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.

In this thesis we have focussed on two types of axially symmetric ion trap mass analysers viz., the quadrupole ion trap mass analyser and the toroidal ion trap mass analyser. We have undertaken three numerical studies in this thesis, one study is on the quadrupole ion trap mass analysers and two studies are on the toroidal ion trap mass analysers. The first study is related to improvement of the sensitivity of quadrupole ion trap mass analysers operated in the resonance ejection mode. In the second study we have discussed methods to determine the multipole coefficients in the toroidal ion trap mass analysers. The third study investigates the stability of ions in the toroidal ion trap mass analysers. The first study presents a technique to cause unidirectional ion ejection in a quadrupole ion trap mass spectrometer operated in the resonance ejection mode. In this technique a modified auxiliary dipolar excitation signal is applied to the endcap electrodes. This modified signal is a linear combination of two signals. The first signal is the nominal dipolar excitation signal which is applied across the endcap electrodes and the second signal is the second harmonic of the first signal, the amplitude of the second harmonic being larger than that of the fundamental. We have investigated the effect of the following parameters on achieving unidirectional ion ejection: primary signal amplitude, ratio of amplitude of second harmonic to that of primary signal amplitude, different operating points, different scan rates, different mass to charge ratios and different damping constants. In all these simulations unidirectional ejection of destabilized ions has been successfully achieved. The second study presents methods to determine multipole coefficients for describing the potential in toroidal ion trap mass analysers. Three different methods have been presented to compute the toroidal multipole coefficients. The first method uses a least square fit and is useful when we have ability to compute potential at a set of points in the trapping region. In the second method we use the Discrete Fourier Transform of potentials on a circle in the trapping region. The third method uses surface charge distribution obtained from the Boundary Element Method to compute these coefficients. Using these multipole coefficients we have presented (1) equations of ion motion in toroidal ion traps (2) the Mathieu parameters in terms of multipole coefficients and (3) the secular frequency of ion motion in these traps. It has been shown that the secular frequency obtained from our method has a good match with that obtained from numerical trajectory simulation. The third study presents stability of ions in practical toroidal ion trap mass analysers. Here we have taken up for investigation four geometries with apertures and truncation of electrodes. The stability is obtained in UDC-VRF plane and later this is converted into A-Q plane on the Mathieu stability plot. Though the plots in terms of Mathieu parameters for these structures are qualitatively similar to the corresponding plot of linear ion trap mass analysers, there is a significant difference. The stability plots of these have regions of nonlinear resonances where ion motion is unstable. These resonances have been briefly investigated and it is proposed that they occur on account of hexapole and octopole contributions to the field in these toroidal ion traps.