Cyclotron motion of two Coulombically interacting ion clouds with implications to Fourier-transform ion cyclotron resonance mass spectrometry

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Abstract
This work investigates the cyclotron motion of two Coulombically interacting ion clouds with different mass-to-charge ratios. Trap geometry as well as the shape of each ion cloud determines the maximum number of ions that can be confined in a Penning-like ion trap. We consider the two important cases of either spherically or cylindrically shaped ion clouds. These models exhibit the most important space charge effects in Fourier-transform ion cyclotron resonance mass spectrometry including frequency shifts, amplitude and phase modulation, and phase locking. Both positive and negative frequency shifts are possible for spherical ion clouds when their cyclotron radii differ. Due to the Coulombic ineraction between ion clouds, both cyclotron-radius and phase modulation occur. This modulation increases inversely to the cyclotron frequency difference. Cyclotron phase locking results when two ion clouds have similar mass-to-charge ratios and a sufficiently large ion population, at which point a mass spectrum shows only a single peak. Spherical ion clouds are usually more likely to phase lock than cylindrically shaped clouds. The phase-locking threshold sets limits on the maximum resolution, mass accuracy, and dynamic range achievable by mass spectrometry. Phase locking is treated in detail and our results are compared to previously published experimental data. The present model quantitatively describes the onset of phase locking as well as the general trends in frequency shifts and measured abundances just before phase locking.