Theory of space-charge shift of ion cyclotron resonance frequencies

A theory of ion space-charge influence on the observed ion cyclotron resonance frequency in static field ion traps is presented. The dependence of this influence on ion density, ion cloud shape, and trapping geometry is investigated. Four trapping geometries are specifically analyzed: the Penning trap, the cubical ICR cell, the common rectangular ICR cell, and an elongated ICR cell. This treatment is readily extended to other geometries. The theory applies to common situations where the exciting or detecting antennae fields are not homogeneous, and individual particle motions are excited/detected as opposed to center-of-mass motions.