Modification of the Stability Regions in Stretched Paul Ion Trap by Damping Force

With the change of an ion trap geometrical shape, ring and end-cap electrodes, and also damping force effects, the first and second stability regions are studied in a stretched Paul ion trap. In this article, according to a new idea, we changed the trap geometry based on the change in distances between the ring electrode (2r˳) and end-cap electrodes (2z˳). For this purpose, the geometrical parameter n=(r˳/z˳)2 was introduced in our calculations. Also, for the damping effects, we entered a viscous damping factor (k) in the Mathieu equation. The set of differential equation governing the motion of the confined ion is considered, taking into account the effect of damping force and the ion trap geometry. The Mathieu type differential equations were solved using Runge-Kutta Verner fifth-order and sixth-order method (RKV56). Comparisons were made with the corresponding stability diagrams without considering the effects of damping force in an ideal ion trap . The numerical results showed that, for a given ion trap mode i.e., rf only mode, the damping force and the trap geometry played important roles in the relocation of the stability diagrams. The first and second stability regions in the presence of the damping force, according to trap’s geometry, are reported for the first time.