Alireza Doroudi
In this paper we have used a modified homotopy perturbation method used previously by A. Belendez and his coworkers, for calculation of axial secular frequencies of a nonlinear ion trap with hexapole, octopole and decapole superpositions. We transform the motion of the ion in a rapidly oscillating field to the motion in an effective potential and obtain a nonlinear differential equation in the form of a Duffing-like equation. With only octopole superposition the resulted nonlinear equations are symmetric; however, in the presence of hexapole and decapole superpositions, they are asymmetric. For asymmetric oscillators, it has been pointed out that the angular frequency for positive amplitudes is different from the angular frequency for negative amplitudes. Considering this problem, the modified homotopy perturbation method is used for solving the resulted nonlinear equations. As a result, the ion axial secular frequencies as a function of nonlinear field parameters are obtained. The calculated secular frequencies are compared with the results of modified Lindstedt-Poincare approximation and the exact results. There is an excellent agreement between the results of this paper and the exact results.
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