Analysis of phase dependent frequency shifts in simulated FTMS transients using the filtered diagonalization method

Space-charge perturbs ion motion and affects mass accuracy in ion trapping mass spectrometers. In Fourier transform mass spectrometry (FTMS), both ion-ion and ion-image charge interactions have been examined by experiments and by multiparticle ion simulations using the particle-in-cell (PIC) approach, and the magnitude of observed frequency shifts as a function of ion number agrees with theoretical models. Frequency shifts due to ion-ion interactions have generally been treated in a time-integrated fashion, that is, for the duration of the transient signal. Aizikov and O’Connor have experimentally shown that there is a time-dependence for such interactions, with a periodicity that correlates to the beat period between isotope peaks. Here, we investigate such interactions using PIC simulations and the filter diagonalization method (FDM) for obtaining frequencies from very short durations of the transient. Periodic decreases in observed frequency correlate with ion clouds of isotope peaks coming into phase in their cyclotron orbit. A similar phenomenon is observed in the simulations of ion motion in an Orbitrap mass analyzer, corresponding to the axial motion of isotope groupings moving in and out of phase.