Effective potential and the ion axial beat motion near the boundary of thefirst stable region in a nonlinear ion trap

Small higher-order field imperfections of the main trapping quadrupole fiel d are well known to have a strong influence on the performance of modern qu adrupole mass spectrometers. Mass selectivity is usually achieved by means of the stability region boundaries. The stability diagram for ion motion is the area on the plane of voltage parameters for which the quadrupole field is able to trap ions of a given mass. Hence, the trapping efficiency of th e quadrupole field is equal to zero at a boundary of the stability region. In this case, the trapping properties of the RF field depend on higher fiel d imperfections regardless of how small they are compared to the quadrupole field. The ion motion with parameters close to the boundary beta (2) = 1 i s investigated in this article. The influence of nonlinear field imperfecti ons is taken into account. A treatment similar to trajectory averaging in a pseudopotential is possible in this case. The ion motion has the character istics of a beat with a fast oscillation at half the frequency of the RF an d a slowly varying envelope. The ion motion is described by a dynamic equat ion for the envelope. This equation has the form of a Newton equation for t he motion of a particle in a potential field. The effective potential funct ion of the envelope is derived and investigated. The effective potential we ll is rather different for the cases of negative and positive even-order hi gher fields. The results are applied to the mass-selective axial instabilit y scan of an ion trap. The influence of negative higher field harmonics exp lains the ejection delay and poor mass resolution of the Paul trap with tru ncated electrodes. Positive even-field imperfections are shown to be benefi cial to the mass selective axial instability scan. This explains why stretc hed or hyperbolic angle modified traps give improved performance. Stable io n motion outside of the first stable region is predicted, This motion has t he character of a limit cycle, and all ions move coherently in the radio fr equency field. (Int J Mass Spectrom 206 (2001) 27-43) (C) 2001 Elsevier Sci ence B.V.