Application of a modified homotopy perturbation method for calculation of axial secular frequencies in a nonlinear ion trap

In this paper a modified version of the homotopy perturbation method is used for calculation of axial secular frequencies of a nonlinear ion trap with hexapole and octupole superpositions. The axial equation of ion motion in a rapidly oscillating field is derived. In the presence of hexapole and octupole superpositions, the equation is asymmetric. Then, the resulting nonlinear equation is solved by using this modified homotopy perturbation method and the axial frequencies are calculated as a function of nonlinear field parameters. The calculated secular frequencies are compared with the results of the homotopy perturbation method and the exact results.