Resonant quadrupole excitation of ions confined in a radio frequency quadrupole field with angular frequency omega by an excitation signal with angular frequency omega has been investigated theoretically. It is shown that the spectrum of excitation frequencies has considerable structure which corresponds to different orders of excitation. The resonance condition for orders K = 1,2,3,... in the general case has been obtained as omega n(K) = (omega/K) magnitude of n + beta, -infinity < n < infinity, where K is the order of the resonance and beta and n determine the unperturbed oscillation frequencies. Resonance curves for ion oscillations with different stability parameters beta = 0.1, 0.5, and 0.9 have been constructed by means of direct numerical solution of the equations of motion. The trajectories of ion motion under resonant excitation of different orders have been investigated. For orders K of two and higher, the ion motion shows a beat character with an overall increase of amplitude with time. The stability diagram for ion motion in a mass filter in the presence of quadrupole excitation has been constructed.
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