Geometry optimization of axially symmetric ion traps

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 A2A2, A4A4, A6A6, A8A8, A10A10 and A12A12, respectively. Poincaré 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 A4/A2A4/A2 ratio. Improved performance of the optimized CIT is suggested by the ion dynamics as seen in Poincaré sections close to the stability boundary. With respect to the SRIT, two variants have been investigated. In the first geometry, A4/A2A4/A2 and A6/A2A6/A2 have been optimized and in the second A4/A2A4/A2, A6/A2A6/A2 and A8/A2A8/A2 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, A10/A2A10/A2 and A12/A2A12/A2, are high; additionally, A10/A2A10/A2 has a negative sign. In spite of this, for both these configurations, the Poincaré sections predict good performance. In the case of the SEIT, a geometry was obtained for which A4/A2A4/A2 and A6/A2A6/A2 are close to their values in the stretched geometry Paul trap and the higher even multipoles (A8/A2A8/A2, A10/A2A10/A2 and A12/A2A12/A2) are all positive and small in magnitude. The Poincaré 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.