Modelling mass analyzer performance with fields determined using the boundary element method

Computer modelling is widely used in the design of mass analysers to evaluate proposed designs and determine the effects of manufacturing imperfections. For quadrupole mass filters and ion traps, the models require accurate values of the electric field throughout the regions of the analyser in which ions travel. Most published results using models to predict mass analyser behaviour use electric fields computed with finite element (FE) or finite difference (FD) method. However, the boundary element method (BEM) is capable of achieving the same, or higher, accuracy with both computation times and memory requirements that are at least an order of magnitude less than those required by FE and FD methods. In this paper, electric field evaluation is performed using the BEM formulated in a manner described by previous workers; modifications to their method are described, which lead to higher accuracy field values. Simultaneous equation solution techniques are incorporated, which avoid solutions that are physically not realistic. The performance of linear quadrupole mass spectrometers with hyperbolic, circular and planar section electrodes has been determined using fields computed using these methods and compared with previous results obtained by alternative field computation techniques and with experiment. Behaviour of an ion trap mass spectrometer with circular symmetry has also been investigated. The results demonstrate that in each case using the BEM to determine the fields produces the observed behaviour.