Two dimensional many particle simulation of trapped ions

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.

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.

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).

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.

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.

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

Using a 'Particle-In-Cell' approach taken from plasma physics we have developed a new three-dimensional (3D) parallel computer code that today yields the highest possible accuracy of ion trajectory calculations in electromagnetic fields. This approach incorporates coulombic ion-ion and ion-image charge interactions into the calculation. The accuracy is achieved through the implementation of an improved algorithm (the so-called Boris algorithm) that mathematically eliminates cyclotron motion in a magnetic field from digital equations for ion motion dynamics. It facilitates the calculation of the cyclotron motion without numerical errors. At every time-step in the simulation the electric potential inside the cell is calculated by direct solution of Poisson's equation. Calculations are performed on a computational grid with up to 128 x 128 x 128 nodes using a fast Fourier transform algorithm. The ion populations in these simulations ranged from 1000 up to 1,000,000 ions. A maximum of 3,000,000 time-steps were employed in the ion trajectory calculations. This corresponds to an experimental detection time-scale of seconds. In addition to the ion trajectories integral time-domain signals and mass spectra were calculated. The phenomena observed include phase locking of particular m/z ions (high-resolution regime) inside larger ion clouds. A focus was placed on behavior of a cloud of ions of a single m/z value to understand the nature of Fourier transform ion cyclotron resonance (FTICR) resolution and mass accuracy in selected ion mode detection. The behavior of two and three ion clouds of different but close m/z was investigated as well. Peak coalescence effects were observed in both cases. Very complicated ion cloud dynamics in the case of three ion clouds was demonstrated. It was found that magnetic field does not influence phase locking for a cloud of ions of a single m/z. The ion cloud evolution time-scale is inversely proportional to magnetic field. The number of ions needed for peak coalescence depends quadratically on the magnetic field.

Investigation of low-voltage on-resonance ion selection for Fourier transform mass spectrometry

Low-voltage on-resonance ion selection (LOIS) was recently introduced as an alternative technique for ion selection and storage. Under high pressure conditions and similar to the technique of quadrupolar axialization, unwanted (unselected) trapped ions are eliminated from the analysis cell through collisions with cell plates following orbital expansion. The ions remaining after tens of seconds of mass selection can be detected with better coherence, leading to improvements in ion detection and sensitivity. Here, experiments designed to test ion remeasurement and ion transfer capabilities are presented. Simulations of ion motion give insight into the possible mechanism of ion cooling, which does appear to be the same as that of the axialization process. Because of its ease of use, lack of need for additional hardware devices, and comparable ion selection results, LOIS is an attractive alternative for trapped ion experiments.