This thesis presents results of investigations that have been carried out to understand dynamics in nonlinear Paul trap mass spectrometers. Of the three problems that have been taken up for study in this thesis, the first concerns understanding early/delayed ejection of ions in mass selective boundary ejection experiments. The second looks at the differential resolution observed in forward and reverse scan resonance ejection experiments. The third study explores a coupled nonlinear resonance within the nominally stable region of trap operation. The method of multiple scales has been to elucidate dynamics associated with early and delayed ejection of ions in mass selective ejection experiments in Paul traps. We develop a slow flow equation to approximate the solution of a weakly nonlinear Mathieu equation to describe ion dynamics in the neighborhood of the stability boundary of ideal traps (where the Mathieu parameter qz = qz* = 0.908046). For positive even multipoles in the ion trapping field, in the stable region of trap operation, the phase portrait obtained from the slow flow consists of three fixed points, two of which are saddles and the third is a center. As the qz value of an ion approaches qz*, the saddles approach each other, and a point is reached where all nonzero solutions are unbounded, leading to an observation of early ejection. The phase portraits for negative even multipoles and odd multipoles of either sign are qualitatively similar to each other and display bounded solutions even for qz > qz*, resulting in the observation of delayed ejection associated with a more gentle increase in ion motion amplitudes, a mechanism different from the case of the positive even multipoles. The second study investigates constraints on pre-ejection dynamical states which cause differential resolution in resonance ejection experiments using Paul traps with stretched geometry. Both analytical and numerical computations are carried out to elucidate the role of damping and scan rate in influencing coherence in ion motion associated with the forward and reverse scan. It has been shown that in the forward scan experiments, for a given damping, low scan rates result in coherent motion of ions oof a given mass at the jump point. At this point, the amplitude and phase of ions of a given mass, starting at different initial conditions, become effectively identical. As the scan rate is increased, coherence is destroyed. For a given scan rate, increasing damping introduces coherence in ion motion, while decreasing damping destroys this coherence. In reverse scan experiments, for a given damping, very low scan rates will cause coherent ion motion. Increasing the scan rate destroys this coherence. The effect of damping in reverse scan experiments is qualitatively similar to that in the forward scan experiments, but settling times in the forward scan are shorter, leading to improved coherence and resolution. For mass spectrometrically relevant scan rates and damping values, significantly greater coherence is obtained in the forward scan. In the third study we investigate the weakly coupled and nonlinear Mathieu equations governing ion motion in axial and radial directions in a Paul trap in the neighborhood of a nonlinear resonance point at az* = -0.2313850427 and qz* = 0.9193009931$. Using harmonic balance based approximate averaging up to second order; we obtain a slow flow that, we numerically demonstrate, approximates the actual ion dynamics. We find that the slow flow is Hamiltonian. We study the slow flow numerically with the objective of exploring and displaying some of the possible types of interesting ion motions. In particular, we choose specific but arbitrary parameter values; study the stability of the individual radial and axial motion invariant manifolds; examine the rather large times associated with escape of ions; notice regions in the averaged phase space wherein trajectories do not, in fact, escape; observe apparently chaotic dynamics preceding escape for ions that do escape; and note that trajectories that do not escape appear to be confined to 4-tori. We conclude with some comments on the implications for practical operation of the Paul trap near this resonant point.

A Paul trap mass spectrometer has a three-electrode geometry mass analyzer consisting of two identical end cap electrodes and a ring electrode. Traditionally, the two end cap electrodes are electrically grounded and an RF potential is applied to the central ring electrode to generate the "trapping field". Ions of the analyte sample are formed in situ by electron bombardment and mass analysis of the fragment ions is performed by mass selectively destabilizing the ions from the trap. The inhornogeneities present in the trapping field (introduced either by misalignment of the trap geometry or by applying a dipolar auxiliary excitation across the end cap electrodes) give rise to various interesting phenomena including, resonance ejection of the trapped ions This thesis is concerned with taking a look into the experimental aspects associated with resonance ejection of ions caused by the dipolar excitation Additionally, u also reports the work undertaken to develop necessary instrumentation for resonant excitation experiments and my contribution to operational>zc the Paul trap mass spectrometer fabricated in the laboratory. The thesis is divided into 5 chapters. Chapter 1 is an introductory chapter. After discussing the conditions for stability of the trapped ions, it goes on to present a brief survey of a variety of applications in literature, which have used resonant excitation. Towards the end, the motivation of the present effort and the scope of work in the thesis have been spelt out. This includes (a) redesign of the ion detector electronics, (b) design of an auxiliary excitation generator, and (c) studies on resonance ejection. Chapter 2 outlines the design considerations, circuit description and fabrication details for the ion detector electronics. The circuits presented in this chapter include (a) electrometer amplifier and (b) -3 kV DC supply for the electron multiplier detector. The electrometer amplifier amplifies the ion current signal from the electron multiplier detector and it needs to have a high input impedance and a high slew rate. The electron multiplier detector requires -3 kV DC power supply for operation. The -3 kV DC power supply is required to have a regulated output voltage with low ripple in the output. Chapter 3 presents the design considerations, circuit description and fabrication details for the auxiliary excitation generator. The auxiliary excitation generator is a three channel DDS (Direct Digital Synthesis) oscillator with independent control of frequency amplitude, and phase of the output signal. Chapter 3 also discusses the micro controller based control sub-system that allows the user to set above mentioned output parameters. The control sub-system provides a user-friendly keyboard interface and 2-line alphanumeric LCD display per channel. It also provides various bus interfaces (such as I2C and SPI) to interface with DDS oscillator ICs, amplitude control DAC, and LCD displays. The chapter then goes on to describe the implementation details of the software written for the control sub-system. The hardware design is simplified by using a micro controller as heart of the control sub-system and employing the software to handle the complex functions. As an example, the design of the keyboard interface is simplified by directly connecting a matrix keyboard to the input/output port of the micro controller. The software is used to scan the keyboard, detect key press and find out the key pressed. Nonetheless, in order to meet specific performance required for the present work, the software needs to have a sense of time, be portable and scalable. Details of the "layered" architecture adopted by as to meet these specific requirements, the lower level "driver" functions implemented for various interfaces of the control sub-system, and the higher level or the "application" software, are described. The application software uses the driver functions to accomplish various tasks required to be executed by the control sub-system. Finally, the chapter presents the design consideration and fabrication details of the coupling transformer used to couple the output of the auxiliary excitation generator to the Paul trap Chapter 4 describes the resonant excitation experiments performed as part of the present work. First of all the chapter presents the improvement in the performance of the Paul trap mass spectrometer as a result of redesigned ion detector electronics It is seen that the resolution is improved significantly due to the improved response time of the electrometer amplifier. The chapter then describes the effect of the resonant excitation on the ions and also that the frequency of the applied auxiliary excitation should be between 500 kHz to 125 kHz. Next, a number of mass spectra for different frequencies of the applied auxiliary excitation are presented. These mass spectra indicate that the resonant ejection sets in for lower masses even at lower amplitude of the auxiliary excitation where as higher amplitude is required for the resonant ejection of the higher masses. It is seen that the resonant excitation of ions improves resolution of the mass spectrum. Moreover, the auxiliary excitation results in ejection of the ions at lower amplitude of the RF voltage and thus allows extending the mass range of the mass spectrometer. We present the mass spectrum of CCI4 which is not possible to normally record in our instrument. We also present results intended to understand the relation between frequency and amplitude of the auxiliary excitation on the mass spectra of benzene. Finally, results of an interesting experiment are presented which indicates the presence of the non-linear resonance points in the Paul trap. Chapter 5 presents the concluding remarks. References cited in the thesis are attached in their alphabetical order at the end of the thesis.

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.

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.