Abstract
Most previous experimental and theoretical studies of the different types of quadrupole mass spectrometer were based on pure quadrupole fields. Ion oscillation trajectories and their stability behaviour have been successfully described by the Mathieu differential equation and are clearly understood. The present paper deals with the non-linear Mathieu differential equation which dominates the ion movement in the non-linear resonance ion trap. A general condition for non-linear resonances caused by the superposition of weak multipole fields on the quadrupole field is derived from basic principles, and some additional rules are presented. A set of important non-linear resonance lines for an ion trap with superpositions of rotationally symmetric hexapole and octopole fields are presented in the first stability diagram. The intensity of non-linear resonances caused by superposition of a weak hexapole field are analyzed.
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