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).

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Journal J. Am. Soc. Mass Spectrom.
Vladimirov, Gleb, Hendrickson, C.L, Blakney, G.T, Marshall, A.G, Heeren, R.M.A, & Nikolaev, E.N. (2012). Fourier transform ion cyclotron resonance mass resolution and dynamic range limits calculated by computer modeling of ion cloud motion. J. Am. Soc. Mass Spectrom., 23(2), 375–384. doi:10.1007/s13361-011-0268-8