Further Development and Refinement of the Effective Potential Concept for Stroboscopic Samplings of Ion Coordinates and Velocities in Quadrupole RF Fields

We consider the concept of effective potential, that has been proposed recently based on analysis of stroboscopic sampling of coordinates and velocities of ions moving in an rf quadrupole field. Exact expressions have been obtained for the stroboscopic model of motion of ions, which are valid at any point of a stability zone. Analysis of these expressions has led to correction of some postulates of the initial effective potential concept of stroboscopic sampling, which was developed for the neighborhood of the stability zone peak.