We present some detailed measurements on instabilities of ion trajectories in a Paul trap caused by deviations of the ideal quadrupole potential by trap imperfections. Numerous lines of reduced stability have been observed. Their position in the stability diagram can be well explained by theory. The identification of a non-linear resonance can be performed by a measurement of the ions' macrofrequencies ωr, ωZ. We have observed space-charge shifts of the resonances. From the strength and shape of a non-linear resonance, one may possibly determine the contribution of a particular perturbation to the quadrupole potential, and thus characterize the specific trap.
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Alheit et al. (1996) studied this question.