Perturbation theory for ion motion in quadrupole radio frequency field

Paper develops a perturbation theory for description of ion motion in quadrupole radio frequency (RF) field. First order corrections for the ion phase coordinates caused by field perturbations over one period of the RF field are derived. Transformation matrix of the phase coordinates over one RF period is obtained and stability parameter of the perturbed ion motion is defined in the first order approximation. Results are applied for investigation of stability diagram of ion motion in a quadrupole mass filter. Boundaries of stability are defined in linear approximation and resolving power dependence from the slope of the operating line is obtained. In contrast to previously known results current approach allows obtaining corresponding dependences in semi analytical form expressed in terms of unique solutions of Mathieu equation at the tip of stability.