No description available.

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.

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.

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.

No description available.

In this thesis we present a computational study of “ion crystals”, the interesting patterns in which ions arrange themselves in ion traps such as Paul and Penning traps. In ion crystals the ions are in equilibrium due to the balance of the repulsive forces between the ions and the overall tendency of the ion trap to pull ions towards the trap centre. We have carried out a detailed investigation of ion crystals in Paul traps by solving their equations of motion numerically. We also propose a model called the spring–mass model to explain the formation of ion crystals. This model is far more efficient than direct numerical simulation for predicting ion crystal structures. Finally, we demonstrate that there is a power law relating distance of an ion from the trap centre in ion crystals to the applied RF voltage amplitude.

No description available.

No description available.

Trapped ions in a Paul trap can experience micromotion on top of the wanted secular motion.Micromotion can for example cause Doppler shifts in spectroscopy measurements, making it important to know the amplitude of the motion. In this master thesis we use the correlation between RF driving the trap and photons emitted by a single Beryllium ion during the fluorescence detection to determine the micromotion. This method also allows us to investigate the effect on micromotion from a phase mismatch between RF electrodes. The photon correlation method is compared to measuring the micromotion by taking the ratio between the micromotion sideband and the carrier transition, and also to a simulation of the residual RF fields in the trap by a finite element method. Finally, we vary the path length of RF lines, to tune the phase on individual RF electrodes. The result is that the phase mismatch effect is more than an order of magnitude less than expected from theory. / Fångade joner i en Paul-fälla upplever mikrorörelse utöver den önskade sekulära rörelsen. Mikrorörelse kan till exempel orsaka Dopplerförskjutning i spektroskopimätningar, vilket gör det viktigt att veta amplituden av rörelsen. I det här examensarbetet använder vi korrelationen mellan RF som driver jonfällan och fotoner utsända från en enskild berylliumjon under fluorescens-detektion, för att mäta mikrorörelsen. Den här metoden tillåter oss också att undersöka effekten på mikrorörelse från en fasförskjutning mellan RF-elektroder. Fotonkorrelationsmetoden jämförs med en mätning av mikrorörelse genom att ta förhållandet mellan mikrorörelse-sidobandet och bärar-övergången, och också med en simulering av RF-fälten i jonfällan med en finit element-metod. Slutligen varierar vi längden på RF-kopplingen, för att justera fasen mellan individuella RF-elektroder. Resultatet är att effekten från fasförskjutningen är mer än en storleksordning mindre än vad teorin förutsagt.

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.