Computation of the third, fourth and fifth stability regions in a Paul trap

The behavior of ions in a Paul trap has been investigated using numerical solution of the set of Mathieus differential equations. Afterwards, the trajectories of two typical ions such as H+ and 208Pb+ in the trap have been obtained using the fourth-order Runge-Kutta method. For specific dimensions of a Paul trap and a given frequency, the stability regions for separation of H+ and 2H+ ions have been determined in terms of the DC and AC voltages applied to the trap. Furthermore, five stability regions in which ion trapping occurs have been obtained accurately. Computation of the fifth stability region has not been reported in the literature previously.