subject:(Paul Traps)

Indian Institute of Science

1. Kotana, Appala Naidu. A Computational Study Of Ion Crystals In Paul Traps.

Degree: MSc Engg, Faculty of Engineering, 2013, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/2042

► 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… (more)

Subjects/Keywords: Ion Crystals; Paul Traps; Ion Crystal Structures; Spring-mass Model; Paul Trap; Crystallography

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APA (6^th Edition):

Kotana, A. N. (2013). A Computational Study Of Ion Crystals In Paul Traps. (Masters Thesis). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/2042

Chicago Manual of Style (16^th Edition):

Kotana, Appala Naidu. “A Computational Study Of Ion Crystals In Paul Traps.” 2013. Masters Thesis, Indian Institute of Science. Accessed March 08, 2021. http://etd.iisc.ac.in/handle/2005/2042.

MLA Handbook (7^th Edition):

Kotana, Appala Naidu. “A Computational Study Of Ion Crystals In Paul Traps.” 2013. Web. 08 Mar 2021.

Vancouver:

Kotana AN. A Computational Study Of Ion Crystals In Paul Traps. [Internet] [Masters thesis]. Indian Institute of Science; 2013. [cited 2021 Mar 08]. Available from: http://etd.iisc.ac.in/handle/2005/2042.

Council of Science Editors:

Kotana AN. A Computational Study Of Ion Crystals In Paul Traps. [Masters Thesis]. Indian Institute of Science; 2013. Available from: http://etd.iisc.ac.in/handle/2005/2042

Indian Institute of Science

2. Shareef, I Khader. Axially Symmetric Equivalents Of Three-Dimensional Rf Ion Traps.

Degree: MSc Engg, Faculty of Engineering, 2013, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/2243

► 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… (more)

▼ 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… Advisors/Committee Members: Menon, A G (advisor), Mohanty, A K (advisor).

Subjects/Keywords: Mass Spectroscopy; Radiofrequency Ion Traps; Axial Symmetry; Paul Trap Mass Spectrometer; Square Ion Trap (SIT); Mass Spectrometer; Paul Trap Geometry; Paul Trap; rf Ion Traps; Cylindrical Ion Trap (CIT); Instrumentation

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APA (6^th Edition):

Shareef, I. K. (2013). Axially Symmetric Equivalents Of Three-Dimensional Rf Ion Traps. (Masters Thesis). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/2243

Chicago Manual of Style (16^th Edition):

Shareef, I Khader. “Axially Symmetric Equivalents Of Three-Dimensional Rf Ion Traps.” 2013. Masters Thesis, Indian Institute of Science. Accessed March 08, 2021. http://etd.iisc.ac.in/handle/2005/2243.

MLA Handbook (7^th Edition):

Shareef, I Khader. “Axially Symmetric Equivalents Of Three-Dimensional Rf Ion Traps.” 2013. Web. 08 Mar 2021.

Vancouver:

Shareef IK. Axially Symmetric Equivalents Of Three-Dimensional Rf Ion Traps. [Internet] [Masters thesis]. Indian Institute of Science; 2013. [cited 2021 Mar 08]. Available from: http://etd.iisc.ac.in/handle/2005/2243.

Council of Science Editors:

Shareef IK. Axially Symmetric Equivalents Of Three-Dimensional Rf Ion Traps. [Masters Thesis]. Indian Institute of Science; 2013. Available from: http://etd.iisc.ac.in/handle/2005/2243

Indian Institute of Science

3. Sridhar, P. A Preliminary Investigation Of The Role Of Magnetic Fields In Axially Symmetric rf Ion Traps.

Degree: MSc Engg, Faculty of Engineering, 2013, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/2111

► 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… (more)

▼ 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… Advisors/Committee Members: Menon, A G (advisor), Mohanty, A K (advisor).

Subjects/Keywords: Radiofrequency Ion Traps; Ion Dynamics; Paul Traps; Cylindrical Ion Trap (CIT); Ion Trap Mass Spectrometry; Mass Spectrometers; Radiofrequency Ion Traps - Magnetic Field; Paul Trap Mass Spectrometer; rf Ion Traps; Quadrupole Ion Trap; Instrumentation

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Sridhar, P. (2013). A Preliminary Investigation Of The Role Of Magnetic Fields In Axially Symmetric rf Ion Traps. (Masters Thesis). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/2111

Chicago Manual of Style (16^th Edition):

Sridhar, P. “A Preliminary Investigation Of The Role Of Magnetic Fields In Axially Symmetric rf Ion Traps.” 2013. Masters Thesis, Indian Institute of Science. Accessed March 08, 2021. http://etd.iisc.ac.in/handle/2005/2111.

MLA Handbook (7^th Edition):

Sridhar, P. “A Preliminary Investigation Of The Role Of Magnetic Fields In Axially Symmetric rf Ion Traps.” 2013. Web. 08 Mar 2021.

Vancouver:

Sridhar P. A Preliminary Investigation Of The Role Of Magnetic Fields In Axially Symmetric rf Ion Traps. [Internet] [Masters thesis]. Indian Institute of Science; 2013. [cited 2021 Mar 08]. Available from: http://etd.iisc.ac.in/handle/2005/2111.

Council of Science Editors:

Sridhar P. A Preliminary Investigation Of The Role Of Magnetic Fields In Axially Symmetric rf Ion Traps. [Masters Thesis]. Indian Institute of Science; 2013. Available from: http://etd.iisc.ac.in/handle/2005/2111

Indian Institute of Science

4. Sonalikar, Hrishikesh Shashikant. A Preliminary Study Of Fields In Split-Electrode Ion Traps.

Degree: MSc Engg, Faculty of Engineering, 2014, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/2373

► 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… (more)

▼ 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. Advisors/Committee Members: Menon, A G (advisor), Mohanty, A K (advisor).

Subjects/Keywords: Electrode Ion Traps; Rectilinear Ion Trap (RIT); Cylindrical Ion Trap (CIT); Split-electrode Geometries; Mass Spectrometer; Split-electrode Ion Traps; Paul Trap; Linear Ion Trap (LIT); Instrumentation

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APA (6^th Edition):

Sonalikar, H. S. (2014). A Preliminary Study Of Fields In Split-Electrode Ion Traps. (Masters Thesis). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/2373

Chicago Manual of Style (16^th Edition):

Sonalikar, Hrishikesh Shashikant. “A Preliminary Study Of Fields In Split-Electrode Ion Traps.” 2014. Masters Thesis, Indian Institute of Science. Accessed March 08, 2021. http://etd.iisc.ac.in/handle/2005/2373.

MLA Handbook (7^th Edition):

Sonalikar, Hrishikesh Shashikant. “A Preliminary Study Of Fields In Split-Electrode Ion Traps.” 2014. Web. 08 Mar 2021.

Vancouver:

Sonalikar HS. A Preliminary Study Of Fields In Split-Electrode Ion Traps. [Internet] [Masters thesis]. Indian Institute of Science; 2014. [cited 2021 Mar 08]. Available from: http://etd.iisc.ac.in/handle/2005/2373.

Council of Science Editors:

Sonalikar HS. A Preliminary Study Of Fields In Split-Electrode Ion Traps. [Masters Thesis]. Indian Institute of Science; 2014. Available from: http://etd.iisc.ac.in/handle/2005/2373

Indian Institute of Science

5. Sevugarajan, S. Studies Of Non-Linear Ion Dynamics And Electron Impact Ionization In Paul Trap Mass Spectrometers.

Degree: PhD, Faculty of Engineering, 2011, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/1206

Subjects/Keywords: Paul Trap Mass Spectrometers; Ions - Dynamics; Paul Traps; Benzene Cation; Electrochemistry

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APA (6^th Edition):

Sevugarajan, S. (2011). Studies Of Non-Linear Ion Dynamics And Electron Impact Ionization In Paul Trap Mass Spectrometers. (Doctoral Dissertation). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/1206

Chicago Manual of Style (16^th Edition):

Sevugarajan, S. “Studies Of Non-Linear Ion Dynamics And Electron Impact Ionization In Paul Trap Mass Spectrometers.” 2011. Doctoral Dissertation, Indian Institute of Science. Accessed March 08, 2021. http://etd.iisc.ac.in/handle/2005/1206.

MLA Handbook (7^th Edition):

Sevugarajan, S. “Studies Of Non-Linear Ion Dynamics And Electron Impact Ionization In Paul Trap Mass Spectrometers.” 2011. Web. 08 Mar 2021.

Vancouver:

Sevugarajan S. Studies Of Non-Linear Ion Dynamics And Electron Impact Ionization In Paul Trap Mass Spectrometers. [Internet] [Doctoral dissertation]. Indian Institute of Science; 2011. [cited 2021 Mar 08]. Available from: http://etd.iisc.ac.in/handle/2005/1206.

Council of Science Editors:

Sevugarajan S. Studies Of Non-Linear Ion Dynamics And Electron Impact Ionization In Paul Trap Mass Spectrometers. [Doctoral Dissertation]. Indian Institute of Science; 2011. Available from: http://etd.iisc.ac.in/handle/2005/1206

Indian Institute of Science

6. Subramanyan, E K Ganapathy. Escape Of High Mass Ions Due To Initial Thermal Energy And Its Implications For RF Trap Design.

Degree: MSc Engg, Faculty of Engineering, 2013, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/2015

► This thesis investigates the loss of high mass ions due to the initial thermal energy in ion trap mass analyzers. It provides an analytical expression… (more)

Subjects/Keywords: Radiofrequency Ion Trap - Instrumentation; Paul Trap Mass Spectrometer; Mass Spectrometry; Ion Trap Mass Spectrometers; Quadrupole Ion Trap (QIT); Boundary Element Method (BEM); RF Trap Design; Paul Trap; Ion Traps; Instrumentation

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Subramanyan, E. K. G. (2013). Escape Of High Mass Ions Due To Initial Thermal Energy And Its Implications For RF Trap Design. (Masters Thesis). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/2015

Chicago Manual of Style (16^th Edition):

Subramanyan, E K Ganapathy. “Escape Of High Mass Ions Due To Initial Thermal Energy And Its Implications For RF Trap Design.” 2013. Masters Thesis, Indian Institute of Science. Accessed March 08, 2021. http://etd.iisc.ac.in/handle/2005/2015.

MLA Handbook (7^th Edition):

Subramanyan, E K Ganapathy. “Escape Of High Mass Ions Due To Initial Thermal Energy And Its Implications For RF Trap Design.” 2013. Web. 08 Mar 2021.

Vancouver:

Subramanyan EKG. Escape Of High Mass Ions Due To Initial Thermal Energy And Its Implications For RF Trap Design. [Internet] [Masters thesis]. Indian Institute of Science; 2013. [cited 2021 Mar 08]. Available from: http://etd.iisc.ac.in/handle/2005/2015.

Council of Science Editors:

Subramanyan EKG. Escape Of High Mass Ions Due To Initial Thermal Energy And Its Implications For RF Trap Design. [Masters Thesis]. Indian Institute of Science; 2013. Available from: http://etd.iisc.ac.in/handle/2005/2015

Indian Institute of Science

7. Gorde, Dnyaneshwar R. System Design For Non-Destructive Detection Of Ions In A Paul Trap Mass Spectrometer.

Degree: MSc Engg, Faculty of Engineering, 2011, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/1208

Subjects/Keywords: Ion Detectors; Paul Trap Mass Spectrometer; Paul Traps; Coupling Transformer; Electrochemistry

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APA (6^th Edition):

Gorde, D. R. (2011). System Design For Non-Destructive Detection Of Ions In A Paul Trap Mass Spectrometer. (Masters Thesis). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/1208

Chicago Manual of Style (16^th Edition):

Gorde, Dnyaneshwar R. “System Design For Non-Destructive Detection Of Ions In A Paul Trap Mass Spectrometer.” 2011. Masters Thesis, Indian Institute of Science. Accessed March 08, 2021. http://etd.iisc.ac.in/handle/2005/1208.

MLA Handbook (7^th Edition):

Gorde, Dnyaneshwar R. “System Design For Non-Destructive Detection Of Ions In A Paul Trap Mass Spectrometer.” 2011. Web. 08 Mar 2021.

Vancouver:

Gorde DR. System Design For Non-Destructive Detection Of Ions In A Paul Trap Mass Spectrometer. [Internet] [Masters thesis]. Indian Institute of Science; 2011. [cited 2021 Mar 08]. Available from: http://etd.iisc.ac.in/handle/2005/1208.

Council of Science Editors:

Gorde DR. System Design For Non-Destructive Detection Of Ions In A Paul Trap Mass Spectrometer. [Masters Thesis]. Indian Institute of Science; 2011. Available from: http://etd.iisc.ac.in/handle/2005/1208

Indian Institute of Science

8. Prasanna, N. Study Of The B=2/5 Resonance And Resonance Excitation In Nonlinear Paul Traps.

Degree: MSc Engg, Faculty of Engineering, 2011, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/1462

Subjects/Keywords: Nonlinear Resonance; Resonance Excitation; Mass Spectrometry; Ion Dynamics; Ion Mobility Spectrometry; Paul Trap Mass Spectrometer; Nonlinear Paul Traps; Paul Traps - Ejection; Paul Trap; Instrumentation

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Prasanna, N. (2011). Study Of The B=2/5 Resonance And Resonance Excitation In Nonlinear Paul Traps. (Masters Thesis). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/1462

Chicago Manual of Style (16^th Edition):

Prasanna, N. “Study Of The B=2/5 Resonance And Resonance Excitation In Nonlinear Paul Traps.” 2011. Masters Thesis, Indian Institute of Science. Accessed March 08, 2021. http://etd.iisc.ac.in/handle/2005/1462.

MLA Handbook (7^th Edition):

Prasanna, N. “Study Of The B=2/5 Resonance And Resonance Excitation In Nonlinear Paul Traps.” 2011. Web. 08 Mar 2021.

Vancouver:

Prasanna N. Study Of The B=2/5 Resonance And Resonance Excitation In Nonlinear Paul Traps. [Internet] [Masters thesis]. Indian Institute of Science; 2011. [cited 2021 Mar 08]. Available from: http://etd.iisc.ac.in/handle/2005/1462.

Council of Science Editors:

Prasanna N. Study Of The B=2/5 Resonance And Resonance Excitation In Nonlinear Paul Traps. [Masters Thesis]. Indian Institute of Science; 2011. Available from: http://etd.iisc.ac.in/handle/2005/1462

Indian Institute of Science

9. Rajanbabu, N. Nonlinear Dynamics Of Resonances In, And Ejection From Paul Traps.

Degree: PhD, Faculty of Engineering, 2008, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/361

► 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… (more)

▼ 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… Advisors/Committee Members: Menon, A G (advisor), Chatterjee, Anindya (advisor).

Subjects/Keywords: Non-linear Dynamics; Ion Dynamics; Paul Trap Mass Spectrometer; Paul Trap; Paul Traps - Ejection; Ions - Ejection; Resonance Ejection; Instrumentation

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APA (6^th Edition):

Rajanbabu, N. (2008). Nonlinear Dynamics Of Resonances In, And Ejection From Paul Traps. (Doctoral Dissertation). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/361

Chicago Manual of Style (16^th Edition):

Rajanbabu, N. “Nonlinear Dynamics Of Resonances In, And Ejection From Paul Traps.” 2008. Doctoral Dissertation, Indian Institute of Science. Accessed March 08, 2021. http://etd.iisc.ac.in/handle/2005/361.

MLA Handbook (7^th Edition):

Rajanbabu, N. “Nonlinear Dynamics Of Resonances In, And Ejection From Paul Traps.” 2008. Web. 08 Mar 2021.

Vancouver:

Rajanbabu N. Nonlinear Dynamics Of Resonances In, And Ejection From Paul Traps. [Internet] [Doctoral dissertation]. Indian Institute of Science; 2008. [cited 2021 Mar 08]. Available from: http://etd.iisc.ac.in/handle/2005/361.

Council of Science Editors:

Rajanbabu N. Nonlinear Dynamics Of Resonances In, And Ejection From Paul Traps. [Doctoral Dissertation]. Indian Institute of Science; 2008. Available from: http://etd.iisc.ac.in/handle/2005/361

Indian Institute of Science

10. Vadakkumbatt, Vaisakh. Experimental Investigation of Multielectron Bubbles in Liquid Helium.

Degree: PhD, Faculty of Science, 2017, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/2822

► Multielectron bubbles (MEBs) are micron sized cavities in liquid helium that contain electrons confined within a nanometer thick layer on the inner surface of a… (more)

▼ Multielectron bubbles (MEBs) are micron sized cavities in liquid helium that contain electrons confined within a nanometer thick layer on the inner surface of a bubble. These objects present a rich platform to study the behavior of a two dimensional electron gas (2DES) on a curved surface. Most crucially, the surface electron densities in MEBs can vary over a wide range, making it a suitable candidate for studying classical Wigner crystallization and quantum melting in a single system. So far, there has been only limited experimental study of MEBs, with most of the previous investigation transient in nature. As we discuss in our presentation, we have built a cryogenic system for performing transport and optical measurements of MEBs down to 1.3 K. We have developed a new technique of generating MEBs, and trapping them using two different methods. In the first method, we trapped MEBs using a Paul trap for more than hundreds of milliseconds. This allows the MEBs to be further manipulated with buoyant and electric forces, such as to obtain reliable measurements of their physical properties. As we observe experimentally, the surface charge density of a single MEB can vary by orders of magnitude during the course of one measurement, thereby covering a previously unexplored section of the 2DES phase diagram. In the second method, we trapped MEBs using a dielectric coated metal electrode over many seconds. This also allowed the properties of MEBs to be measured in a non-destructive manner. Since MEBs are charged bubbles, their motion can be controlled by electric fields, which allowed us to measure the drag of MEBs as a function of Reynolds number by analysing the trajectories. Due to the low viscosity and surface tension of helium compared to other liquids, these measurements could be performed at Morton Numbers that have never been explored. We also show that how the shape of a single MEB evolves from spherical to ellipsoidal as their speeds vary. During the course of experiments, we observed number of interesting phenomena, such as coalescence of similarly charged bubbles, as well as their splitting into secondary bubbles at high speeds. Most interestingly, we have imaged their dynamics in the presence of static, as well as oscillating electric fields, which may provide insight into the phase of the electronic system present inside the bubbles. Advisors/Committee Members: Ghosh, Ambarish (advisor).

Subjects/Keywords: Liquid Helium; Multielectron Bubbles (MEBs); Two Dimensional Electron Gas; Multielectron Bubble Trapping; Paul Traps; Dielectric Coated Metal; Helium Electrons; Pulsed Electric Fields; Physics

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APA (6^th Edition):

Vadakkumbatt, V. (2017). Experimental Investigation of Multielectron Bubbles in Liquid Helium. (Doctoral Dissertation). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/2822

Chicago Manual of Style (16^th Edition):

Vadakkumbatt, Vaisakh. “Experimental Investigation of Multielectron Bubbles in Liquid Helium.” 2017. Doctoral Dissertation, Indian Institute of Science. Accessed March 08, 2021. http://etd.iisc.ac.in/handle/2005/2822.

MLA Handbook (7^th Edition):

Vadakkumbatt, Vaisakh. “Experimental Investigation of Multielectron Bubbles in Liquid Helium.” 2017. Web. 08 Mar 2021.

Vancouver:

Vadakkumbatt V. Experimental Investigation of Multielectron Bubbles in Liquid Helium. [Internet] [Doctoral dissertation]. Indian Institute of Science; 2017. [cited 2021 Mar 08]. Available from: http://etd.iisc.ac.in/handle/2005/2822.

Council of Science Editors:

Vadakkumbatt V. Experimental Investigation of Multielectron Bubbles in Liquid Helium. [Doctoral Dissertation]. Indian Institute of Science; 2017. Available from: http://etd.iisc.ac.in/handle/2005/2822

Indian Institute of Science

11. Naveen Reddy, D S Srinivas. Numerical Study of Directionality of Ion Ejection In Axially Symmetric Ion Traps.

Degree: MSc Engg, Faculty of Engineering, 2013, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/1922

► 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… (more)

Subjects/Keywords: Ion Ejection Instruments; Ion Trapping Instruments; Quadrupole Ion Trap (QIT); Cylindrical Ion Trap (CIT); Nonlinear Ion Trap; Green’s Functions; Paul Trap; Ion Traps; Instrumentation

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Naveen Reddy, D. S. S. (2013). Numerical Study of Directionality of Ion Ejection In Axially Symmetric Ion Traps. (Masters Thesis). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/1922

Chicago Manual of Style (16^th Edition):

Naveen Reddy, D S Srinivas. “Numerical Study of Directionality of Ion Ejection In Axially Symmetric Ion Traps.” 2013. Masters Thesis, Indian Institute of Science. Accessed March 08, 2021. http://etd.iisc.ac.in/handle/2005/1922.

MLA Handbook (7^th Edition):

Naveen Reddy, D S Srinivas. “Numerical Study of Directionality of Ion Ejection In Axially Symmetric Ion Traps.” 2013. Web. 08 Mar 2021.

Vancouver:

Naveen Reddy DSS. Numerical Study of Directionality of Ion Ejection In Axially Symmetric Ion Traps. [Internet] [Masters thesis]. Indian Institute of Science; 2013. [cited 2021 Mar 08]. Available from: http://etd.iisc.ac.in/handle/2005/1922.

Council of Science Editors:

Naveen Reddy DSS. Numerical Study of Directionality of Ion Ejection In Axially Symmetric Ion Traps. [Masters Thesis]. Indian Institute of Science; 2013. Available from: http://etd.iisc.ac.in/handle/2005/1922

Indian Institute of Science

12. Sevugarajan, S. Frequency Perturbation In Non-Linear Paul Traps.

Degree: MSc Engg, Faculty of Engineering, 2012, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/1612

Subjects/Keywords: Potential Theory; Ion Oscillations - Pertubation; Vibrations - Mechanics; Paul Traps; Non-linear Ion Traps; Acoustics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Sevugarajan, S. (2012). Frequency Perturbation In Non-Linear Paul Traps. (Masters Thesis). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/1612

Chicago Manual of Style (16^th Edition):

Sevugarajan, S. “Frequency Perturbation In Non-Linear Paul Traps.” 2012. Masters Thesis, Indian Institute of Science. Accessed March 08, 2021. http://etd.iisc.ac.in/handle/2005/1612.

MLA Handbook (7^th Edition):

Sevugarajan, S. “Frequency Perturbation In Non-Linear Paul Traps.” 2012. Web. 08 Mar 2021.

Vancouver:

Sevugarajan S. Frequency Perturbation In Non-Linear Paul Traps. [Internet] [Masters thesis]. Indian Institute of Science; 2012. [cited 2021 Mar 08]. Available from: http://etd.iisc.ac.in/handle/2005/1612.

Council of Science Editors:

Sevugarajan S. Frequency Perturbation In Non-Linear Paul Traps. [Masters Thesis]. Indian Institute of Science; 2012. Available from: http://etd.iisc.ac.in/handle/2005/1612

Indian Institute of Science

13. Tallapragada, Pavan K. Geometry Optimization Of Axially Symmetric Ion Traps.

Degree: MSc Engg, Faculty of Engineering, 2009, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/497

► 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… (more)

▼ 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… Advisors/Committee Members: Menon, A G (advisor), Mohanty, A (advisor).

Subjects/Keywords: Ionizing Radiation; Particle Characteristics; Paul Trap; Ideal Paul Trap; Nonlinear Ion Traps; Trap Geometries - Optimization; Ion Traps - Geometry Optimization; Axially Symmetric Ion Traps; Cylindrical Ion Trap (CIT); SRIT; SEIT; Instrumentation

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Tallapragada, P. K. (2009). Geometry Optimization Of Axially Symmetric Ion Traps. (Masters Thesis). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/497

Chicago Manual of Style (16^th Edition):

Tallapragada, Pavan K. “Geometry Optimization Of Axially Symmetric Ion Traps.” 2009. Masters Thesis, Indian Institute of Science. Accessed March 08, 2021. http://etd.iisc.ac.in/handle/2005/497.

MLA Handbook (7^th Edition):

Tallapragada, Pavan K. “Geometry Optimization Of Axially Symmetric Ion Traps.” 2009. Web. 08 Mar 2021.

Vancouver:

Tallapragada PK. Geometry Optimization Of Axially Symmetric Ion Traps. [Internet] [Masters thesis]. Indian Institute of Science; 2009. [cited 2021 Mar 08]. Available from: http://etd.iisc.ac.in/handle/2005/497.

Council of Science Editors:

Tallapragada PK. Geometry Optimization Of Axially Symmetric Ion Traps. [Masters Thesis]. Indian Institute of Science; 2009. Available from: http://etd.iisc.ac.in/handle/2005/497

Indian Institute of Science

14. Srinivasan, S Deepak. Study of Subharmonic Oscillations In Resonance Excitation Experiments In Nonlinear Paul Traps.

Degree: MSc Engg, Faculty of Engineering, 2009, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/554

► This thesis presents the results of studies on the problem of subharmonic oscillations in nonlinear Paul trap mass spectrometry. The objective of this thesis is… (more)

▼ This thesis presents the results of studies on the problem of subharmonic oscillations in nonlinear Paul trap mass spectrometry. The objective of this thesis is to determine whether the subharmonic oscillations of ions in the trap could in any way aﬀect the quality of mass spectrum in resonance ejection experiments. This is accomplished by studying the existence and stability criteria of these oscillations. This study is done for two casesone in which the auxiliary excitation frequency is close to thrice the ion axial secular frequency and other in which it is close to twice the ion axial secular frequency. Initially, the equations describing the ion motion in the presence of auxiliary excitation are derived. The equations describing the ion motion are then brought into a form easily amenable to analysis by techniques of perturbation theory. The necessary background and deﬁnitions to understand the basis for the thesis, along with a survey of results obtained in relevant areas in mass spectrometry and nonlinear dynamics is then developed. The ﬁrst problem is the study of subharmonic oscillations when the auxiliary excitation frequency is in the vicinity of thrice the ion axial secular frequencies taken up. The application of the multiple time scales technique to the equations describing ion motion gives the slow ﬂow equations, that describe the evolution of amplitudes of axial and radial oscillations. The expression for the steady state amplitudes of these oscillations are then derived. From these expressions the conditions for the existence of the oscillations are obtained in terms of the auxiliary amplitude and the frequency detuning. This is then followed by a detailed stability analysis for the subharmonic oscillation with a given amplitude and phase. The study ends with the discussion of the results obtained, the pertinent numerical studies and the relevance of this study to mass spectrometry. The second study is regarding the problem of subharmonic oscillations when the auxiliary excitation frequency is close to twice the ion axial secular frequency is analyzed. When PoincareLindstedt’s method is applied to the ion motion equations, the amplitude frequency relationship that describes the relation between the steady state subharmonic oscillation amplitude and the frequency detuning is obtained. The variation of the oscillation amplitude with the frequency detuning is then studied. Then follows the analysis of stability. The stability of subharmonic oscillation is analyzed using the results from the standard analysis of Hill’s equation of fourth order. This study ends with the discussion of the results obtained in the context of mass spectrometry. Finally, a summary of the results obtained is discussed. Advisors/Committee Members: Menon, A G (advisor).

Subjects/Keywords: Mass Spectrometry; Resonance Excitation; Subharmonic Oscillation; Ions - Dynamics; Nonlinear Paul Traps; Paul Trap Mass Spectrometry; Perturbation Analysis; Hill's Equation; Instrumentation

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Srinivasan, S. D. (2009). Study of Subharmonic Oscillations In Resonance Excitation Experiments In Nonlinear Paul Traps. (Masters Thesis). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/554

Chicago Manual of Style (16^th Edition):

Srinivasan, S Deepak. “Study of Subharmonic Oscillations In Resonance Excitation Experiments In Nonlinear Paul Traps.” 2009. Masters Thesis, Indian Institute of Science. Accessed March 08, 2021. http://etd.iisc.ac.in/handle/2005/554.

MLA Handbook (7^th Edition):

Srinivasan, S Deepak. “Study of Subharmonic Oscillations In Resonance Excitation Experiments In Nonlinear Paul Traps.” 2009. Web. 08 Mar 2021.

Vancouver:

Srinivasan SD. Study of Subharmonic Oscillations In Resonance Excitation Experiments In Nonlinear Paul Traps. [Internet] [Masters thesis]. Indian Institute of Science; 2009. [cited 2021 Mar 08]. Available from: http://etd.iisc.ac.in/handle/2005/554.

Council of Science Editors:

Srinivasan SD. Study of Subharmonic Oscillations In Resonance Excitation Experiments In Nonlinear Paul Traps. [Masters Thesis]. Indian Institute of Science; 2009. Available from: http://etd.iisc.ac.in/handle/2005/554

Indian Institute of Science

15. Sonalikar, Hrishikesh Shashikant. Numerical Investigation of Segmented Electrode Designs for the Cylindrical Ion Trap and the Orbitrap Mass Analyzers.

Degree: PhD, Faculty of Engineering, 2018, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/3075

► 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… (more)

▼ 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,… Advisors/Committee Members: Mohanty, A K (advisor).

Subjects/Keywords: Quadrupole Ion Trap Mass Analyzer; Cylindrical Ion Trap Mass Analyzer; Orbitrap Mass Analyzer; Segmented Electrode Orbitraps; Segmented Electrode Cylindrical Ion Traps; Segmented Planar Orbitraps; Quadrupole Ion Trap (QIT); Boundary Element Methods (BEM); Cylindrical Ion Trap (CIT); Orbitrap; Paul Trap; Instrumentation

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Sonalikar, H. S. (2018). Numerical Investigation of Segmented Electrode Designs for the Cylindrical Ion Trap and the Orbitrap Mass Analyzers. (Doctoral Dissertation). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/3075

Chicago Manual of Style (16^th Edition):

Sonalikar, Hrishikesh Shashikant. “Numerical Investigation of Segmented Electrode Designs for the Cylindrical Ion Trap and the Orbitrap Mass Analyzers.” 2018. Doctoral Dissertation, Indian Institute of Science. Accessed March 08, 2021. http://etd.iisc.ac.in/handle/2005/3075.

MLA Handbook (7^th Edition):

Sonalikar, Hrishikesh Shashikant. “Numerical Investigation of Segmented Electrode Designs for the Cylindrical Ion Trap and the Orbitrap Mass Analyzers.” 2018. Web. 08 Mar 2021.

Vancouver:

Sonalikar HS. Numerical Investigation of Segmented Electrode Designs for the Cylindrical Ion Trap and the Orbitrap Mass Analyzers. [Internet] [Doctoral dissertation]. Indian Institute of Science; 2018. [cited 2021 Mar 08]. Available from: http://etd.iisc.ac.in/handle/2005/3075.

Council of Science Editors:

Sonalikar HS. Numerical Investigation of Segmented Electrode Designs for the Cylindrical Ion Trap and the Orbitrap Mass Analyzers. [Doctoral Dissertation]. Indian Institute of Science; 2018. Available from: http://etd.iisc.ac.in/handle/2005/3075

Indian Institute of Science

16. Marathe, Amol. A Study Of Four Nonlinear Systems With Parametric Forcing.

Degree: PhD, Faculty of Engineering, 2010, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/695

► This thesis considers four nonlinear systems with parametric forcing. The first problem involves an inverted pendulum with asymmetric elastic restraints subjected to harmonic vertical base… (more)

▼ This thesis considers four nonlinear systems with parametric forcing. The first problem involves an inverted pendulum with asymmetric elastic restraints subjected to harmonic vertical base excitation. On linearizing trigonometric terms the pendulum is governed by an asymmetric Mathieu equation. Solutions to this equation are scaleable. The stability regions in the parameter plane are studied numerically. Periodic solutions at the boundaries of stable regions in the parameter plane are found numerically and then their existence is proved theoretically. The second problem involves use of the method of multiple scales to elucidate the dynamics associated with early and delayed ejection of ions from Paul traps. A slow flow equation is developed to approximate the solution of a weakly nonlinear Mathieu equation to describe ion dynamics in the neighborhood of the nominal stability boundary of ideal traps. Since the solution to the unperturbed equation involves linearly growing terms, some care in identification and elimination of secular terms is needed. Due to analytical difficulties, harmonic balance approximations are used within the formal implementation of the method. The third problem involves the attenuation, caused by weak damping, of harmonic waves through a discrete, periodic structure with wave frequency nominally within the Propagation Zone. Adapting the transfer matrix method and using the harmonic balance for nonlinear terms, a four-dimensional map governing the dynamics is obtained. This map is analyzed by applying the method of multiple scales upto first order. The resulting slow evolution equations give the amplitude decay rate in the structure. The fourth problem involves the dynamic response of a strongly nonlinear single-degree-of-freedom oscillator under a constant amplitude, parametric, periodic, impulsive forcing, e.g., a pendulum with strongly nonlinear torsional spring that is periodically struck in the axial direction. Single-term harmonic balance gives an approximate, but explicit, 2-dimensional map governing the dynamics. The map exhibits many fixed points (both stable and unstable), higher period orbits, transverse intersections of stable and unstable manifolds of unstable fixed points, and chaos. Advisors/Committee Members: Chatterjee, Anindya (advisor).

Subjects/Keywords: Non-linear Systems; Vibrations (Machine Engineering); Ion Dynamics; Paul Traps; Wave Attenuation; Nonlinear Oscillator; Nonlinear Dynamics; Nonlinear Mathieu Equations; Parametric Forcing; Asymmetric Mathieu Equations; Machine Engineering

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Marathe, A. (2010). A Study Of Four Nonlinear Systems With Parametric Forcing. (Doctoral Dissertation). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/695

Chicago Manual of Style (16^th Edition):

Marathe, Amol. “A Study Of Four Nonlinear Systems With Parametric Forcing.” 2010. Doctoral Dissertation, Indian Institute of Science. Accessed March 08, 2021. http://etd.iisc.ac.in/handle/2005/695.

MLA Handbook (7^th Edition):

Marathe, Amol. “A Study Of Four Nonlinear Systems With Parametric Forcing.” 2010. Web. 08 Mar 2021.

Vancouver:

Marathe A. A Study Of Four Nonlinear Systems With Parametric Forcing. [Internet] [Doctoral dissertation]. Indian Institute of Science; 2010. [cited 2021 Mar 08]. Available from: http://etd.iisc.ac.in/handle/2005/695.

Council of Science Editors:

Marathe A. A Study Of Four Nonlinear Systems With Parametric Forcing. [Doctoral Dissertation]. Indian Institute of Science; 2010. Available from: http://etd.iisc.ac.in/handle/2005/695

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