Tailoring of fields and development of multipole expansion in planar ion trap geometries

Abstract

In this research work two studies have been taken up: (1) to provide a systematic method to linearize and tailor fields in planar ion trap geometries. The proposed method is general and is demonstrated on two trap geometries, one of which is a single-PCB (printed circuit board) geometry and the other is a two-PCB geometry, and (2) to develop the multipole expansion for potentials in planar trap structures. These studies have relied on numerical simulations and analytical investigations. The thesis is divided into six chapters. Chapter 1 presents an introduction to planar ion traps. Following a description of the three-dimensional (3D) ion trap mass analyzer, which includes a discussion on the stability of ions in 3D traps as well as a brief description of the use of multipole expansion for describing potential, it goes on to provide an overview of the planar ion traps discussed in mass spectrometry literature. This chapter ends with a presentation of the motivation and scope of the thesis. Chapter 2 presents a description of computational methods used in this research. It details the Boundary Element Method (BEM) that has been used for field calculation. The developed method is capable of analyzing structures that comprise of both conductors and dielectrics. Next, the method used for determination of ion trajectory and frequency of ion motion has been discussed. Chapter 3 takes up for investigation a single-PCB planar ion trap to gain insights into the behaviour of planar traps. This geometry, referred to as the Test Ion Trap Geometry, is similar to a well-known five-wire geometry discussed in literature. The studies undertaken include the role of DC and RF potentials in trapping ions. Based on these studies, the desired characteristics of fields in a planar ion trap have been discussed for its use as a mass analyzer. It was concluded that for a planar trap to be used as a mass analyzer, two features need to be ensured, namely, the need for having RF and DC field zero crossing heights should coincide and the field in the principal direction of ion motion should be linear. In chapter 4, a method has been developed to linearize and tailor fields in planar trap geometries. The proposed method has been applied to two planar trap geometries. One of these is a single-PCB design referred to as One-Sheet Ion Trap Geometry and the other is a two-PCB design referred to as Two-Sheet Ion Trap Geometry. In order to linearize and tailor fields in these planar geometries, the following scheme was adopted: the central DC electrode was split into segments. To these segmented electrodes, appropriate DC potentials (obtained by the least squares method) were applied. This technique has been shown to be successful in achieving linear as well as mildly superlinear fields. Chapter 5 develops a multipole expansion to characterize potentials and fields in ar bitrary ion trap geometries. The need for this arose because planar traps do not have any of the symmetries of the existing traps that have been discussed in literature. The coefficients of the expansion were computed from the surface charge distribution obtained from the BEM. From the multipole expansion, a formula has been derived to estimate the ion oscillation frequency. The agreement between the frequencies obtained by this formula and those obtained from numerical simulation was seen to be reasonably good for four different ion trap geometries