Non-linear resonances in quadrupole mass spectrometers due to imperfect fields: II. The quadrupole mass filter and the monopole mass spectrometer

Abstract

Peak-shape distortions and peak-splitting are commonly observed phenomena with all members of the quadrupole family of mass spectrometers. Errors in electrode shape, or spacing, or harmonics in the r.f. field may produce non-linear resonances. The resonances result in peak splitting by causing some ion trajectories to become unstable that otherwise, in a perfect field, would be stable and limited in amplitude. In Part I a theory of non-linear resonances in quadrupole fields was applied to the three-dimensional rotationally symmetric quadrupole ion trap. In the present paper, the theory of non-linear resonances is applied to the quadrupole mass filter and to the monopole mass spectrometer. Numerical computation of ion trajectories was used to determine the extent of peak-splitting for various amounts of third and fourth order spacial distortion and to determine the positions of resonance lines in the stability diagram. The calculations were used in the case of the mass filter to relate the performance to possible spacing errors in assembling the electrode structure. The monopole operating point can be chosen to avoid the resonance lines. The focusing quality is, however, affected by the presence of distortions. For the monopole, peak shapes were determined from the computed ion trajectories. A small amount of one type of third-order distortion is shown to be beneficial.