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

Abstract

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.

A Method of Computing Accurate 3D Fields of a Quadrupole Mass Filter and Their Use for Prediction of Filter Behavior

“…The method of [23] for 2D fields replaces each electrode by a set of infinite line charges parallel to the filter axis. Points on the electrode surface, referred to as defined points, are required to be at the electrode potential.…”

“…Each electrode section is replaced by a set of line charges of the same length and parallel to the z axis; about 40 line charges per electrode section are adequate. For finite length charges the problem of setting the potential to zero an infinite distance from the charges [23] does not exist so the solution is simplified.…”

“…The number of defined points [23] is double the number of charges and they are placed at the plate surfaces. The fields close to the entrance and exit apertures in the end plates are complicated; the field due to the filter rods, although very weak near the axis, penetrates into the ion source and the field from the ion source electrodes penetrates into the filter region.…”

“…where A + is the pseudo-inverse of A and is found using singular value decomposition, SVD, as previously [23]. The solution yields charge values that give potentials at the Figure 1.…”

“…Fields are computed by solving Laplace's equation with boundary conditions set by the electrodes. We showed [23] that the boundary element method (BEM) formulated as introduced by Read and coworkers [24,25] produced accurate field values, especially in regions distant from the electrodes where the ions move. This technique was also used by Beaty [26] and by Douglas et al [27].…”