Application of a Modified Homotopy Perturbation Method for Calculation of Secular Axial Frequencies in a Nonlinear Ion Trap with Hexapole, Octopole and Decapole Superpositions

Sevugarajan and Menon [4-6] have studied the nonlinear Paul ion trap. They have applied the Lindstedt-Poincare technique, the modified Lindstedt-Poincare technique and the multiple scales perturbation technique for solving the nonlinear equation of ion motion in nonlinear ion trap. Also, in two previous studies [7,8] done on nonlinear ion traps by one of the present authors, the homotopy perturbation method was used to study the secular frequencies in nonlinear ion traps. When the hexapole superposition is considered, the resulting nonlinear equation has a quadratic nonlinearity and we know that the angular frequency for positive amplitudes is different from the angular frequency for negative amplitudes in nonlinear oscillator with quadratic nonlinearity. In all the above studies [4-8] the assumption is that the angular frequency for positive amplitudes is equal to the angular frequency for negative amplitudes.