# Geometry optimization of axially symmetric ion traps

Tallapragada, Pavan K and Mohanty, Atanu K and Chatterjee, Anindya and Menon, AG (2007) Geometry optimization of axially symmetric ion traps. In: International Journal of Mass Spectrometry, 264 (1). pp. 38-52.

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## Abstract

This paper presents numerical optimization of geometries of axially symmetric ion traps for mass analyzers. Four geometries have been taken up for investigation: one is the well known cylindrical ion trap (CIT) and three others are new geometries. Two of these newer geometries have a step in the region of the midplane of the cylindrical ring electrode (SRIT) and the third geometry has a step in its endcap electrodes (SEIT). The optimization has been carried out around different objective functions composed of the desired weights of higher order multipoles. The Nelder-Mead simplex method has been used to optimize trap geometries. The multipoles included in the computations are quadrupole, octopole, dodecapole, hexadecapole, ikosipole and tetraikosipole having weights $A_2, A_4, A_6, A_8, A_{10} \hspace{2mm} and A_{12}$, respectively. Poincar´e sections have been used to understand dynamics of ions in the traps investigated. For the CIT, it has been shown that by changing the aspect ratio of the trap the harmful effects of negative dodecapole superposition can be eliminated, although this results in a large positive $A_4/A_2$ ratio. Improved performance of the optimized CIT is suggested by the ion dynamics as seen in Poincar´e sections close to the stability boundary. With respect to the SRIT, two variants have been investigated. In the first geometry, $A_4/A_2$ and $A_6/A_2$ have been optimized and in the second $A_4/A_2$, $A_6/A_2$ and $A_8/A_2$ have been optimized; in both cases, these ratios have been kept close to their values reported for stretched hyperboloid geometry Paul traps. In doing this, however, it was seen that the weights of still higher order multipoles not included in the objective function, $A_{10}/A_2$ and $A_{12}/A_2$, are high; additionally, $A_{10}/A_2$ has a negative sign. In spite of this, for both these configurations, the Poincar´e sections predict good performance. In the case of the SEIT, a geometry was obtained for which $A_4/A_2$ and $A_6/A_2$ are close to their values in the stretched geometry Paul trap and the higher even multipoles $(A_8/A_2$, $A_{10}/A_2$ and $A_{12}/A_2)$ are all positive and small in magnitude. The Poincar´e sections predict good performance for this configuration too. Finally, direct numerical simulations of coupled nonlinear axial/radial dynamics also predict good performance for the SEIT, which seems to be the most promising among the geometries studied here.

Item Type: Journal Article International Journal of Mass Spectrometry Elsevier Copyright of this article belongs to Elsevier. Cylindrical ion trap;Nonlinear rf ion trap;Geometry optimization;Poincare' section Division of Physical & Mathematical Sciences > Instrumentation Appiled PhysicsDivision of Interdisciplinary Sciences > Supercomputer Education & Research CentreDivision of Mechanical Sciences > Mechanical Engineering 15 Oct 2007 19 Sep 2010 04:39 http://eprints.iisc.ac.in/id/eprint/11784