typical inhomogeneity strengths. The effect of a magnetized ICR trap on the homogeneity of the magnetic field is studied by analytical methods. We find that the leading magnetic bottle field decreases as d⁻³, where d is the cylindrical ion trap diameter.     

Simplified electron ejection in Fourier transform ion cyclotron resonance mass spectrometry by suspended trapping

Suspended trapping is used to eject electrons in negative-ion Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometric experiments. In contrast to electron ejection by resonant excitation of the trapping motion, suspended trapping involves allowing the electrons to escape along the z-axis (perpendicular to the trap plates) while the trapping potential is briefly removed. The duration of this event is sufficiently short (～10 μs) so that ion losses are negligible; the overall effect is that of a ‘high-pass mass filter’. Suspended trapping is simpler to implement and more generally applicable to various cell geometries than resonant electron ejection. The effectiveness of the suspended trapping technique is not compromised by the anharmonicity of the potential well in ‘elongated’ ICR traps, but depends simply on the time it takes the electrons to escape the cell. Finally, a small, positive offset potential (～+0.25 V) applied to the trap plates during the suspended trapping event increases the efficiency of the ejection.     

Simulated ion trajectory and induced signal in ion cyclotron resonance ion traps. Effect of ion initial axial position on ion coherence,induced signal,and radial or z ejection in a cubic trap

The effects of ion initial axial position on coherence of ion motion, induced ion cyclotron resonance (ICR) signal. and radial and z ejection have been evaluated by numerical simulation for a cubic Fourier transform-ion cyclotron resonance ion trap. For a given initial ion cyclotron phase and radius, ions of different initial z position are shown to be excited to significantly different ion cyclotron radii (and ultimately radially ejected at significantly different excitation amplitude-duration products). Ion initial z displacement from the trap midplane affects observed ICR signal magnitude in two ways: (1) for the same postexcitation cyclotron radius, an ion with larger initial z displacement induces a smaller ICR signal and (2) an ion with larger initial z displacement is excited to a smaller cyclotron radius. We also evaluate the induced ICR signal as a function of excitation amplitude-duration product for spatially uniform or Gaussian ion initial z distributions. In general, if the excitation waveform contains components at frequency, 2 ω_z or (ω₊ + 2 ω_z, in which ω_z is the axial C“trapping”) oscillation frequency, then ejection occurs axially. However, the resulting excitation amplitude-duration product for such axial ejection is significantly higher (factor of, ～ 4) than that required for radial ejection (at ω₊) for ions of small initial radius. The present results offer the first explanation of how, even if the ion is initially at rest on the z axis (i.e., zero excitation electric field amplitude on the z axis), z ejection (axial ejection) may nevertheless occur if the excitation waveform contains frequency components at ω₊ + 2ω_z and/or 2_{w z} Namely, our simulations reveal that off-resonant excitation pushes ions away from the z axis, after which the ions are exposed to z excitation and eventual z ejection.     

Comparison of equilibrium ion density distribution and trapping force in penning, Paul, and combined ion traps

Starting from the classical Boltzmann distribution, we obtain the ion density distribution in the limit of either high temperature/low density (Coulomb interaction energy much less than ion kinetic energy) or low temperature/high density (kinetic energy much less than Coulomb interaction energy), and the trapping force for an ion cloud in Penning ion cyclotron resonance, Paul (quadrupole), and combined (Paul trap in a uniform axial static magnetic field) traps. At equilibrium (total angular momentum conserved), the ion cloud rotates at a constant frequency in Penning and combined traps. In a Penning trap, the maximum ion density is proportional to B ²/m (B is magnetic field and m is the mass of ions), whereas the maximum ion density in a Paul trap is proportional to (V _rf ² /mΩ² r ₀ ⁴ ), with Mathieu equation axial q value <0.4 to satisfy the pseudopotential approximation. Ion maximum densities in both Penning and Paul ion traps depend on the trapping field (magnetic or electric) and ion mass, but not on ion charge. In a Penning trap at maximum ion density (zero pressure), the radial (but not the axial) trapping potential is mass dependent, whereas both radial and axial potentials in a Paul trap at maximum ion density are mass dependent.     

Novel ion traps using planar resistive electrodes: Implications for miniaturized mass analyzers

In radiofrequency ion traps, electric fields are produced by applying time-varying potentials between machined metal electrodes. The electrode shape constitutes a boundary condition and defines the field shape. This paper presents a new approach to making ion traps in which the electrodes consist of two ceramic discs, the facing surfaces of which are lithographically imprinted with sets of concentric metal rings and overlaid with a resistive material. A radial potential function can be applied to the resistive material such that the potential between the plates is quadrupolar, and ions are trapped between the plates. The electric field is independent of geometry and can be optimized electronically. The trap can produce any trapping field geometry, including both a toroidal trapping geometry and the traditional Paul-trap field. Dimensionally smaller ion trajectories, as would be produced in a miniaturized ion trap, can be achieved by increasing the potential gradient on the resistive material and operating the trap at higher frequency, rather than by making any physical changes to the trap or the electrodes. Obstacles to miniaturization of ion traps, such as fabrication tolerances, surface smoothness, electrode alignment, limited access for ionization or ion injection, and small trapping volume are addressed using this design.     

Simplified application of quadrupolar excitation in Fourier transform ion cyclotron resonance mass spectrometry

A new method for application of quadrupolar excitation to the trapped ion cell of a Fourier transform ion cyclotron resonance (FTICR) mass spectrometer is presented. Quadrupolar excitation is conventionally applied to the two pairs of opposed electrodes that normally perform the excitation and detection functions in the FTICR experiment. Symmetry arguments and numerically calculated isopotential contours within the trapped ion cell lead to the conclusion that quadrupolar excitation can be applied to a single pair of opposed side electrodes. Examples of effective quadrupolar axialization via this method include a sevenfold signal-to-noise enhancement derived from 50 remeasurements of a single population of trapped bovine insulin ions and the selective isolation of a single charge state of horse heart myoglobin after an initial measurement that revealed the presence of 14 charge states.     

Laser-induced fluorescence of trapped gas-phase molecular ions generated by internal source matrix-assisted laser desorption/ionization in a Fourier transform ion cyclotron resonance mass spectrometer

The combination of laser-induced fluorescence with mass spectrometry opens up new possibilities both for detection purposes and for structural studies of trapped biomolecular ions in the gas phase. However, this approach is experimentally very challenging, and only a handful of studies have been reported so far. In this contribution, a novel scheme for laser-induced fluorescence measurements of ions trapped inside a Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometer will be introduced. It is based on an open FT-ICR cell design, continuous wave axial excitation of the fluorescence, orthogonal photon collection by fiber optics, and single photon counting detection. Rhodamine 6G ions generated by an internal matrix-assisted laser desorption/ionization source were used to develop and test the set-up. Due to photobleaching processes, the excitation laser power and the observation time window have to be carefully optimized. An ion tomography method was used to align the excitation laser. Potential applications for studying the gas-phase structure of fluorescent biomolecular ions and for investigating fluorescence resonance energy transfer of donor-acceptor pairs will be presented.     

Influence on mass‐selective ion ejection of the phase difference between the drive r.f. and the axial modulation potentials

The phase difference between the drive r.f. and the axial modulation potential is known to influence significantly the mass shift, and all commercial ion trap mass spectrometers use a fixed value for this difference. However, although this important parameter is partly responsible for the good precision achievable today in most commercial ion traps, little discussion on the variation of the phase difference between the drive r.f. and the axial modulation potential has appeared in the literature. We present here an examination of the influence of a low‐level axial modulation potential superimposed by capacitive coupling between the electrodes. Low‐level axial modulation potentials are used for certain analytical scans such as reverse scan or slow scan speeds. Such low‐level potentials help to prevent deterioration of mass resolution due to, for example, the dissociation of the ions during their resonant ejection from the ion trap. Reverse and forward scans are used to illustrate the mass shift and change in resolution, caused by a change in the phase difference between the drive r.f. potential applied to the ring electrode and the axial modulation potential applied on an end‐cap electrode, in electrospray ionization mass spectra. Copyright © 2005 John Wiley & Sons, Ltd.