Some properties of charged particle trajectories in quadrupole mass spectrometers: Part II. The results of trajectory analysis

Abstract

In this article, we show that the dependence of the amplitude of ion oscillation within hyperboloidal mass spectrometers (QMSs) on the stability parameter β 0 has a “spiking” structure: the amplitude vs. the stability parameter β 0 curve exhibits narrow dips at some points. We show that the dips appear at those points of the stability diagram that lie on quasi-stability lines; that is to say the novel spiking structure of the observed amplitude vs. β 0 curve is determined by fine structure of the stability diagram. We have found that the amplitude-phase characteristic (APC) of the first kind has a plateau with amplitude equal to 1 at the points lying at quasi-stability lines. Trajectory analysis demonstrates an one-to-one correspondence (for meander and β 0=0) of the APC of the first and second kinds with the theory developed in Part I of this article. The shape of the dips discovered in this work was investigated. The width of these dips depends on the exposure time (the time that ions are exposed to the rf field). For the exposure time that exceeds 100 rf cycles, the width of the dips can be characterized in terms of “resolution” ( a 2 2/Δ a 2 2) of about several hundreds. We show that the smooth component of the amplitude vs. β 0 curve is described precisely by Eq. (14) developed in Part I.