title: Calculation of coupled secular oscillation frequencies and axial secular frequency in a nonlinear ion trap by a homotopy method.
abstract: In this paper the homotopy perturbation method is used for calculation of the frequencies of the coupled secular oscillations and axial secular frequencies of a nonlinear ion trap. The motion of the ion in a rapidly oscillating field is transformed to the motion in an effective potential. The equations of ion motion in the effective potential are in the form of a Duffing-like equation. The homotopy perturbation method is used for solving the resulted system of coupled nonlinear differential equations and the resulted axial equation for obtaining the expressions for ion secular frequencies as a function of nonlinear field parameters and amplitudes of oscillations. The calculated axial secular frequencies are compared with the results of Lindstedt-Poincare method and the exact results.
authors.affiliation: Physics Department, Nuclear Science Research School, Nuclear Science and Technology Research Institute, Tehran, Iran. adoroudi@aeoi.org.ir
authors.forename: Alireza
authors.initials: A
authors.lastname: Doroudi