Comparison of calculated axial secular frequencies in nonlinear ion trap by homotopy method with the exact results and the results of Lindstedt–Poincare approximation

Abstract

In this paper the homotopy perturbation method is used for calculation of axial secular frequencies of a nonlinear ion trap with only hexapole superposition. The motion of the ion in a rapidly oscillating field is transformed to the motion in an effective potential. The equation of ion motion in the effective potential is the equation of an anharmonic oscillator with quadratic nonlinearity. The homotopy perturbation method is used for solving the resulted nonlinear equation and obtaining the expression for ion secular frequency as a function of nonlinear field parameter. The calculated secular frequencies are compared with the results of L.–P. method and the exact results.