Turbulence in the ionosphere is important to understand because it can negatively affect communication signals. This work examines different scenarios in the ionosphere in which turbulence may develop. The two main causes of turbulence considered in this work are the gradient drift instability (GDI) and the Kelvin-Helmholtz instability (KHI). The likelihood of the development of the GDI during the August 17, 2017 total solar eclipse is studied numerically. This analysis uses the ``Sami3 is Also a Model of the Ionosphere" (SAMI3) model to study the effect of the eclipse on the plasma density. The calculated GDI growth rates are small compared to how quickly the eclipse moves over the Earth. Therefore, the GDI is not expected to occur during the solar eclipse. A novel 2D electrostatic pseudo-spectral fluid model is developed to study the growth of these two instabilities and the problem of ionospheric turbulence in general. To focus on the ionospheric turbulence, a set of perturbed governing equations are derived. The model accurately captures the GDI growth rate in different limits; it is also benchmarked to the evolution of instability development in different collisional regimes of a plasma cloud. The newly developed model is used to study if the GDI is the cause of density irregularities observed in subauroral polarization streams (SAPS). Data from Global Positioning System (GPS) scintillations and the Super Dual Auroral Radar Network (SuperDARN) are used to examine the latitudinal density and velocity profiles of SAPS. It is found that the GDI is stabilized by velocity shear and therefore will only generate density irregularities in regions of low velocity shear. Furthermore, the density irregularities cannot extend through regions of large velocity shear. In certain cases, the turbulence cascade power laws match observation and theory. The transition between the KHI and the GDI is studied by understanding the effect of collisions. In low collisionality regimes, the KHI is the dominant instability. In high collisionality regimes, the GDI is the dominant instability. Using nominal ionospheric parameters, a prediction is provided that suggests that there exists an altitude in the upper textit{F} region ionosphere above which the turbulence is dominated by the KHI. / Doctor of Philosophy / In the modern day, all wireless communication signals use electromagnetic waves that propagate through the atmosphere. In the upper atmosphere, there exists a region called the ionosphere, which consists of plasma (a mixture of ions, electrons, and neutral particles). Because ions and electrons are charged particles, they interact with the electromagnetic communication signals. A better understanding of ionospheric turbulence will allow for aid in forecasting space weather as well as improve future communication equipment. Communication signals become distorted as they pass through turbulent regions of the ionosphere, which negatively affects the signal quality at the receiving end. For a tangible example, when Global Positioning System (GPS) signals pass through turbulent regions of the ionosphere, the resulting position estimate becomes worse. This work looks at two specific causes of ionospheric turbulence: the gradient drift instability (GDI) and the Kelvin-Helmholtz instability (KHI). Under the correct background conditions, these instabilities have the ability to generate ionospheric turbulence. To learn more about the GDI and the KHI, a novel simulation model is developed. The model uses a method of splitting the equations such that the focus is on just the development of the turbulence while considering spatially constant realistic background conditions. The model is shown to accurately represent results from previously studied problems in the ionosphere. This model is applied to an ionospheric phenomenon known as subauroral polarization streams (SAPS) to study the development of the GDI and the KHI. SAPS are regions of the ionosphere with large westward velocity that changes with latitude. The shape of the latitudinal velocity profile depends on many other factors in the ionosphere such as the geomagnetic conditions. It is found that for certain profiles, the GDI will form in SAPS with some of these examples matching observational data. At higher altitudes, the model predicts that the KHI will form instead. While the model is applied to just the development of the GDI and the KHI in this work, it is written in a general manner such that other causes of ionospheric turbulence can be easily studied in the future.

This last decade experienced a sudden increase of interest in the control of thermo-acoustic instabilities, in particular through the use of fuel modulation techniques. The primary goal of this research was to design, construct and characterize a high bandwidth proportional fuel injection system, which could be used to study the effect of specific levels of fuel modulation on the combustion process and the reduction of thermo-acoustic instabilities. A fuel injection system, incorporating the use of a closed loop piston and check valve, was designed to modulate the primary fuel supply of an atmospheric liquid-fueled swirl stabilized combustor operating at a mean volumetric fuel flow rate of 0.4 GPH. The ability of the fuel injection system to modulate the fuel was examined by measuring the fuel line pressure and the flow rate produced during operation. The authority of this modulation over the combustion process was investigated by examining the effect of fuel modulation on the combustor pressure and the heat release of the flame. Sinusoidal operation of the fuel injection system demonstrated: a bandwidth greater that 800 Hz, significant open loop authority (averaging 12 dB) with regards to the combustor pressure, significant open loop authority (averaging 33 dB) with regards to the unsteady heat release rate and an approximate 8 dB reduction of the combustor pressure oscillation present at 100 Hz, using a phase shift controller. It is possible to scale the closed loop piston and check valve configuration used to create the fuel injection system discussed in this work to realistic combustor operating conditions for further active combustion control studies. / Master of Science

In recent years, the discontinuous Galerkin (DG) method has been successfully applied to solving hyperbolic conservation laws. Due to its compactness, high order accuracy, and versatility, the DG method has been extensively applied to convection-diffusion problems. In this dissertation, a numerical package, texttt{PHORCE}, is introduced to solve a number of convection-diffusion problems in neutral fluids and plasmas. Unstructured grids are used in order to randomize grid errors, which is especially important for complex geometries. texttt{PHORCE} is written in texttt{C++} and fully parallelized using the texttt{MPI} library. Memory optimization has been considered in this work to achieve improved efficiency. DG algorithms for hyperbolic terms are well studied. However, an accurate and efficient diffusion solver still constitutes ongoing research, especially for a nodal representation of the discontinuous Galerkin (NDG) method. An affine reconstructed discontinuous Galerkin (aRDG) algorithm is developed in this work to solve the diffusive operator using an unstructured NDG method. Unlike other reconstructed/recovery algorithms, all computations can be performed on a reference domain, which promotes efficiency in computation and storage. In addition, to the best of the authors' knowledge, this is the first practical guideline that has been proposed for applying the reconstruction algorithm on a nodal discontinuous Galerkin method. TVB type and WENO type limiters are also studied to deal with numerical oscillations in regions with strong physical gradients in state variables. A high-order positivity-preserving limiter is also extended in this work to prevent negative densities and pressure. A new interface tracking method, mass of fluid (MOF), along with its bound limiter has been proposed in this work to compute the mass fractions of different fluids over time. Hydrodynamic models, such as Euler and Navier-Stokes equations, and plasma models, such as ideal-magnetohydrodynamics (MHD) and two-fluid plasma equations, are studied and benchmarked with various applications using this DG framework. Numerical computations of Rayleigh-Taylor instability growth with experimentally relevant parameters are performed using hydrodynamic and MHD models on planar and radially converging domains. Discussions of the suppression mechanisms of Rayleigh-Taylor instabilities due to magnetic fields, viscosity, resistivity, and thermal conductivity are also included. This work was partially supported by the US Department of Energy under grant number DE-SC0016515. The author acknowledges Advanced Research Computing at Virginia Tech for providing computational resources and technical support that have contributed to the results reported within this work. URL: http://www.arc.vt.edu / Doctor of Philosophy / High-energy density (HED) plasma science is an important area in studying astrophysical phenomena as well as laboratory phenomena such as those applicable to inertial confinement fusion (ICF). ICF plasmas undergo radial compression, with an aim of achieving fusion ignition, and are subject to a number of hydrodynamic instabilities that can significantly alter the implosion and prevent sufficient fusion reactions. An understanding of these instabilities and their mitigation mechanisms is important allow for a stable implosion in ICF experiments. This work aims to provide a high order accurate and robust numerical framework that can be used to study these instabilities through simulations. The first half of this work aims to provide a detailed description of the numerical framework, texttt{PHORCE}. texttt{PHORCE} is a high order numerical package that can be used in solving convection-diffusion problems in neutral fluids and plasmas. Outstanding challenges exist in simulating high energy density (HED) hydrodynamics, where very large gradients exist in density, temperature, and transport coefficients (such as viscosity), and numerical instabilities arise from these region if there is no intervention. These instabilities may lead to inaccurate results or cause simulations to fail, especially for high-order numerical methods. Substantial work has been done in texttt{PHORCE} to improve its robustness in dealing with numerical instabilities. This includes the implementation and design of several high-order limiters. An novel algorithm is also proposed in this work to solve the diffusion term accurately and efficiently, which further enriches the physics that texttt{PHORCE} can investigate. The second half of this work involves rigorous benchmarks and experimentally relevant simulations of hydrodynamic instabilities. Both advection and diffusion solvers are well verified through convergence studies. Hydrodynamic and plasma models implemented are also validated against results in existing literature. Rayleigh-Taylor instability growth with experimentally relevant parameters are performed on both planar and radially converging domains. Although this work is motivated by physics in HED hydrodynamics, the emphasis is placed on numerical models that are generally applicable across a wide variety of fields and disciplines.

A careful study of plasma-material interactions is essential to understand and improve the operation of devices where plasma contacts a wall such as plasma thrusters, fusion devices, spacecraft-environment interactions, to name a few. This work aims to advance our understanding of fundamental plasma processes pertaining to plasma-material interactions, sheath physics, and kinetic instabilities through theory and novel numerical simulations. Key contributions of this work include (i) novel continuum kinetic algorithms with novel boundary conditions that directly discretize the Vlasov/Boltzmann equation using the discontinuous Galerkin method, (ii) fundamental studies of plasma sheath physics with collisions, ionization, and physics-based wall emission, and (iii) theoretical and numerical studies of the linear growth and nonlinear saturation of the kinetic Weibel instability, including its role in plasma sheaths. The continuum kinetic algorithm has been shown to compare well with theoretical predictions of Landau damping of Langmuir waves and the two-stream instability. Benchmarks are also performed using the electromagnetic Weibel instability and excellent agreement is found between theory and simulation. The role of the electric field is significant during nonlinear saturation of the Weibel instability, something that was not noted in previous studies of the Weibel instability. For some plasma parameters, the electric field energy can approach magnitudes of the magnetic field energy during the nonlinear phase of the Weibel instability. A significant focus is put on understanding plasma sheath physics which is essential for studying plasma-material interactions. Initial simulations are performed using a baseline collisionless kinetic model to match classical sheath theory and the Bohm criterion. Following this, a collision operator and volumetric physics-based source terms are introduced and effects of heat flux are briefly discussed. Novel boundary conditions are developed and included in a general manner with the continuum kinetic algorithm for bounded plasma simulations. A physics-based wall emission model based on first principles from quantum mechanics is self-consistently implemented and demonstrated to significantly impact sheath physics. These are the first continuum kinetic simulations using self-consistent, wall emission boundary conditions with broad applicability across a variety of regimes. / Ph. D. / An understanding of plasma physics is vital for problems on a wide range of scales: from large astrophysical scales relevant to the formation of intergalactic magnetic fields, to scales relevant to solar wind and space weather, which poses a significant risk to Earth’s power grid, to design of fusion devices, which have the potential to meet terrestrial energy needs perpetually, and electric space propulsion for human deep space exploration. This work aims to further our fundamental understanding of plasma dynamics for applications with bounded plasmas. A comprehensive understanding of theory coupled with high-fidelity numerical simulations of fundamental plasma processes is necessary, this then can be used to improve improve the operation of plasma devices. There are two main thrusts of this work. The first thrust involves advancing the state-of-the-art in numerical modeling. Presently, numerical simulations in plasma physics are typically performed either using kinetic models such as particle-in-cell, where individual particles are tracked through a phase-space grid, or using fluid models, where reductions are performed from kinetic physics to arrive at continuum models that can be solved using well-developed numerical methods. The novelty of the numerical modeling is the ability to perform a complete kinetic calculation using a continuum description and evolving a complete distribution function in phase-space, thus resolving kinetic physics with continuum numerics. The second thrust, which is the main focus of this work, aims to advance our fundamental understanding of plasma-wall interactions as applicable to real engineering problems. The continuum kinetic numerical simulations are used to study plasma-material interactions and their effects on plasma sheaths. Plasma sheaths are regions of positive space charge formed everywhere that a plasma comes into contact with a solid surface; the charge inequality is created because mobile electrons can quickly exit the domain. A local electric field is self-consistently created which accelerates ions and retards electrons so the ion and electron fluxes are equalized. Even though sheath physics occurs on micro-scales, sheaths can have global consequences. The electric field accelerates ions towards the wall which can cause erosion of the material. Another consequence of plasma-wall interaction is the emission of electrons. Emitted electrons are accelerated back into the domain and can contribute to anomalous transport. The novel numerical method coupled with a unique implementation of electron emission from the wall is used to study plasma-wall interactions. While motivated by Hall thrusters, the applicability of the algorithms developed here extends to a number of other disciplines such as semiconductors, fusion research, and spacecraft-environment interactions.

Thermoacoustic instabilities are a problem in modern pre-mixed combustors causing reduced performance and leading in the extreme to combustor failure from excessive pressure cycles. Much work has been done using linear controllers to eliminate these instabilities. Many experimenters in the field have used pulsed and subharmonic fuel controllers to eliminate these instabilities, but very little investigative work has been done on these controllers. The goal of this work is to explain the mechanism of control behind pulsed controllers. It is shown that the combustion system can be treated as a linear system, thus meaning that frequency components of the control signal at the desired instability frequency are the dominant means of control, with nonlinear effects only serving to slightly reduce the gain necessary for control. Fourier analysis is thus performed on pulsed signals and the components analyzed, showing that there will indeed be a component of a pulsed signal at the frequency of the instability, aside from a few select cases. It is then proven that this frequency component is largely responsible for control of the thermoacoustic system using proportional height pulse train signals, which will change pulse height based on the amplitude of the instability. This analysis is then used to predict the height of instabilities resulting from the use of fixed height pulse control signals. Finally, numerical simulations and experimental observations support the analytical constructs. Acoustic control is mainly used for these experiments, although some preliminary work with liquid fuel controllers is also presented. / Master of Science

Lean premixed fuel-air conditions in large gas turbines are used to improve efficiency and reduce emissions. These conditions give rise to large undamped pressure oscillations at the combustor's natural frequencies which reduce the turbine's longevity and reliability. Active control of the pressure oscillations, called thermoacoustic instabilities, has been sought as passive abatement of these instabilities does not provide adequate damping and is often impractical on a large scale. Phase shift control of the instabilities is perhaps the simplest and most popular technique employed but often does not provide good performance in that controller induced secondary instabilities are generated with increasing loop gain. This thesis investigates the general underlying cause of the secondary instabilities and shows that high average group delay through the frequency region of the instability is the root of the problem. This average group delay is then shown to be due not only the controller itself but can also be associated with other components and inherent characteristics of the control loop such as actuators and time delay, respectively. An "optimum" phase shift controller, consisting of an appropriate shift in phase and a low order, wide bandwidth bandpass filter, is developed for a Rijke tube combustor and shown to closely match the response of an LQG controller designed only for system stabilization. Both the optimal phase shifter and the LQG controller are developed based on a modified model of the thermoacoustic loop which takes into account the change in density of the combustion reactants at the flame location. Additionally, the system model is coupled with a model of the control loop and then validated by comparison of simulated results to experimental results using nearly identical controllers. / Master of Science

<p>Theoretical studies of dusty plasmas have been performed by focusing attention principally on collective phenomena and on grain motion. This thesis consists of a collection of seven published papers that explore both the collective behavior of a complex plasma system as well as the dynamics of grains in plasmas. In paper 1, a mechanism that explains the energy gain which leads to the self excited grain oscillations is theoretically formulated. The newly developed mechanism explains the observed self excited oscillations through the coupling of plasma sheath fluctuations with the electrostatic force, which holds the dust grain. In paper 2, theoretical and simulation studies have been conducted to study the vertical oscillations of dust grains that are levitated in plasma sheaths, under low pressure conditions. The oscillations were driven either by an external force or by a plasma number density modulation. The proposed model gives a full picture of the dust grains dynamics and is capable of successfully explaining the experimental observations. Paper 3 explores both theoretically and numerically the origin of the nonlinearities that lead to the observed oscillation resonances. The feature of the confining potential well which traps the grain, the influence of an electrode voltage modulation on the trapping well, and hence on the grain dynamics, and the resulting nonlinear resonances are analyzed in detail. The numerical simulations presented successfully reproduce a broad range of dynamical phenomena, including the self excited oscillations, for a range of different parameters. Paper 4 is dedicated to the analysis of the propagation of Dust Acoustic Waves (DAW) in a medium with an equilibrium dust density distribution. It has been theoretically shown that only some harmonics of the dust density distribution will influence the propagation of the DAW, thus modifying its frequency. Paper 5 presents a theoretical and numerical analysis of the excitation of higher harmonics of electrostatic dust cyclotron waves. The instability is driven by the ion and electron currents flowing along the magnetic field. The dispersion relation and the wave instability conditions have been derived, and a detailed numerical analysis has been performed. In Paper 6, we explore theoretically some cross field instabilities of low frequency, long wavelength electrostatic modes in fully and weakly ionized plasmas. It is shown that in a magnetoplasma with a transverse equilibrium dc electric field, the energy associated with the cross field motion of the plasma particles can be coupled to low frequency electrostatic waves. Paper 7 explores the properties and instabilities of low frequency electrostatic waves propagating in a current carrying magnetoplasma with equilibrium density and field aligned ion flow with a transverse gradient. The paper contains previous results as limiting cases, together with additional instabilities related to the equilibrium plasma density distribution. </p>

Theoretical studies of dusty plasmas have been performed by focusing attention principally on collective phenomena and on grain motion. This thesis consists of a collection of seven published papers that explore both the collective behavior of a complex plasma system as well as the dynamics of grains in plasmas. In paper 1, a mechanism that explains the energy gain which leads to the self excited grain oscillations is theoretically formulated. The newly developed mechanism explains the observed self excited oscillations through the coupling of plasma sheath fluctuations with the electrostatic force, which holds the dust grain. In paper 2, theoretical and simulation studies have been conducted to study the vertical oscillations of dust grains that are levitated in plasma sheaths, under low pressure conditions. The oscillations were driven either by an external force or by a plasma number density modulation. The proposed model gives a full picture of the dust grains dynamics and is capable of successfully explaining the experimental observations. Paper 3 explores both theoretically and numerically the origin of the nonlinearities that lead to the observed oscillation resonances. The feature of the confining potential well which traps the grain, the influence of an electrode voltage modulation on the trapping well, and hence on the grain dynamics, and the resulting nonlinear resonances are analyzed in detail. The numerical simulations presented successfully reproduce a broad range of dynamical phenomena, including the self excited oscillations, for a range of different parameters. Paper 4 is dedicated to the analysis of the propagation of Dust Acoustic Waves (DAW) in a medium with an equilibrium dust density distribution. It has been theoretically shown that only some harmonics of the dust density distribution will influence the propagation of the DAW, thus modifying its frequency. Paper 5 presents a theoretical and numerical analysis of the excitation of higher harmonics of electrostatic dust cyclotron waves. The instability is driven by the ion and electron currents flowing along the magnetic field. The dispersion relation and the wave instability conditions have been derived, and a detailed numerical analysis has been performed. In Paper 6, we explore theoretically some cross field instabilities of low frequency, long wavelength electrostatic modes in fully and weakly ionized plasmas. It is shown that in a magnetoplasma with a transverse equilibrium dc electric field, the energy associated with the cross field motion of the plasma particles can be coupled to low frequency electrostatic waves. Paper 7 explores the properties and instabilities of low frequency electrostatic waves propagating in a current carrying magnetoplasma with equilibrium density and field aligned ion flow with a transverse gradient. The paper contains previous results as limiting cases, together with additional instabilities related to the equilibrium plasma density distribution.

The common observation that the onset of a core MARFE (edge localized, poloidally asymmetric, highly radiating region) is followed immediately by a High-to-Low confinement mode transition in DIII-D was investigated by comparing a theoretical prediction of the threshold non-radiative power across the separatrix needed to maintain H-mode with an experimental determination of the non-radiative power flowing across the separatrix. It was found that in three shots with continuous gas fueling that the increased neutral influx associated with the MARFE formation caused a sharp increase in the predicted threshold non-radiative power crossing the separatrix that was required for the plasma to remain in H-mode to a value comparable to the experimental power crossing the separatrix, indicating a theoretical prediction of a H-L transition in agreement with experimental observation.

The work of this thesis sets out to give a clearer in-depth understanding of the failure mechanics of thin-walled compression members which are associated with complex interactions between the different buckling modes during the loading process. This thesis employs the finite element method in order to examine the effect of the modelling techniques imposed at the section junctions of short struts and to investigate the influence of the local and global end conditions with regard to support and loading on the compressive response of various sections, i.e. I-sections, plain channel sections, box-sections, and lipped channel sections. The thesis also details appropriate finite element modelling strategies and solution procedures taking due account of the influence of material nonlinearity and geometrical imperfections for the determination of the coupled mode interactive response of thin-walled compression members. A detailed account of the complete loading history of the compression members from the beginning of loading through to final collapse is given in the thesis. This involves elastic local buckling, nonlinear elastic and elasto-plastic post-buckling interaction behaviour and yield propagation leading to the development of an appropriate failure mechanism which causes final collapse and unloading. A new finite element modelling strategy has been developed in the thesis with particular reference to being able to deal with the classical assumption of the stress-free in-plane boundary conditions existing at the section junctions of short length strut members during post-local buckling. Also, for fixed-ended columns, with particular reference to singly-symmetric plain channel sections, it has been shown that column deflections are initiated from the onset of local buckling for the case of the constituent plate elements of the section being locally rotationally constrained at their ends. Such columns should not therefore be considered as an overall bifurcation problem of the locally buckled member. In the case of the pinned and fixed-ended boundary conditions of the columns, the finite element simulations are shown to be able to accurately describe the rather different complex failure mechanics with a high degree of imperfection sensitivity being shown to be in evidence for the pin-ended case. Considerably good agreement has been shown to occur with the independent simulations of other researchers using the finite strip method of analysis, with the analytical solution procedures of others and with the findings from independent test work and this has provided confidence in the viability and usefulness of the modelling strategies and solution procedures developed in this thesis.