Collective motion of ions in an ion trap for Fourier transform ion cyclotron resonance mass spectrometry

When two kinds of ions with a very small mass difference are trapped at high density in the Fourier transform ion cyclotron resonance (FT-ICR) cell and are coherently rotating in their cyclotron orbits, collective motion of two ion packets takes place due to the Coulomb interaction and only one peak appears in the spectrum rather than two peaks at their own mass-to-charge ratios. The phenomenon is theoretically studied with a model of two charged particles orbiting in a plane perpendicular to a uniform magnetic field. This model shows that, while the center-of-mass is rotating in a circular orbit at a frequency corresponding to the weighted average of the two cyclotron resonance frequencies, the two particles are rotating around the center-of-mass with an oscillating radius. The potential between the two particles is calculated and the resonance condition which decouples the coupling motion is derived as a function of mass, number of charges, the orbital radius of the center-of-mass and the magnetic field strength. The condition is experimentally examined with CO+ (m/z = 27.9949) and C2H4+ (m/z = 28.0313) ions, varying the number of charges and the cyclotron radius, and an agreement with the theory is found. The collective motion of highly multiply charged heavy ions produced from biomolecules is also discussed.