Theory for Ion Cyclotron Resonance Absorption Line Shapes

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Abstract
Explicit expressions have been calculated for the ion cyclotron resonance (ICR) absorption line shapes for reactive and for unreactive ionic species, in terms of ionic mass and charge, applied rf electric field frequency and magnitude, observing magnetic field strength, and electric drift potentials in various parts of the ICR spectrometer cell. The calculations are based on a zero-pressure equation of motion for the velocity of a charged ion which moves under the influence of a static magnetic field perpendicular to a static electric field and a sinusoidal time-varying electric field. The zero-pressure equation is applied only during the time intervals between ion–molecule collisions, and the power absorption contribution from ions in a particular region of the analyzer region of the ICR spectrometer cell is computed. The relative number of ions in a given region of the ICR cell is determined from that set of ion current expressions which follow from a particular specified kinetic scheme. The power absorption contributions from all regions of the analyzer are then summed; the resultant power absorption expression reduces to a Lorentzian line shape for reactive ions in the limit of very large collision frequency. It is shown that any process which interrupts ion power absorption may contribute to the linewidth of the ion cyclotron resonance. Computer-generated absorption and derivative line shapes are displayed for some representative cases, and plots of calculated ICR absorption linewidth vs collision frequency are given for several line-shape models. The relation of the present work to other models for ICR line shape is extensively discussed.