Abstract
[Display omitted]
▶ Power series solution of the Mathieu equation. ▶ Minimization of the computational time. ▶ Numerical solution for the excited ions and buffer gas cooling.
We present a method based on the series solution of the differential equations to solve numerically the equation of motion of a single ion trapped in an ideal quadrupole ion trap. Every time step, the solution is approximated by a polynomial whose degree and the time step have been optimized to get the minimum computational time with the best accuracy. The initial results were compared to those given by the analytical solution of the Mathieu equation, then the effects of a dipolar and quadrupolar excitation, and the cooling by a buffer gas, presented as a viscous drag, have been added without reference to any analytical solution. The results were compared to chosen examples from the ion trap literature.