Fourier Transform Ion Cyclotron Resonance Mass Resolution and Dynamic Range Limits Calculated by Computer Modeling of Ion Cloud Motion

Abstract

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. . 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).

From Supercomputer Modeling to Highest Mass Resolution in FT-ICR

“…In previous PIC-based simulations, "ion condensation" has been observed, 13,14,18) resulting in formation of a compact elliptical ion cloud if the number of ions in the cloud is higher than some critical value. In a spatially homogeneous magnetic field, the condensation effect is not influenced by…”

“…This limitation is extremely important for cases of inharmonic electric field and inhomogeneous magnetic field. 12,13,17) 3) Maximal ion number at which peaks of spectra do not coalesce. 13) 4) Capacity of ICR cell determined by equality of coulomb repulsive force and trapping force of the cell.…”

“…Later Nikolaev's group has extended this particle-in-cell approach to allow for the simulation of many particle dynamics inside the FTICR cell on the basis of improved computational algorithms and using the most powerful computers available at this time. 12,13) They have implemented the new 3D particle-in-cell code. The code can model a complete FTICR experiment with up to 10 6 coulombically interacting ions in the ICR cell for 10,000,000 time-steps.…”

“…In a cubic and cylindrical cells (in contrast to the cell with hyperbolic potential) at small ion number comet structures are formed leading to disappearance of the ICR signal after about 1 s at 1 T and 7 T 12,13) corresponding to mass resolution in accordance with the expression for FT-ICR resolution as a function of observation period. In previous works, 12,13) we have determined the dependence of minimum number N, of ions in the cloud for onset of coalescence on magnetic field strength B, cyclotron radius R, ion mass m, and difference between ion masses m 2 -m 1 , for two ion ensembles of different m/z and equal abundance, excited to the same nominal cyclotron radius. Empirical expressions for N as a function of each of the above listed experimental parameters have been obtained.…”

“…Empirical expressions for N as a function of each of the above listed experimental parameters have been obtained. 13) …”