ION SEPARATION IN IMPERFECT FIELDS OF THE QUADRUPOLE MASS ANALYZER .1. ION-BEAM DYNAMICS IN THE PHASE-SPACE

The theoretical aspects of ion separation in imperfect fields of the quadrupole mass analyzer are discussed by applying analysis of the beam dynamics in a phase-space. The analytical method which uses an approximate solution of the Hill equation with a small heterogeneous part which indicates that the trap mechanism of ion separation is conditioned by the properties of characteristic solutions is improved. These solutions are reduced to an approximate solution in the form of a general solution of a homogeneous Mathieu equation with combined factors taking into account a small heterogeneous part which defines the region of beam capture (acceptance) in a phase-space. The estimation criterion of simulation accuracy is the relative deviation of an operating point on the Mathieu diagram from the top of a stability triangle. The infringement of independence principle of ion oscillations about each of the positional axes caused by distortions increases the cross-sectional area of the beam. The beam is cut out by the mass analyzer aperture. This causes transmission losses which depend on phase. Therefore, the ion current at the mass analyzer exit is amplitude modulated by the frequency of the alternate component of field. The maximum current is at zero phase. The modulation depth is proportional to the relative value of the distortions.