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.
- Secular frequencies are predicted using the Mathieu parameters. These frequencies agree well with those obtained numerically.
- Prominent nonlinear resonances have been identified as βr=23, βz=23 and βr + βz = 1 have been observed in the example traps investigated.
- Ion trajectories at resonances are presented.

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 βr=23 and βz=23 in both the traps. In one of the two traps there is an additional prominent nonlinear resonance at βr + βz = 1.

This paper presents a method for generating stability plots for an arbitrary toroidal ion trap mass analyser geometry on the a-q plane. Schematic view of toroidal ion trap obtained from an asymmetric quadrupole ion trap rotated on edge to form the toroid. Stability region in terms of Mathieu parameters a and q. 88