Analysis of electric fields in mass spectrometry

Abstract Analysis of two-dimensional and, in particular, three-dimensional fringing electric fields in quadrupole mass spectrometers is a challenging task. In this work, we consider an analytical approach for such analysis. We show how to obtain precise amplitudes of multipole components of 2D and 3D electric fields. We describe some mathematical methods for accurate evaluation of realistic three-dimensional electric fields generated by quadrupole mass filters. This technique can be applied to obtain precise amplitudes of multipole components of 3D electric fields as distributions along some axis. All methods described here, are implemented in the PAnalyser application, which we use to analyse electric fields in different quadrupole systems. We provide some practical examples, which include analysis of quadrupole mass filters with hyperbolic and circular electrodes, a 3D Paul ion trap, and a linear ion trap with triangular electrodes. We also investigate 3D fringing electric fields: a DC and Quadrupole fringing fields within quadrupole mass filters with circular electrodes. Another example, interesting both theoretically and practically, is the analysis of the fringing field between two adjacent quadrupole systems – electrodes of a Brubaker pre-filter and an analytical mass filter. We also show how to synthesize an electric field from a given axial expansion of multipole components.