Theoretical investigation of unstable axial mass-selective extraction of ions from a nonlinear trap

The unstable axial mass-selective extraction of ions from a three-dimensional quadrupole ion trap is studied theoretically. A method for mapping the ion coordinates over the period of the RF power-supply voltage is developed with allowance for nonlinear distortions of the quadrupole potential. Equations for the envelope of ion oscillations are derived in the form of the equation of motion of a material point in the field of effective forces. The effect of the “delayed extraction” of ions in the presence of negative even field harmonics is explained. The positive even harmonics of the distorted quadrupole potential are shown to be favorable for ion extraction. The dynamics of the extracted ions is investigated.