The thesis aims at building an experimental setup for conducting the boundary ejection and resonance ejection experiments on wide variety of ion trap mass analyzers. The experimental setup has two parts namely power electronics circuits and mechanical assembly. The focus of the thesis is on the electronics hardware which provides various power sources required for the operation of ion trap mass spectrometer. The electronics circuits discussed in the thesis have better performance, flexibility and ruggedness compared to the existing setup. The traditional power supplies used in ion trap mass spectrometers are all linear supplies. But one major drawback of these supplies is the high power dissipation and consequently, the power efficiency degrades. We are trying to introduce switch mode power supplies to reduce the power dissipation loss and eventually increase the power efficiency. In the course of the work the following power supplies have been developed. The supplies are - 1.Constant current source, 2.Filament base, 3.gating power supply and pulsing circuit, 4.High voltage DC power supply and 5. High voltage RF generator.

This thesis is a numerical study of fields within ion traps having segmented electrodes1. The focus is on two cylindrical ion trap structures, two Orbit rap structures and one planar structure which mimics the field of the Orbit rap. In all these geometries, the segments which comprise the electrodes are easily Machin able rings and plates. By applying suitable potential to the different segments, the fields within these geometries are made to mimic the fields in the respective ideal structures. This thesis is divided into 6 chapters. Chapter 1 presents introduction and background information relevant to this work. A brief description of the Quadrupole Ion Trap (QIT) and the Orbit rap is given. The role of numerical simulations in the design of an ion trap geometry is briefly outlined. The motivation of this thesis is presented. The chapter ends by describing the scope of the thesis. Chapter 2 presents a general description of computational methods used throughout this work. The Boundary Element Methods (BEM) is first described. Both 2D and 3D BEM are used in this work. The software for 3D BEM is newly developed and hence 3D BEM is described in more detail. A verification of 3D BEM is presented with a few examples. The Runge-Kutta method used to compute the trajectory of ion is presented. A brief overview of the Nelder-Mead method of function minimization is given. The computational techniques specifically used to obtain the results in Chapter 3, 4 and 5 are presented in the respective chapters. Chapter 3 presents segmented electrode geometries of the Cylindrical Ion Trap (CIT). In these geometries, the electrodes of the CIT are split into number of mini-electrodes and different voltages are applied to these segmented electrodes to achieve the desired field. Two geometries of the segmented electrode CIT will be investigated. In the first, we retain the flat end cap electrodes of the CIT but split the ring electrode into five mini-rings. In the second configuration, we split the ring electrode of the CIT into three mini-rings and 1The term ‘segmented electrode’ used in this thesis has the same connotation as the term ‘split-electrode’ used in Sonalikar and Mohanty (2013). also divide the end caps into two mini-discs. By applying different potentials to the mini-rings and mini-discs of these geometries we will show that the field within the trap can be optimized to desired values. Two different types of fields will be targeted. In the first, potentials are adjusted to obtain a linear electric field and, in the second, a controlled higher order even multipole field are obtained by adjusting the potential. It will be shown that the different potentials to the segmented electrodes can be derived from a single RF generator by connecting appropriate capacitor terminations to segmented electrodes. The field within the trap can be modified by changing the value of the external capacitors. Chapter 4 presents segmented electrode geometries which are possible alternatives for the Orbitrap. Two segmented-electrode structures, ORB1 and ORB2, to mimic the electric field of the Orbitrap, will be investigated. In the ORB1, the inner spindle-like electrode and the outer barrel-like electrode of the Orbitrap are replaced by rings and discs of fixed radii, respectively. In this structure two segmented end cap electrodes are added. In this geometry, different potentials are applied to the different electrodes keeping top-bottom symmetry intact. In the second geometry, ORB2, the inner and outer electrodes of the Orbitrap are replaced by an approximate step structure which follows the profile of the Orbitrap electrodes. For the purpose of comparing the performance of ORB1 and ORB2 with that of the Orbitrap, the following studies will be undertaken: (1) variation of electric potential, (2) computation of ion trajectories, (3) measurement of image currents. These studies will be carried out using both 2D and 3D Boundary Element Method (BEM), the 3D BEM is developed specifically for this study. It will be seen in these investigations that ORB1 and ORB2 have performance similar to that of the Orbitrap, with the performance of the ORB1 being seen to be marginally superior to that of the ORB2. It will be shown that with proper optimization, geometries containing far fewer electrodes can be used as mass analysers. A novel technique of optimization of the electric field is proposed with the objective of minimizing the dependence of axial frequency of ion motion on the initial position of an ion. The results on the optimization of 9 and 15 segmented-electrode trap having the same design as ORB1 show that it can provide accurate mass analysis. Chapter 5 presents a segmented electrode planar geometry named as PORB used to mimic the electric field of the Orbit rap. This geometry has two planes, each plane consisting of 30 concentric ring electrodes. Although the geometry of PORB does not have conventional inner and outer electrodes of the Orbit rap, it will be shown that by selecting appropriate geometry parameters and suitable potentials for the ring electrodes, this geometry can trap the ions into an orbital motion similar to that in the Orbit rap. The performance of the planar geometry is studied by comparing the variation of potential, ion trajectories and image current in this geometry with that in the Orbit rap. The optimization of applied potentials is performed to correct the errors in the electric field so that the variation of axial frequency of ions with their initial position is minimized. Chapter 6 presents the summary and a few concluding remarks

The cylindrical ion trap (CIT) is made up of two planar endcap electrodes and a cylindrical ring electrode. The investigation of simpler geometries like CIT has been started off in recent years with a view towards miniaturization. As a step towards this, numerical studies on CITs were carried out in our laboratory. Here in this study, our motive is to characterize a CIT through experiments. We have designed a mass spectrometer where a CIT is used as the mass analyzer. The trap performance was observed by varying six parameters associated with our experiment. The parameters are (1) the ionization voltage, (2) the ramp time, (3) the ionization time, (4) the cooling time, (5) the dead time and (6) the bias voltage applied across the filaments. All the experiments have been performed in the mass selective boundary ejection mode.

Mass spectrometry is a technique that analyzes the chemical compositions of compounds based on the mass-to-charge ratio of their ionized constituents. Miniaturized ion trap mass spectrometry finds application in a wide range of fields where portable, rugged, and reliable analytical instruments are required. Ion traps of various designs have been introduced over the past decades, each with their own unique advantages and capabilities. However, the process of developing a novel miniaturized ion trap mass spectrometer continues to be fraught with challenges. This dissertation discusses simulation studies pertaining to the development of a novel dual ion trap, the simplified coaxial ion trap, consisting of a simplified toroidal ion trap and a cylindrical ion trap. Ions are initially trapped in the toroidal region and the target ions are transferred to the cylindrical region where they are fragmented and mass analyzed, while the rest of the ion population remains securely trapped in the toroidal region. The compact design and extended trapping volume secure several advantages that are not available to conventional ion trap designs. The simulations were geared towards the determination of an optimized geometry and optimal operating conditions for the simplified coaxial ion trap. Four main criteria were used in the determination of the ideal geometric and operating conditions; namely, mass-selectivity of transfer from the toroidal to cylindrical traps, transfer and trapping efficiency in the cylindrical ion trap, mass resolution, and unidirectional ejection. The optimized geometry demonstrates successful trapping of ions in the toroidal region and selective transfer of target ions to the cylindrical region. Unidirectional inward ejection of ions could be achieved with a positive hexapole component in the electric field. The mass resolution under optimized conditions of the toroidal trap was 0.3 Da (FWHM), which agrees with the experimental value. The simplified coaxial ion trap yielded a total transfer and trapping efficiency of 25%. A number of suggestions to improve the efficiency are also discussed as part of this work.

In the normal operation of quadrupole ion trap mass spectrometers, the trapped ions are ejected symmetrically through both the upper (detector) and lower(source) endcap electrodes during mass selective boundary ejection experiment. This reduces the sensitivity of the instrument by almost 50%. In this preliminary study, we altered the geometry parameters of the quadrupole ion traps to introduce asymmetry. The asymmetry displaced the ion cloud towards the detector endcap which resulted in a preferential ejection through this endcap, thus imparting directionality to the ejected ions and hence to the sensitivity enhancement. Two symmetrical mass analyzers have been taken up for numerical study. They include the Paul trap(QIT) and the cylindricaliontrap(CIT). Asymmetry to these geometries is introduced in two ways, one by varying the upper endcap hole radius alone and in other by stretching the trap along the upper endcap only. The escape velocity plots and mass selective boundary ejection simulations are used to demonstrate the directionality of ion ejection for these geometries. The simulations revealed a significant increase in the number of ions getting ejected in the direction of asymmetry.

Ion traps used in mass spectrometers are of two classes. One class consists of traps having three electrode geometries which have rotational symmetry about central axis. They are called axially symmetric ion traps. Paul trap, Cylindrical Ion Trap(CIT) are examples in this class. Other class of traps contain 2D electric field inside them which has same profile along the central axis due to translational symmetry. Linear Ion Trap(LIT) and Rectilinear Ion Trap(RIT) are examples in this class. In the ideal hyperbolic geometries of Paul trap and LIT, electric field is a perfectly linear function of distance from the center of the trap. But when these ideal geometries are simplified in to simpler geometries of the CIT and the RIT for ease in machining, linearity of field, which is a specialty of Paul trap and LIT is lost. In this thesis, an effort is made to optimize the field within the traps by using split electrodes. The ring electrode of the CIT and both pairs of electrodes in the RIT are divided into more number of parts. Suitable voltages are applied on these parts to improve the linearity of the field. This thesis contains six chapters. Chapter 1 contains a background information about mass spectrometry. Chapter 2 discusses the Boundary Element Method (BEM) used to calculate charge distribution and Nelder-Mead method used for optimization. It also shows the calculation of multipoles. In Chapter 3, two new geometries namely split-electrode RIT and split-electrode CIT are considered with the objective of improving the linearity of electric field inside them. It is shown here that by applying certain external potential on various parts of split electrodes of these geometries, it is possible to improve the linearity of electric field inside them. In Chapter 4, capacitor models of new geometries proposed in chapter 3 are discussed. The use of external capacitors as a replacement to external power supply is also discussed in this chapter. InChapter5, study similar to that ofChapter3is carried out by splitting the geometries in more number of parts. The possibility of improved field profile is investigated by applying full potential to some of these parts and keeping other parts at ground potential. In Chapter 6, concluding remarks are discussed.

This thesis presents axially symmetric equivalents of three-dimensional rf ion traps. Miniaturization in mass spectrometry has focused on miniaturizing mass analyzers. Decrease in mass analyzer size facilitates reduction of the size of other components of a mass spectrometer, especially the radio frequency electronics and vacuum system. Miniaturized mass analyzers are made using advanced microfabrication techniques. Due to micromachining limitations, it is not possible to fabricate ion traps with exact axial symmetry. The motivation for this thesis is to investigate newer three-dimensional geometries which do not possess axial symmetry, but are equivalent in performance to axially symmetric ion traps. We introduce a 3D geometry called square ion trap(SIT) having a ring electrode made off our square shaped planar surfaces and square shaped endcap electrodes resembling a cuboid. Initially, a SIT geometry is taken and it will be investigated if this unknown 3D geometry can be made equivalent to a well characterized, axially symmetric ion trap like the CIT. The purpose of showing equivalence will be to understand the ion dynamics and fields inside the new 3D SIT. This thesis consists of five chapters. In Chapter 1, we present the necessary background information required to understand the operation of a mass spectrometer. The Paul trap geometry is introduced followed by the derivation of equation of ion motion inside the Paul trap. The Mathieu stability plot and the modes of operation of a mass spectrometer are briefly discussed. The chapter ends by outlining scope of the thesis. Chapter 2 describes the computational methods employed by us in the thesis. First, the geometry of square ion trap is introduced. Then the boundary element method(BEM) which is used to compute the charge distribution on the electrode surfaces is discussed. This is followed by the three-dimensional Green’s function which should be employed for non-axially symmetric structures. The method to calculate potential and field inside the ion trap from charge distribution is shown. Calculation of multipole coefficients for non-axially symmetric traps using charge distribution is shown. The methods used to generate ion trajectory and stability plot are discussed. The Nelder-Mead simplex method used for optimization is also presented. To verify our numerical methods of charge calculation, we have taken standard textbook problems and compared our results with those presented therein. The multipoles calculation, field and ion trajectory was verified by comparing the results for the Paul trap and cylindrical ion traps. Chapter 3 presents the results for axially symmetric equivalents of 3D rf ion traps. SIT geometry of dimensions equivalent to the CIT0 are taken and field and multipoles are studied in it. Then optimization is applied to create a CIT geometry equivalent to the SIT under study. Axial field and ion trajectory was compared and observed to be matching. Finally, stability plot was generated for both SIT and its equivalent CIT and was found to present a close match. Chapter 4 presents the numerical results obtained for three-dimensional rf ion trap equivalent of CIT. In this chapter, we have considered two standard geometries, the CIT0 and the CITopt. Optimization was applied to create SIT geometries equivalent to the CIT0 and the CITopt respectively. Comparison of fields and ion trajectory confirmed the fact that non-axially symmetric traps can be created equivalent to any axially symmetric ion trap. We have also considered another case of axially symmetric circular planar ion trap which has an annular ring electrode and two planar endcap electrodes. Square equivalent of circular planar trap was created by the optimizer and its equivalent was verified by ion trajectory comparison. Chapter 5 summarizes the thesis with a few concluding remarks.

This thesis presents numerical optimization of geometries of axially symmetric ion trap mass analyzers. The motivation for this thesis is two fold. First is to demonstrate how the automated scheme can be applied to achieve geometry parameters of axially symmetric ion traps for a desired field configuration. Second is, through the Geometries investigated in this thesis, to present practically achievable geometries for mass spectroscopists to use. Here the underlying thought has been to keep the design simple for ease of fabrication (with the possibility of miniaturization) and still ensure that the performance of these analyzers is similar to the stretched geometry Paul traps. Five geometries have been taken up for investigation: one is the well known Cylindrical ion trap (CIT), three are new geometries and the last is the Paul trap under development in our laboratory. Two of these newer geometries have a step in the region of the midline 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 deferent objective functions composed of the desired weights of higher order multiples. 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 A2, A4, A6, A8, A10 and A12, respectively.Poincare 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 ejects of negative dodecapole superposition can be eliminated, although this results in a large positive A4=A2 ratio. Improved performance of the optimized CIT is suggested by the ion dynamics as seen in Poincare sections close to the stability boundary. With respect to the SRIT, two variants have been investigated. In the first geometry, A4=A2 and A6=A2 have been optimized and in the second A4=A2, A6=A2 and A8=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 multipole not included in the objective function, A10=A2 and A12=A2, are high; additionally, A10=A2 has a negative sign. In spite of this, for both these configurations, the Poincare sections predict good performance. In the case of the SEIT, a geometry was obtained for which A4=A2 and A6=A2 are close to their values in the stretched geometry Paul trap and the higher even multipole (A8=A2, A10=A2 and A12=A2) are all positive and small in magnitude. The Poincare sections predict good performance for this con¯guration too. 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 proposed here. Finally, for the Paul trap under development in our laboratory, Poincare sections and numerical simulations of coupled ion dynamics suggest a stretch of 79:7% is the best choice.

Axially symmetric rf ion traps consists of a mass analyser having three electrodes, one of which is a central ring electrode and the other two are endcap electrodes. In the ideal Paul trap mass spectrometer, the electrodes have hyperboloidal shape (March and Hughes, 1989) and in mass analyser with simplified geometry, such as the cylindrical ion trap (Wu et al.,2005) the central electrode is a cylinder and the two endcap electrode and flat plates. rf-only or rf/dc potential is applied across the ring electrode and the grounded endcap electrodes for conducting the basic experiments of the mass spectrometer. In recent times, the miniaturisation of ion trap is one of the research interests in the field of mass spectrometry. The miniaturisation has the advantages of compactness, low power consumption and portability. However, this is achieved at the cost of the overall performance of the mass spectrometer with its deleterious effect on resolution. Research groups study the field distribution in the trap for better understanding of ion dynamics in the direction of achieving improved performance with the miniaturised traps. One aspect which has not received any attention in research associated with quadrupole ion traps is the possible role of the magnetic field in improving performance of these traps. Since in the quadrupole ion trap mass analyser ion is confined by an oscillating (rf) field, magnetic fields have been considered superfluous. The motivation of the thesis is to understand the dynamics of ions in axially symmetric rf ion traps, in the presence of the magnetic field. The axially symmetric rf ion trap geometries considered in this thesis are the Paul trap and the cylindrical ion trap (CIT). The changes incurred to the ion motion and Mathieu stability diagram in the presence of magnetic field is observed in this work. Also, the relation between the magnetic field and the Mathieu parameter is shown. The thesis contains 4 chapters: Chapter 1 provides the basic back ground of mass spectrometry and the operating principles. The equations of ion motion in the Paul trap is derived and also the solution to Mathieu equation is provided. The solution to the Mathieu equation are the Mathieu parameters and , when plotted with on the x-axis and on the y-axis, results in the Mathieu stability plot, the explanation of which is also given in the chapter. A brief description of the secular frequency associated with the ion dynamics is given in this chapter. The popular experiments conducted (i.e. the mass selective boundary ejection and resonance ejection) with a mass spectrometer is described here. Finally at the end of the chapter is the scope of the thesis. Chapter 2 facilitates with the preliminary study required fort he accomplishment of the task. The Paul trap and the CIT are the rf ion traps considered in this work. The geometries of these two traps are described in this chapter. The computational methods used for the analysis of various aspects of mass spectrometer is introduced. The computational methods used involve the methods used for calculating the charge distribution on the electrodes, potentials, multipole co-efficients and trajectory calculations. The boundary element method(BEM), calculation for Potentials and the Runge-Kutta method used for the trajectory calculations are introduced in this chapter. The expressions for calculating the multipole co-efficients are also specified. Chapter 3 presents the results obtained. The equations of ion motion in a quadrupole ion trap in the presence of magnetic field is derived here. Verification of numerical results with and without the magnetic field are presented at the end of this chapter. The chapter also presents various graphs showing the impact of magnetic field on the ion dynamics in the Paul trap and the CIT. The impact of the presence of magnetic field on the micro motion in -, -and -directions of the rf ion traps are shown in this chapter. Also the figures showing the variation in the Mathieu stability plots, with varying magnetic field intensity are presented in the chapter. At the end of this chapter the relation between the magnetic field and the Mathieu parameter is derived and plotted. Chapter 4 explains the various observations made from the results obtained. This chapter also highlights the future scope of the work for making this a more applicable one. References in the text have been given by quoting the author’s name and year of publication. Full references have been provide, in an alphabetic order, at the end of the thesis.