Unveiling the Intricacies of the Curved-Field Ion Mirror

Abstract

In time-of-flight (ToF) mass spectrometry, non-linear ion mirrors, i.e. mirrors that produce a non-linear potential in which the ions fly, can focus ions exhibiting a very broad kinetic energy distribution. Besides the quadratic potential, the so-called curved field has been used in mirrors as a non-linear potential over the past 20 years. The curved field has, however, only been loosely defined. The focusing properties of the curved field appear to have never been mathematically investigated and explained. In this work, we put forward a rigid definition of the curved field and investigate the properties of it in terms of focusing and transmission. This rigid definition shows the curved field as a two-parameter function for a given mirror length and maximum potential, which can be optimized in terms of ToF distribution/resolution. Such an optimization was performed in one-dimension (1D) by solving the ToF integral equation numerically. The characteristics of optimized configurations arrived at through a comparison with mirrors with polynomial distance–potential relationships are assessed. These optimised solutions cannot be approximated in 1D by a common set of polynomial terms. There are optimised configurations affording ideal energy focussing, but on closer inspection, these potential distributions are found to be, in fact, quadratic potentials. There are other optimised solutions that afford good energy focussing in cases of there being significant field-free regions between the source/detector and the entrance to the mirror. Some of these configurations are approximated by a linear plus a quadratic term, others need higher-order terms to be approximated. To facilitate 3D investigation, the optimised solutions in 1D were used to set the initial voltages on electrodes in a rotationally symmetric mirror, which was modelled with the computer package SIMION 8.0. The SIMION ion-flight simulations revealed that the other optimised solutions with higher-order terms have the disadvantage of lowering the transmittance. That is to say, in 3D the configurations of the curved field, which give good resolution and transmittance with field-free regions between source/detector and mirror, can all be approximated by a potential consisting of a linear plus a quadratic term.