Realistic modeling of ion cloud motion in a Fourier transform ion cyclotron resonance cell by use of a particle-in-cell approach

IDSimF: An Open-Source Framework for the Simulation of Molecular Ion Dynamics in Mass Spectrometry and Ion Mobility Spectrometry

The development of mass spectrometric and ion mobility devices heavily depends on a comprehensive understanding of the behavior of ions within such systems. Therefore, numerical modeling of ion paths helps to optimize and verify existing devices, and contributes to the development of innovative ion optical systems and multipole geometries. This Article introduces IDSimF (Ion Dynamics Simulation Framework), an open-source simulation tool tailored to the nonrelativistic dynamics of molecular ions in mass and ion mobility spectrometry applications. Addressing limitations in existing software packages, as for example SIMION, OpenFOAM, and COMSOL, IDSimF offers a specialized platform for simulating ion trajectories in electric fields. IDSimF efficiently accounts for space charge effects and considers various ion-neutral collision models while handling chemical kinetics. The framework is highly modular with reduced user input configuration complexity and aims to support simulation efforts in development and optimization of in mass spectrometers.

Ultra-Accurate Correlation between Precursor and Fragment Ions in Two-Dimensional Mass Spectrometry: Acetylated vs Trimethylated Histone Peptides

Two-dimensional mass spectrometry (2D MS) is a method for tandem mass spectrometry in which precursor and fragment ions are correlated by manipulating ion radii rather than by ion isolation. A 2D mass spectrum contains the fragmentation patterns of all analytes in a sample, acquired in parallel. We report ultrahigh-resolution narrowband 2D mass spectra of a mixture of two histone peptides with the same sequence, one of which carries an acetylation and the other a trimethylation (m/z 0.006 difference). We reduced the distance between data points in the precursor ion dimension and compared the accuracy of the precursor-fragment correlation with the resolving power. We manage to perform label-free quantification on the histone peptide mixture and show that precursor and fragment ions can be accurately correlated even though the precursor ions are not resolved. Finally, we show that increasing the resolution of a 2D mass spectrum in the precursor ion dimension too far can lead to a decline in the signal-to-noise ratio.

Generalization of an Open Dynamically Harmonized Cell for Ultrahigh FT ICR Resolution

FT ICR mass spectrometry is the leader in resolving power among all mass spectrometry methods. Introduction of the dynamically harmonized measuring cell─a closed-cylindrical cell with specifically shaped electrodes─helps to reach the resolving power of more than 10⁷ with a magnetic field of about 7 T. From the theory of FT ICR mass spectrometry it follows that the resolving power of this type of instrument depends linearly on the magnetic field under various conditions. However, the results obtained on this type of mass spectrometer with the maximum magnetic field achievable today did not show a proportional increase in resolving power. In one of our previous papers, we assumed that the reason for this was insufficient vacuum inside the cell, since vacuum quality should be at least proportional to the magnetic field, since the mean free run time decreases proportionally to the magnetic field growth. We have presented an open modification of the dynamically harmonized cell that can help improve the cell pumping conditions. However, the electric potential distribution inside this new cell is slightly different from the ideal (harmonic) one, obtained inside the closed version of the cell, and the resolving power may have been limited by this difference.

Evaluation of major historical ICR cell designs using electric field simulations

In Fourier-transform ion cyclotron resonance mass spectrometry, ions are detected by measuring image current induced in the detecting electrodes by trapped ions rotating in a magnetic field at their cyclotron frequencies. The ion trap used for this purpose is called the Penning trap. It can have various configurations of electrodes that are used to create a trapping electric field, to excite cyclotron motion, and to detect the induced signal. The evolution of this type of mass spectrometry is mainly driven by progress in the technology of superconducting magnets and in the constantly improved design of the ion cyclotron resonance (ICR) measuring cell. In this review, we focus on ICR cell designs. We consider that the driving forces of this evolution are the desire to increase resolution, mass accuracy and dynamic range, as well as to adapt new methods for creating and trapping ions.

Fourier transform ion cyclotron resonance mass spectrometry at the true cyclotron frequency

Ion cyclotron resonance (ICR) cells provide stability and coherence of ion oscillations in crossed electric and magnetic fields over extended periods of time. Using the Fourier transform enables precise measurements of ion oscillation frequencies. These precisely measured frequencies are converted into highly accurate mass-to-charge ratios of the analyte ions by calibration procedures. In terms of resolution and mass accuracy, Fourier transform ICR mass spectrometry (FT-ICR MS) offers the highest performance of any MS technology. This is reflected in its wide range of applications. However, in the most challenging MS application, for example, imaging, enhancements in the mass accuracy of fluctuating ion fluxes are required to continue advancing the field. One approach is to shift the ion signal power into the peak corresponding to the true cyclotron frequency instead of the reduced cyclotron frequency peak. The benefits of measuring the true cyclotron frequency include increased tolerance to electric fields within the ICR cell, which enhances frequency measurement precision. As a result, many attempts to implement this mode of FT-ICR MS operation have occurred. Examples of true cyclotron frequency measurements include detection of magnetron inter-harmonics of the reduced cyclotron frequency (i.e., the sidebands), trapping field-free (i.e., screened) ICR cells, and hyperbolic ICR cells with quadrupolar ion detection. More recently, ICR cells with spatially distributed ion clouds have demonstrated attractive performance characteristics for true cyclotron frequency ion detection. Here, we review the corresponding developments in FT-ICR MS over the past 40 years.

Particle-in-cell techniques for the study of space charge effects in an electrostatic ion beam trap

We developed a simulation technique to study the effect of space charge interaction between trapped ions in the electrostatic ion beam trap (EIBT). The importance of space charge is demonstrated in both the dispersive and the self-bunching regime of the ion trap. The simulation results provide an estimate for the space charge effect on the trapping efficiency. They also allow for a better understanding of the enhanced diffusion and the self-bunching effect and provide a better characterization of the EIBT as a mass spectrometer, where peak coalescence is important. The numerical results reproduce all experimental data, demonstrating the critical importance of including space charge effects, even at low ion density, to understand the ion trap dynamics.

Application of Optimal Control Theory to Fourier Transform Ion Cyclotron Resonance

We study the application of Optimal Control Theory to Ion Cyclotron Resonance. We test the validity and the efficiency of this approach for the robust excitation of an ensemble of ions with a wide range of cyclotron frequencies. Optimal analytical solutions are derived in the case without any pulse constraint. A gradient-based numerical optimization algorithm is proposed to take into account limitation in the control intensity. The efficiency of optimal pulses is investigated as a function of control time, maximum amplitude and range of excited frequencies. A comparison with adiabatic and SWIFT pulses is done. On the basis of recent results in Nuclear Magnetic Resonance, this study highlights the potential usefulness of optimal control in Ion Cyclotron Resonance.

Analytical Solution for the Electric Field Inside Dynamically Harmonized FT-ICR Cell

Dynamically harmonized FT-ICR cell has a saddle-like hyperbolic field distribution inside when averaged over a cyclotron trajectory around the axis of the cell. Such a field distribution makes the motion along the magnetic field independent of the motion in the x,y-plane, as well as the cyclotron motion independent of the magnetron motion and prevents any disintegration of excited coherent ion clouds, which is ruining the resolution in the other types of FT-ICR cells providing by this ideal phasing of single-m/z ion clouds in the entire volume of the cell. FT-ICR instruments with such a cell show resolutions of more than ten million at m/z 1000 at relatively small magnetic fields like 7 Tesla in quadrupole detection mode, what is not reachable by any other type of modern mass spectrometers. We have found that for such ion traps, it is possible to find the analytical solution in the working volume of the trap without any averaging. The potential distribution for the almost whole volume of such a cell can be presented in the form ϕ(x, y, z) = αz² + f_2D(x, y), where f_2D(x, y) is the solution of 2D Poisson equation, which could be found by the method of conformal transformation. This solution is applicable in the practical case and can serve as a base for an analytical theory of signal detection using such cells and as a standard for solutions obtained by numerical simulations of the cell field.

Two-dimensional mass spectrometry: new perspectives for tandem mass spectrometry

Fourier transform ion cyclotron resonance mass analysers (FT-ICR MS) can offer the highest resolutions and mass accuracies in mass spectrometry. Mass spectra acquired in an FT-ICR MS can yield accurate elemental compositions of all compounds in a complex sample. Fragmentation caused by ion-neutral, ion-electron, or ion-photon interactions leads to more detailed structural information on compounds. The most often used method to correlate compounds and their fragment ions is to isolate the precursor ions from the sample before fragmentation. Two-dimensional mass spectrometry (2D MS) offers a method to correlate precursor and fragment ions without requiring precursor isolation. 2D MS therefore enables easy access to the fragmentation patterns of all compounds from complex samples. In this article, the principles of FT-ICR MS are reviewed and the 2D MS experiment is explained. Data processing for 2D MS is detailed, and the interpretation of 2D mass spectra is described.

Cyclotron Phase-Coherent Ion Spatial Dispersion in a Non-Quadratic Trapping Potential is Responsible for FT-ICR MS at the Cyclotron Frequency

Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) at the cyclotron frequency instead of the reduced cyclotron frequency has been experimentally demonstrated using narrow aperture detection electrode (NADEL) ICR cells. Here, based on the results of SIMION simulations, we provide the initial mechanistic insights into the cyclotron frequency regime generation in FT-ICR MS. The reason for cyclotron frequency regime is found to be a new type of a collective motion of ions with a certain dispersion in the initial characteristics, such as pre-excitation ion velocities, in a highly non-quadratic trapping potential as realized in NADEL ICR cells. During ion detection, ions of the same m/z move in phase for cyclotron ion motion but out of phase for magnetron (drift) ion motion destroying signals at the fundamental and high order harmonics that comprise reduced cyclotron frequency components. After an initial magnetron motion period, ion clouds distribute into a novel type of structures - ion slabs, elliptical cylinders, or star-like structures. These structures rotate at the Larmor (half-cyclotron) frequency on a plane orthogonal to the magnetic field, inducing signals at the true cyclotron frequency on each of the narrow aperture detection electrodes. To eliminate the reduced cyclotron frequency peak upon dipolar ion detection, a number of slabs or elliptical cylinders organizing a star-like configuration are formed. In a NADEL ICR cell with quadrupolar ion detection, a single slab or an elliptical cylinder is sufficient to minimize the intensity of the reduced cyclotron frequency components, particularly the second harmonic. Graphical Abstract ᅟ.

Multiparticle Simulations of Quadrupolar Ion Detection in an Ion Cyclotron Resonance Cell with Four Narrow Aperture Detection Electrodes

The current paradigm in FT-ICR cell design is to approximate the ideal three-dimensional quadratic trapping potential as closely as possible to maintain ion cloud spatial coherence and achieve long transients, either with hyperbolically shaped electrodes, shimming electrodes, or by dynamic harmonization. In sharp contrast, the FT-ICR analyzer cell with four narrow aperture detection electrodes (NADEL) introduces significant anharmonic terms to the trapping potential. This analyzer cell is capable of quadrupolar detection by which one can measure a signal that is close to the unperturbed cyclotron frequency. This is far less sensitive to trapping potential and space charge shifts than the reduced cyclotron frequency measured in conventional ICR cells. The quadrupolar mode of ion detection in NADEL cells has been examined previously by SIMION simulations of ion clouds with up to 500 ions per simulation. Here, the behavior of the NADEL analyzer cell is examined through particle-in-cell (PIC) simulations, which allows us to examine the behavior of large populations (tens of thousands) of ions with space charge considerations, and to calculate the induced charge on the NADEL detection electrodes, and thus the transient signal. PIC simulations confirm a unique spatial distribution of the ions, with a coherent motion that results in long transient signals. Dependence of the ion cloud and image current signal on cell design, ion energy, and magnetron radius are examined. Coalescence effects are compared with those found in a dynamically harmonized cell. The insensitivity of the measured cyclotron frequency to space-charge is demonstrated both with simulations and experimentally. Graphical Abstract ᅟ.

Effect of ion clouds micromotion on measured signal in Fourier transform ion cyclotron resonance: Computer simulation

Particle-in-cell-based realistic simulation of Fourier transform ion cyclotron resonance experiments could be used to generate ion trajectories and a signal induced on the detection electrodes. It has been shown recently that there is a modulation of "reduced" cyclotron frequencies in ion cyclotron resonance signal caused by Coulomb interaction of ion clouds. In this work it was proposed to use this modulation in order to determine frequency difference between an ion of known m/z and all other ions generating signal in ion cyclotron resonance cell. It is shown that with an increase of number of ions in ion cyclotron resonance trap, the modulation index increases, which lead to a decrease in the accuracy of determination of peak intensities by super Fourier transform resolution methods such as filter diagonalization method.

Reducing Space Charge Effects in a Linear Ion Trap by Rhombic Ion Excitation and Ejection

Space charge effects play important roles in ion trap operations, which typically limit the ion trapping capacity, dynamic range, mass accuracy, and resolving power of a quadrupole ion trap. In this study, a rhombic ion excitation and ejection method was proposed to minimize space charge effects in a linear ion trap. Instead of applying a single dipolar AC excitation signal, two dipolar AC excitation signals with the same frequency and amplitude but 90° phase difference were applied in the x- and y-directions of the linear ion trap, respectively. As a result, mass selective excited ions would circle around the ion cloud located at the center of the ion trap, rather than go through the ion cloud. In this work, excited ions were then axially ejected and detected, but this rhombic ion excitation method could also be applied to linear ion traps with ion radial ejection capabilities. Experiments show that space charge induced mass resolution degradation and mass shift could be alleviated with this method. For the experimental conditions in this work, space charge induced mass shift could be decreased by ~50%, and the mass resolving power could be improved by ~2 times at the same time. Graphical Abstract ᅟ.

Fourier transform ion cyclotron resonance (FT ICR) mass spectrometry: Theory and simulations

Fourier transform ion cyclotron resonance (FT ICR) mass spectrometer offers highest resolving power and mass accuracy among all types of mass spectrometers. Its unique analytical characteristics made FT ICR important tool for proteomics, metabolomics, petroleomics, and investigation of complex mixtures. Signal acquisition in FT ICR MS takes long time (up to minutes). During this time ion-ion interaction considerably affects ion motion and result in decreasing of the resolving power. Understanding of those effects required complicated theory and supercomputer simulations but culminated in the invention of the ion trap with dynamic harmonization which demonstrated the highest resolving power ever achieved. In this review we summarize latest achievements in theory and simulation of FT ICR mass spectrometers.

Effect of magnetic field inhomogeneity on ion cyclotron motion coherence at high magnetic field

A three-dimensional code based on the particle-in-cell algorithm modified to account for the inhomogeneity of the magnetic field was applied to determine the effect of Z(1), Z(2), Z(3), Z(4), X, Y, ZX, ZY, XZ(2) YZ(2), XY and X(2)-Y(2) components of an orthogonal magnetic field expansion on ion motion during detection in an FT-ICR cell. Simulations were performed for magnetic field strengths of 4.7, 7, 14.5 and 21 Tesla, including experimentally determined magnetic field spatial distributions for existing 4.7 T and 14.5 T magnets. The effect of magnetic field inhomogeneity on ion cloud stabilization ("ion condensation") at high numbers of ions was investigated by direct simulations of individual ion trajectories. Z(1), Z(2), Z(3) and Z(4) components have the largest effect (especially Z(1)) on ion cloud stability. Higher magnetic field strength and lower m/z demand higher relative magnetic field homogeneity to maintain cloud coherence for a fixed time period. The dependence of mass resolving power upper limit on Z(1) inhomogeneity is evaluated for different magnetic fields and m/z. The results serve to set the homogeneity requirements for various orthogonal magnetic field components (shims) for future FT-ICR magnet design.

Application of printed circuit board technology to FT-ICR MS analyzer cell construction and prototyping

Although Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) remains the mass spectrometry platform that provides the highest levels of performance for mass accuracy and resolving power, there is room for improvement in analyzer cell design as the ideal quadrupolar trapping potential has yet to be generated for a broadband MS experiment. To this end, analyzer cell designs have improved since the field's inception, yet few research groups participate in this area because of the high cost of instrumentation efforts. As a step towards reducing this barrier to participation and allowing for more designs to be physically tested, we introduce a method of FT-ICR analyzer cell prototyping utilizing printed circuit boards at modest vacuum conditions. This method allows for inexpensive devices to be readily fabricated and tested over short intervals and should open the field to laboratories lacking or unable to access high performance machine shop facilities because of the required financial investment.

Least-squares fitting of time-domain signals for Fourier transform mass spectrometry

To advance Fourier transform mass spectrometry (FTMS)-based molecular structure analysis, corresponding development of the FTMS signal processing methods and instrumentation is required. Here, we demonstrate utility of a least-squares fitting (LSF) method for analysis of FTMS time-domain (transient) signals. We evaluate the LSF method in the analysis of single- and multiple-component experimental and simulated ion cyclotron resonance (ICR) and Orbitrap FTMS transient signals. Overall, the LSF method allows one to estimate the analytical limits of the conventional instrumentation and signal processing methods in FTMS. Particularly, LSF provides accurate information on initial phases of sinusoidal components in a given transient. For instance, the phase distribution obtained for a statistical set of experimental transients reveals the effect of the first data-point problem in FT-ICR MS. Additionally, LSF might be useful to improve the implementation of the absorption-mode FT spectral representation for FTMS applications. Finally, LSF can find utility in characterization and development of filter-diagonalization method (FDM) MS.

Twelve million resolving power on 4.7 T Fourier transform ion cyclotron resonance instrument with dynamically harmonized cell--observation of fine structure in peptide mass spectra

Resolving power of about 12,000 000 at m/z 675 has been achieved on low field homogeneity 4.7 T magnet using a dynamically harmonized Fourier transform ion cyclotron resonance (FT ICR) cell. Mass spectra of the fine structure of the isotopic distribution of a peptide were obtained and strong discrimination of small intensity peaks was observed in case of resonance excitation of the ions of the whole isotopic cluster to the same cyclotron radius. The absence of some peaks from the mass spectra of the fine structure was explained basing on results of computer simulations showing strong ion cloud interactions, which cause the coalescence of peaks with m/z close to that of the highest magnitude peak. The way to prevent peak discrimination is to excite ion clouds of different m/z to different cyclotron radii, which was demonstrated and investigated both experimentally and by computer simulations.

Ion dynamics in a trapped ion mobility spectrometer

In the present paper, theoretical simulations and experimental observations are used to describe the ion dynamics in a trapped ion mobility spectrometer. In particular, the ion motion, ion transmission and mobility separation are discussed as a function of the bath gas velocity, radial confinement, analysis time and speed. Mobility analysis and calibration procedure are reported for the case of sphere-like molecules for positive and negative ion modes. Results showed that a maximal mobility resolution can be achieved by optimizing the gas velocity, radial confinement (RF amplitude) and ramp speed (voltage range and ramp time). The mobility resolution scales with the electric field and gas velocity and R = 100-250 can be routinely obtained at room temperature.

Space charge induced nonlinear effects in quadrupole ion traps

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

Elemental composition validation from stored waveform inverse Fourier transform (SWIFT) isolation FT-ICR MS isotopic fine structure

Elemental composition assignment confidence in mass spectrometry is typically assessed by monoisotopic mass accuracy. For a given mass accuracy, resolution and detection of other isotopologues can further narrow the number of possible elemental compositions. However, such measurements require ultrahigh resolving power and high dynamic range, particularly for compounds containing low numbers of nitrogen and oxygen (both (15)N and (18)O occur at less than 0.4% natural abundance). Here, we demonstrate validation of molecular formula assignment from isotopic fine structure, based on ultrahigh resolution broadband Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS). Dynamic range is enhanced by external quadrupole and internal stored waveform inverse Fourier transform (SWIFT) isolation to facilitate detection of low abundance heavy atom isotopologues.

Scaling properties and intermittency of two-dimensional turbulence in pure electron plasmas

When the cold nonrelativistic guiding center approximation is valid, the transverse dynamics of highly magnetized electron plasma columns confined in Penning-Malmberg traps is analogous to that of an incompressible, inviscid, two-dimensional (2D) fluid whose vorticity corresponds, up to a constant of proportionality, to the axially averaged electron plasma density. In this work intermittency phenomena in the freely decaying 2D electron plasma turbulence are investigated through scaling properties of the probability density functions and flatness of spatial vorticity increments, computed by analyzing the results of experiments performed in the Penning-Malmberg trap ELTRAP. It is shown that the intermittency properties of the turbulence strongly depends on the initial conditions and the relation of these results to the dynamics of the system is discussed.

Mass resolution and mass accuracy: how much is enough?

Accurate mass measurement requires the highest possible mass resolution, to ensure that only a single elemental composition contributes to the mass spectral peak in question. Although mass resolution is conventionally defined as the closest distinguishable separation between two peaks of equal height and width, the required mass resolving power can be ∼10× higher for equal width peaks whose peak height ratio is 100 : 1. Ergo, minimum resolving power requires specification of maximum dynamic range, and is thus 10-100× higher than the conventional definition. Mass resolving power also depends on mass-to-charge ratio. Mass accuracy depends on mass spectral signal-to-noise ratio and digital resolution. Finally, the reliability of elemental composition assignment can be improved by resolution of isotopic fine structure. Thus, the answer to the question of "how much is enough mass resolving power" requires that one first specify S/N ratio, dynamic range, digital resolution, mass-to-charge ratio, and (if available) isotopic fine structure. The highest available broadband mass resolving power and mass accuracy is from Fourier transform ion cyclotron resonance mass spectrometry. Over the past five years, FT-ICR MS mass accuracy has improved by about an order of magnitude, based on higher magnetic field strength, conditional averaging of time-domain transients, better mass calibration (spectral segmentation; inclusion of a space charge term); radially dispersed excitation; phase correction to yield absorption-mode display; and new ICR cell segmentation designs.

From Supercomputer Modeling to Highest Mass Resolution in FT-ICR

Understanding of behavior of ion ensembles inside FT-ICR cell based on the computer simulation of ion motion gives rise to the new ideas of cell designs. The recently introduced novel FT-ICR cell based on a Penning ion trap with specially shaped excitation and detection electrodes prevents distortion of ion cyclotron motion phases (normally caused by non-ideal electric trapping fields) by averaging the trapping DC electric field during the ion motion in the ICR cell. Detection times of 5 min resulting in resolving power close to 40,000,000 have been reached for reserpine at m/z 609 at a magnetic field of only 7 Tesla. Fine structures of resolved 13Cn isotopic cluster groups could be measured for molecular masses up to 5.7 kDa (insulin) with resolving power of 4,000,000 at 7 Tesla. Based on resolved fine structure patterns atomic compositions can be directly determined using a new developed algorithm for fine structure processing. Mass spectra of proteins and multimers of proteins reaching masses up to 186 kDa (enolase tetramer) could be measured with isotopic resolution. For instance, at 7 Tesla resolving power of 800,000 was achieved for enolase dimer (96 kDa) and 500,000 for molecular masses above 100 kDa. Experimental data indicate that there is practically no limit for the resolving power of this ICR cell except by collisional damping in the ultrahigh vacuum chamber.

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 500-1000 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.

Accelerated simulation study of space charge effects in quadrupole ion traps using GPU techniques

Space charge effects play important roles in the performance of various types of mass analyzers. Simulation of space charge effects is often limited by the computation capability. In this study, we evaluate the method of using graphics processing unit (GPU) to accelerate ion trajectory simulation. Simulation using GPU has been compared with multi-core central processing unit (CPU), and an acceleration of about 390 times have been obtained using a single computer for simulation of up to 10(5) ions in quadrupole ion traps. Characteristics of trapped ions can be investigated at detailed levels within a reasonable simulation time. Space charge effects on the trapping capacities of linear and 3D ion traps, ion cloud shapes, ion motion frequency shift, mass spectrum peak coalescence effects between two ion clouds of close m/z are studied with the ion trajectory simulation using GPU.

Data processing for 3D mass spectrometry imaging

Data processing for three dimensional mass spectrometry (3D-MS) imaging was investigated, starting with a consideration of the challenges in its practical implementation using a series of sections of a tissue volume. The technical issues related to data reduction, 2D imaging data alignment, 3D visualization, and statistical data analysis were identified. Software solutions for these tasks were developed using functions in MATLAB. Peak detection and peak alignment were applied to reduce the data size, while retaining the mass accuracy. The main morphologic features of tissue sections were extracted using a classification method for data alignment. Data insertion was performed to construct a 3D data set with spectral information that can be used for generating 3D views and for data analysis. The imaging data previously obtained for a mouse brain using desorption electrospray ionization mass spectrometry (DESI-MS) imaging have been used to test and demonstrate the new methodology.

Performance of Orbitrap mass analyzer at various space charge and non-ideal field conditions: simulation approach

The orbital trap mass analyzer provides a number of unique analytical features along with inevitable limitations as an electrostatic instrument operating in high space charge regimes resulting in systematic measured frequency errors as an effect of stored ion clouds on the trap field and each other effect of non-ideal machining the trap electrodes, effect of injection slot, effect of real versus theoretical trap dimensions, etc. This paper deals with determining the influence of the space charge effect and imperfection of the electrostatic field on the motion of ion ensembles in the orbital trap. We examine effects of theoretically modeled non-harmonicity of the electrostatic potential and the number of confined ions on stability of coherent ion motion in the trap that determines the frequency shifts of axial ion oscillation. Three different Orbitrap geometries were considered: geometry close to preproduction Orbitrap, close to standard Orbitrap, close to high field Orbitrap. Frequency shifts for m/z = 500 and for charge state +23 of cytochrome c isotopic cluster particles with 10(4)-6*10(6) elemental charges in the trap were considered. Refined spectra were calculated using the filter diagonalization method proposed by Mandelshtam et al. and applied to mass spectrometry by O'Connor and Aizikov.

Fourier transform ion cyclotron resonance mass resolution and dynamic range limits calculated by computer modeling of ion cloud motion

Particle-in-Cell (PIC) ion trajectory calculations provide the most realistic simulation of Fourier transform ion cyclotron resonance (FT-ICR) experiments by efficient and accurate calculation of the forces acting on each ion in an ensemble (cloud), including Coulomb interactions (space charge), the electric field of the ICR trap electrodes, image charges on the trap electrodes, the magnetic field, and collisions with neutral gas molecules. It has been shown recently that ion cloud collective behavior is required to generate an FT-ICR signal and that two main phenomena influence mass resolution and dynamic range. The first is formation of an ellipsoidal ion cloud (termed "condensation") at a critical ion number (density), which facilitates signal generation in an FT-ICR cell of arbitrary geometry because the condensed cloud behaves as a quasi-ion. The second phenomenon is peak coalescence. Ion resonances that are closely spaced in m/z coalesce into one resonance if the ion number (density) exceeds a threshold that depends on magnetic field strength, ion cyclotron radius, ion masses and mass difference, and ion initial spatial distribution. These two phenomena decrease dynamic range by rapid cloud dephasing at small ion density and by cloud coalescence at high ion density. Here, we use PIC simulations to quantitate the dependence of coalescence on each critical parameter. Transitions between independent and coalesced motion were observed in a series of the experiments that systematically varied ion number, magnetic field strength, ion radius, ion m/z, ion m/z difference, and ion initial spatial distribution (the present simulations begin from elliptically-shaped ion clouds with constant ion density distribution). Our simulations show that mass resolution is constant at a given magnetic field strength with increasing ion number until a critical value (N) is reached. N dependence on magnetic field strength, cyclotron radius, ion mass, and difference between ion masses was determined for two ion ensembles of different m/z, equal abundance, and equal cyclotron radius. We find that N and dynamic range depend quadratically on magnetic field strength in the range 1-21 Tesla. Dependences on cyclotron radius and Δm/z are linear. N depends on m/z as (m/z)(-2). Empirical expressions for mass resolution as a function of each of the experimental parameters are presented. Here, we provide the first exposition of the origin and extent of trade-off between FT-ICR MS dynamic range and mass resolution (defined not as line width, but as the separation between the most closely resolved masses).

Fourier transform mass spectrometry

This article provides an introduction to Fourier transform-based mass spectrometry. The key performance characteristics of Fourier transform-based mass spectrometry, mass accuracy and resolution, are presented in the view of how they impact the interpretation of measurements in proteomic applications. The theory and principles of operation of two types of mass analyzer, Fourier transform ion cyclotron resonance and Orbitrap, are described. Major benefits as well as limitations of Fourier transform-based mass spectrometry technology are discussed in the context of practical sample analysis, and illustrated with examples included as figures in this text and in the accompanying slide set. Comparisons highlighting the performance differences between the two mass analyzers are made where deemed useful in assisting the user with choosing the most appropriate technology for an application. Recent developments of these high-performing mass spectrometers are mentioned to provide a future outlook.

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.

Two-dimensional Fourier transform ion cyclotron resonance mass spectrometry: reduction of scintillation noise using Cadzow data processing

In two-dimensional Fourier transform ion cyclotron resonance mass spectrometry (2D FTICR-MS), scintillation noise, caused mostly by fluctuations in the number of ions in the ICR cell, is the leading cause for errors in spectrum interpretation. In this study, we adapted an algorithm based on singular value decomposition and first introduced by Cadzow et al. (IEE Proceedings Pt. F 1987, 134, 69) to 2D FTICR-MS and we measured its performance in terms of noise reduction without losing signal information in the 2D mass spectrum.

Ion Behavior in an Electrically Compensated Ion Cyclotron Resonance Trap

We recently described a new electrically compensated trap in FT ion cyclotron resonance mass spectrometry and developed a means of tuning traps of this general design. Here, we describe a continuation of that research by comparing the ion transient lifetimes and the resulting mass resolving powers and signal-to-noise (S/N) ratios that are achievable in the compensated vs. uncompensated modes of this trap. Transient lifetimes are ten times longer under the same conditions of pressure, providing improved mass resolving power and S/N ratios. The mass resolving power as a function of m/z is linear (log-log plot) and nearly equal to the theoretical maximum. Importantly, the ion cyclotron frequency as a function of ion number decreases linearly in accord with theory, unlike its behavior in the uncompensated mode. This linearity should lead to better control in mass calibration and increased mass accuracy than achievable in the uncompensated mode.

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.

Automated broadband phase correction of Fourier transform ion cyclotron resonance mass spectra

It has been known for 35 years that phase correction of FTICR data can in principle produce an absorption-mode spectrum with mass resolving power as much as a factor of 2 higher than conventional magnitude-mode display, an improvement otherwise requiring a (much more expensive) increase in magnetic field strength. However, temporally dispersed excitation followed by time-delayed detection results in steep quadratic variation of signal phase with frequency. Here, we present a robust, rapid, automated method to enable accurate broadband phase correction for all peaks in the mass spectrum. Low-pass digital filtering effectively eliminates the accompanying baseline roll. Experimental FTICR absorption-mode mass spectra exhibit at least 40% higher resolving power (and thus an increased number of resolved peaks) as well as higher mass accuracy relative to magnitude mode spectra, for more complete and more reliable elemental composition assignments for mixtures as complex as petroleum.

Peak coalescence, spontaneous loss of coherence, and quantification of the relative abundances of two species in the plasma regime: particle-in-cell modeling of Fourier transform ion cyclotron resonance mass spectrometry

Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS) is often limited by space-charge effects. Previously, particle-in-cell (PIC) simulations have been used to understand these effects on FTICR-MS signals. However, none have extended fully into the space-charge dominated (plasma) regime. We use a two-dimensional (2-D) electrostatic PIC code, which facilitates work at very high number densities at modest computational cost to study FTICR-MS in the plasma regime. In our simulation, we have observed peak coalescence and the rapid loss of signal coherence, two common experimental problems. This demonstrates that a 2-D model can simulate these effects. The 2-D code can handle a larger numbers of particles and finer spatial resolution than can currently be addressed by 3-D models. The PIC method naturally takes into account image charge and space charge effects in trapped-ion mass spectrometry. We found we can quantify the relative abundances of two closely spaced (such as (7)Be(+) and (7)Li(+)) species in the plasma regime even when their peaks have coalesced. We find that the frequency of the coalesced peak shifts linearly according to the relative abundances of these species. Space charge also affects more widely spaced lines. Singly-ionized (7)BeH and (7)Li have two separate peaks in the plasma regime. Both the frequency and peak area vary nonlinearly with their relative abundances. Under some conditions, the signal exhibited a rapid loss of coherence. We found that this is due to a high order diocotron instability growing in the ion cloud.

Fourier transform ion cyclotron resonance mass spectrometer with coaxial multi-electrode cell ('O-trap'): first experimental demonstration

The conceptual design of the O-trap Fourier transform ion cyclotron resonance (FT-ICR) cell addresses the speed of analysis issue in FT-ICR mass spectrometry. The concept of the O-trap includes separating the functions of ion excitation and detection between two different FT-ICR cell compartments. The detection compartment of the O-trap implements additional internal coaxial electrodes around which ions with excited cyclotron motion revolve. The expected benefits are higher resolving power and the lesser effect of the space charge. In this work we present the first experimental demonstration of the O-trap cell and its features, including the high ion transfer efficiency between two distinct compartments of an ICR cell after excitation of the coherent cyclotron motion. We demonstrate that utilization of the multiple-electrode detection in the O-trap provides mass resolving power enhancement (achieved over a certain time) equal to the order of the frequency multiplication. In an O-trap installed in a 5 T desk-top cryogen-free superconducting magnet, the resolving power of R = 80,000 was achieved for bradykinin [M + 2H](2+) (m/z 531; equivalent to 100,000 when recalculated for m/z 400) in 0.2 s analysis time (transient length), and R = 300,000 at m/z 531 for a 1 s transient. In both cases, detection on the third multiple of the cyclotron frequency was implemented. In terms of the acquisition speed at fixed resolving power, such performance is equivalent to conventional FT-ICR detection using a 15 T magnet.

Transformative effects of higher magnetic field in Fourier transform ion cyclotron resonance mass spectrometry

The relationship of magnetic field strength and Fourier transform ion cyclotron resonance mass spectrometry performance was tested using three instruments with the same design but different fields of 4.7, 7, and 9.4 tesla. We found that the theoretically predicted "transformative" effects of magnetic field are indeed observed experimentally. The most striking effects were that mass accuracy demonstrated approximately second to third order improvement with the magnetic field, depending upon the charge state of the analyte, and that peak splitting, which prohibited automated data analysis at 4.7 T, was not observed at 9.4 T.

Comparison of particle-in-cell simulations with experimentally observed frequency shifts between ions of the same mass-to-charge in Fourier transform ion cyclotron resonance mass spectrometry

It has been previously observed that the measured frequency of ions in a Fourier transform mass spectrometry experiment depend upon the number of trapped ions, even for populations consisting exclusively of a single mass-to-charge. Since ions of the same mass-to-charge are thought not to exert a space-charge effect among themselves, the experimental observation of such frequency shifts raises questions about their origin. To determine the source of such experimentally observed frequency shifts, multiparticle ion trajectory simulations have been conducted on monoisotopic populations of Cs(+) ranging from 10(2) ions to 10(6) ions. A close match to experimental behavior is observed. By probing the effect of ion number and orbital radius on the shift in the cyclotron frequency, it is shown that for a monoisotopic population of ions, the frequency shift is caused by the interaction of ions with their image-charge. The addition of ions of a second mass-to-charge to the simulation allows the comparison of the magnitude of the frequency shift resulting from space-charge (ion-ion) effects versus ion interactions with their image charge.

Ion trap mass analysis at high pressure: a theoretical view

The mass-selective manipulation of ions at elevated pressure, including mass analysis, ion isolation, or excitation, is of great interest for the development of mass spectrometry instrumentation, particularly for systems in which ion traps are employed as mass analyzers or storage devices. While experimental exploration of high-pressure mass analysis is limited by various difficulties, such as ion detection or electrical discharge at high-pressure, theoretical methods have been developed in this work to study ion/neutral collision effects within quadrupole ion traps and to explore their performance at pressures up to 1 Torr. Ion trapping, isolation, excitation, and resonance ejection were investigated over a wide pressure range. The theoretically calculated data were compared with available experimental data for pressures up to 50 mTorr, allowing the prediction of ion trap performance at pressures more than 10 times higher.

Theory of peak coalescence in Fourier transform ion cyclotron resonance mass spectrometry

Peak coalescence, i.e. the merging of two close peaks in a Fourier transform ion cyclotron resonance (FTICR) mass spectrum at a high number of ions, plays an important role in various FTICR experiments. In order to describe the coalescence phenomenon we would like to propose a new theory of motion for ion clouds with close mass-to-charge ratios, driven by a uniform magnetic field and Coulomb interactions between the clouds. We describe the motion of the ion clouds in terms of their averaged drift motion in crossed magnetic and electric fields. The ion clouds are considered to be of constant size and their motion is studied in two dimensions. The theory deals with the first-order approximation of the equations of motion in relation to dm/m, where dm is the mass difference and m is the mass of a single ion. The analysis was done for an arbitrary inter-cloud interaction potential, which makes it possible to analyze finite-size ion clouds of any shape. The final analytical expression for the condition of the onset of coalescence is found for the case of uniformly charged spheres. An algorithm for finding this condition for an arbitrary interaction potential is proposed. The critical number of ions for the peak coalescence to take place is shown to depend quadratically on the magnetic field strength and to be proportional to the cyclotron radius and inversely proportional to the ion masses.

The spontaneous loss of coherence catastrophe in Fourier transform ion cyclotron resonance mass spectrometry

The spontaneous loss of coherence catastrophe (SLCC) is a frequently observed, yet poorly studied, space-charge related effect in Fourier-transform ion cyclotron resonance mass spectrometry (FTICR-MS). This manuscript presents an application of the filter diagonalization method (FDM) in the analysis of this phenomenon. The temporal frequency behavior reproduced by frequency shift analysis using the FDM shows the complex nature of the SLCC, which can be explained by a combination of factors occurring concurrently, governed by electrostatics and ion packet trajectories inside the ICR cell.

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.