Composite field approximations for ion traps with apertures on electrodes

Abstract

Two dimensional (2D) trap Boundary element method (BEM) Electric field in the vicinity of aperture Multipole a b s t r a c t 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 formwhere E noaperture is the field within an imagined trap which is identical to the practical trap except that the apertures are missing and E aperture 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 E aperture , classical results of electrostatics have been extended to electrodes with finite thickness and different aperture shapes.E noaperture 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.

Off-axis field approximations for ion traps with apertures

“…This paper complements and completes our recent work [5], and presents approximate analytical expressions for off-axis fields in axially symmetric (referred to as 3D) and two dimensional (2D) ion trap mass analyzers with apertures in their electrodes. The expression for the field we present has two parts.…”

“…We thank Anindya Chatterjee and A.G. Menon for discussions and suggestions on the manuscript, and thank an anonymous reviewer of our earlier work [5] for pointing us in this direction.…”

“…Because of the top-bottom symmetry, the corresponding fields on the lower endcap are −E 0 and −E 1 , respectively. As in Chattopadhyay et al [5] we approximate the hole in the endcap with nonzero thickness as two holes in two parallel infinitely thin ground planes and, as seen in Fig. 3, the two holes are at z = z 0 , and at z = z 1 .…”

“…Our earlier effort [5] was able to extract the contribution of the aperture by subtracting the field in the vicinity of an aperture on an infinitely thin grounded plane from the field across this plane in the absence of the aperture. Extension of the same idea to fields at off-axis points, it turns out, involves significant new analysis with its own challenges, and is the subject of the present paper.…”

Miniature and Fieldable Mass Spectrometers: Recent Advances

“…Homebuilt algorithms using similar mathematical methods have been written to model ion trajectories in high-pressure (0.1–10 Torr) ion traps (Collisional Ion Trap Simulator, CITSIM), , to study the effect of surface roughness and geometry deviations on ion trap performance, to calculate the electric fields in ion traps with apertures and linear ion traps with half round rod electrodes, to investigate ion/neutral collisions in 3D traps, and to find analytical expressions for ion motion and secular frequency in a superimposed octopole field using a harmonic balance method . Since simulations of multiple ions can be very computationally intensive, Xu et al have implemented GPU acceleration, wherein a computer’s graphics card is used as a parallel processing unit, in order to decrease computational time of space charge calculations by at least 2 orders of magnitude compared to a single core CPU .…”