Computation of Mathieu stability plot for an arbitrary toroidal ion trap mass analyser

This paper presents a method to construct Mathieu stability plot for any arbitrary toroidal ion trap mass analyser. The proposed method is demonstrated on two toroidal ion trap mass analyser geometries. Two additional studies have also been carried out. These include prediction of ion secular frequency and ion trajectories at resonances in these traps. In this numerical study, toroidal multipole coefficients of the respective traps are first evaluated and these are used for computing Mathieu parameters, a and q. These Mathieu parameters are used for constructing the stability plot, predicting secular frequency of ion motion and evaluating nonlinear resonances. The stability regions of both the traps considered in this paper are qualitatively similar to the corresponding plot of the linear ion trap mass analyser. There are, however two significant differences. First, the stability plots for toroidal ion trap mass analysers have prominent resonances. Second the apices of the stability plots of the toroidal ion trap mass analysers are different from those of the linear ion trap mass analyser. The secular frequency obtained using the Mathieu parameters in this paper agrees well with those obtained numerically, except close to the stability boundaries. Finally, the prominent nonlinear resonances have been identified as beta(r) = 2/3 and beta(r) = 2/3 in both the traps. In one of the two traps there is an additional prominent nonlinear resonance at beta(r) + beta(z) =1. (C) 2016 Elsevier B.V. All rights reserved.