Ion dynamics in non-perfect quadrupole traps

Ion dynamics in non-perfect quadrupole traps differ from those in a pure quadrupole field. We obtain an analytic expression for a quadrupole field superimposed with weak, higher-order multipole fields. Single ion dynamics in such trapping fields close to the instability point are investigated. We show that for an in-phase octopole field, oscillating envelopes of the axial displacement grow exponentially with the parameter deviation; whereas for an out-of-phase octopole field the growth of the oscillating envelopes follows a square-root law. A hard-sphere scattering model is assumed to incorporate collisions with buffer-gas molecules. The collision frequency and cross-section are defined. A simulation algorithm for many-ion dynamics is developed based on the Verlet algorithm and Monte Carlo techniques. We show how a weak octopole field affects the mass resolution in a significant way.