Theory of Ion Cyclotron Resonance

Abstract

A theoretical analysis is given of the most commonly used type of ion cyclotron resonance (ICR) spectrometer, which has a cell of rectangular cross section. Though the equations of motion of the ions in this cell are extremely nonlinear, it has been possible to simplify the analysis by exploiting the facts that the longitudinal oscillations in the trapping potential are approximately decoupled from the cyclotron motion and that the cyclotron frequency [Formula: see text] the trapping oscillation frequency [Formula: see text] the spread of instantaneous cyclotron frequencies in the trap. A method is described for constructing an ensemble of ions appropriate to the mechanism of ion production and to the various drift and trapping voltages employed in the ICR cell. Line shapes are calculated in the collisionless regime. An ad hoc "average ion" model is presented, which simplifies the analysis of the spatial distribution of the ions through the dependence of the effective ICR frequency and line width on cell voltages and dimensions. Finally, an explicit distribution function is derived for the ion kinetic energy in the cell. The effect of a uniform RF electric field at resonance is shown to increase not only the average kinetic energy, but the spread of energies as well. A substantial spread of energies is also produced by the trapping oscillations. The breadth of the kinetic energy distribution complicates the interpretation of energy dependent processes using ICR under conditions normally used up to now. Some improved techniques for the study of energy dependent cross sections are proposed.