Resonance ejection from the paul trap:  a theoretical treatment incorporating a weak octapole field

In response to the growing experimental evidence of the importance of nonlinear phenomena in ion trap operation, a new theoretical model of ion ejection is developed. The pseudopotential well approximation for forced ion oscillations in an ion trap under the conditions of ion-molecule collisions is modified to include octapole perturbations on the quadrupole field. Ion ejection is investigated using the first-order Mitropol'skii asymptotic method for both infinitesimal and finite scan rates. It is shown that the combined action of collisional damping and nonlinearity distorts the resonance curve in such a way that "quenching" of oscillations takes place. As a result, with appropriate excitation and direction of scanning, the amplitude increases as if no damping exists! The main characteristics of the jump are derived as functions of scan rate and used for analytical estimation of mass resolution, mass peak width, and excitation voltage. Satisfactory agreement between calculated and experimental peak widths is demonstrated for the range of scanning rates in excess of 6 orders of magnitude.