Frequency perturbation in nonlinear Paul traps:: A simulation study of the effect of geometric aberration, space charge, dipolar excitation, and damping on ion axial secular frequency

Abstract

This article develops an expression that relates perturbation in ion axial secular frequency to geometric aberration, space charge, dipolar excitation, and collisional damping in nonlinear Paul trap mass spectrometers. A multipole superposition model incorporating hexapole and octopole superposition has been adopted to represent field inhomogeneities. A uniform charge density distribution has been assumed for characterizing space charge. Dipolar excitation has been represented as a forcing term weighted by dipole superposition, and damping is represented in terms of reduced collision frequency in the equation of ion motion. The perturbed secular frequency of the ion has been obtained by using a modified Lindstedt–Poincaré perturbation technique. The expression for perturbed frequency adequately reflects the reported experimental and simulation results. Perturbation is sign sensitive for octopole superposition and sign insensitive for hexapole superposition. Larger shifts occur with octopole aberrations. Perturbation of secular frequency based on the number of ions is mass dependent. Lower masses show larger negative frequency shifts with an increase in the number of ions within the trap. Dipolar excitation potential shifts the secular frequency in the positive direction and is larger for lower masses than for higher masses. Damping plays a minor role in shifting the secular frequencies. The shift increases as we increase the pressure of the bath gas. The shift in ion secular frequency with the axial distance from the center of the trap shows quadratic variation.