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 102 ions to 106 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. Particle-in-cell simulation of the behavior of 7000 ions with three mass-to-charge values in a cubic analyzer cell of a Fourier transform ICR mass spectrometer.