Characteristics of stability boundary and frequency in nonlinear ion trap mass spectrometer

In this article, the Poincare-Lighthill-Kuo (PLK) method is used to derive an analytical expression on the stability boundary and the ion trajectory. A multipole superposition model mainly including octopole component is adopted to represent the inhomogeneities of the field. In this method, both the motional displacement and secular frequency of ions have been expanded to asymptotic series by the scale of nonlinear term epsilon, which represents a weak octopole field. By solving the zero and first-order approximate equations, it is found that a frequency shift exists between the ideal and nonlinear conditions. The motional frequency of ions in nonlinear ion trap depends on not only Mathieu parameters, a and q, but also the percentage of the nonlinear field and the initial amplitude of ions. In the same trap, ions have the same mass-to-charge ratio (m/z) but they have different initial amplitudes or velocities. Consequently, they will be ejected at different time through after a mass-selective instability scan. The influences on the mass resolution in quadrupole ion trap, which is coupled with positive or negative octopole fields, have been discussed respectively.