Composite field approximations for ion traps with apertures on electrodes

This paper presents two approximate analytical expressions for nonlinear electric fields in the principal direction in axially symmetric (3D) and two dimensional (2D) ion trap mass analysers with apertures (holes in case of 3D traps and slits in case of 2D traps) on the electrodes. Considered together (3D and 2D), we present composite approximations for the principal unidirectional nonlinear electric fields in these ion traps. The composite electric field E has the formE=Enoaperture+Eaperture,E=Enoaperture+Eaperture,where EnoapertureEnoaperture is the field within an imagined trap which is identical to the practical trap except that the apertures are missing and EapertureEaperture is the field contribution due to apertures on the two trap electrodes. The field along the principal axis of the trap can in this way be well approximated for any aperture that is not too large.To derive EapertureEaperture, classical results of electrostatics have been extended to electrodes with finite thickness and different aperture shapes.EnoapertureEnoaperture is a modified truncated multipole expansion for the imagined trap with no aperture. The first several terms in the multipole expansion are in principle exact (though numerically determined using the BEM), while the last term is chosen to match the field at the electrode. This expansion, once computed, works with any aperture in the practical trap.The composite field approximation for axially symmetric (3D) traps is checked for three geometries: the Paul trap, the cylindrical ion trap (CIT) and an arbitrary other trap. The approximation for 2D traps is verified using two geometries: the linear ion trap (LIT) and the rectilinear ion trap (RIT). In each case, for two aperture sizes (10% and 50% of the trap dimension), highly satisfactory fits are obtained. These composite approximations may be used in more detailed nonlinear ion dynamics studies than have been hitherto attempted.

This paper presents analytical formulae for the contribution of apertures (holes/slits) to the field inside ion traps in terms of aperture size.Figure optionsDownload as PowerPoint slide