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Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1991. / Vita. Abstract. Includes bibliographical references (leaves 101-102). Also available via the Internet.

Thesis (Ph. D.)--University of Texas at Austin, 2004. / Supervisors: Bill Drummond and Frank Waelbroeck. Vita. Includes bibliographical references. Also available from UMI.

The effects of time-dependent electron density fluctuations on a synthesized time domain reflectometry response of a one-dimensional cold plasma sheath are considered. Numerical solutions of the Helmholtz wave equation, which describes the electric field of a normally incident plane wave in a specified static electron density profile, are used. Included in this work is a study of the effects of Doppler shifts resulting from moving density fluctuations in the electron density profile of the sheath. / Master of Science

A numerical study is done of a plasma in contact with a cold solid surface that is emitting a neutral gas. Two numerical models have been developed to describe the dominant phenomena of surface plasma structures. The first model entails a steady-state, kinetic treatment of the transport equations in one space dimension and one velocity dimension, to determine self-consistently the distribution functions of the interacting species and the electrostatic potential near the solid surface. The dominant phenomena in this region are the ionization of the neutral gas and the acceleration of the resulting ions by the electrostatic field in a pre-sheath region. Other effects involved are a Debye sheath structure between the solid surface and pre-sheath, and collisional trapping and untrapping of electrons in an electrostatic potential well that is predicted in the pre-sheath region. Results are presented from a nondimensional model with a monatomic returning neutral species and for diatomic molecular hydrogen returning from the surface. For each set of physical parameters chosen, a one parameter family of solutions is obtained. The second numerical model involves a steady-state treatment of the transport equations in a (x,v∥,v⊥) phase space for the interacting species. Included in this model are ionization of the refluxing monatomic neutrals, a self-consistently determined electrostatic potential and a nonlinear Fokker-Planck treatment of ion-ion Coulomb collisions. Both the region near the surface dominated by kinetic effects and the region away from the surface in which Coulomb collisional effects are significant are treated. Results are presented which identify the correct physical solution for the region near the surface from the permitted family found with the kinetic model. Additionally, results are shown which span a temperature range from the high temperature kinetic regime where Coulomb collisional effects are negligible, to the low temperature, highly collisional fluid regime. At low temperatures the collisional model agrees well with standard fluid techniques.

When plasmas come in contact with the boundaries that confine them, various complex processes occur between the plasma and the materials in the boundary. These processes, called plasma-material interactions (PMI) lead to physical and chemical modifications in the materials and in the plasma. In the case of a tokamak, a magnetic confinement fusion reactor, the interactions between the plasma and the material in the bounding walls can negatively impact the performance and service life of the reactor. Furthermore, PMI are also found in other areas of significant engineering interest, such as plasma-based spacecraft propulsion engines, where interactions affect the transport properties of the plasma and consequently the performance of the engine. Therefore, gaining a fundamental understanding of the various plasma-material interactions is necessary for the development and improvement of these devices. PMI are dictated by the plasma sheath, a layer of net positive charge that forms at the plasma-boundary interface. The sheath regulates the energy and particle fluxes to the boundary, mediating the interactions. Sheaths, however, are only stable and well-developed when the ions enter the sheath with a speed equal to or greater than the `Bohm speed'. The Bohm speed is a landmark result in sheath theory and various mathematical expressions for it have been derived from fluid and kinetic treatment of plasmas. Although these models are widely used, they are only accurate in cases where the thickness of the sheath is negligible when compared to the scale length of the plasma in consideration. These cases are said to satisfy the `asymptotic limit'. To resolve this, a new Bohm speed model that considers the effects of transport terms such as the electron heat flux, thermal force, and temperature isotropization has been recently proposed [Y. Li et al., Physical Review Letters (2022)]. The model is verified using particle-in-cell (PIC) kinetic simulations and is shown to accurately predict the Bohm speed in cases away from the asymptotic limit. This thesis investigates the new model using the continuum kinetic approach on the Gkeyll software framework. The continuum kinetic approach numerically solves the Vlasov-Maxwell equations using the discontinuous Galerkin method and captures the kinetic phenomena of the plasma without needing to track individual particles. Multiple collisional cases ranging from a Knudsen number of 20 to 5000 are considered in a 1X3V simulation domain using the Lenard-Bernstein collisional operator. The results of the continuum kinetic simulations are benchmarked to the PIC simulation results. It is concluded that across a wide range of collisionalities, the continuum kinetic method captures much of the same physics as the PIC method while offering noise-free results. However, there is a discrepancy between the Bohm speed prediction and the simulation results in the continuum kinetic case. This discrepancy is explored and significant error in the collisional integral derived transport terms between the continuum kinetic method and PIC method is found, suggesting that the difference in collisional operator may be the source of the discrepancy. Nevertheless, the sheath profiles developed in the PIC simulations and the continuum kinetic simulations are in reasonable agreement. / Master of Science / Nuclear fusion is a process in which two light atomic nuclei (like hydrogen) fuse to form a heavier nucleus (like helium) and release tremendous amounts of energy. The resultant energy from these reactions powers the sun and has the potential to provide clean energy for our terrestrial needs. Harnessing fusion energy has been one of the biggest scientific and engineering challenges of our time due to various reasons. One of these reasons is the interaction of plasma, which is the fuel for the fusion reaction, and the materials of the walls that bound the plasma. These interactions are called plasma-material interactions (PMI) and can affect the longevity and performance of fusion reactors. The main governing phenomenon behind these interactions is the plasma sheath, a layer of plasma that is formed when the plasma encounters a boundary. For a sheath to form it is also necessary that ions in the plasma possess a speed greater than the so-called `Bohm speed'. While many expressions have been derived for the Bohm speed, these expressions are only valid when there is a clear sheath entrance that divides the bulk plasma and the sheath. This condition is not satisfied in many cases of interest. Instead, a sheath-transition region is found to exist between the bulk plasma and the sheath. A recently proposed Bohm speed model [Y. Li et al., Physical Review Letters (2022)] resolves this. This model is accurate in cases where the sheath-transition region exists and is derived by considering previously overlooked transport physics. In this work, this new model is studied using a different computational approach known as `continuum kinetics' using an open-source solver called Gkeyll. The results of the continuum kinetic simulations are compared to the results used to verify the model.

Space-charge effects play a dominant role in many areas of physics. In high-power microwave devices using high-current, relativistic electron beams, it places a limit on the amount of radiation a device can produce. Because the beam's space-charge can actually reflect a portion of the beam, the ability to accurately predict the amount of current a device can carry is needed. This current value is known as the space-charge limited current. Because of the mathematical difficulties, this limit is typically estimated from a one-dimensional theory. This work presents a two-dimensional theory for calculating an upper-bound for the space-charge limited current of relativistic electron beams propagating in grounded coaxial drift tubes. Applicable to annular beams of arbitrary radius and thickness, the theory includes the effect introduced by a finite-length drift tube of circular cross-section. Using Green's second identity, the need to solve Poisson's equation is transferred to solving a Sturm-Liouville eigenvalue problem, which is easily solved by elementary methods. In general, the resulting eigenvalue, which is required to estimate the limiting current, must be numerically determined. However, analytic expressions can be found for frequently encountered limiting cases. Space-charge effects also produce the fundamental collective behavior found in plasmas, especially in plasma sheaths. A plasma sheath is the transition region between a bulk plasma and an adjacent plasma-facing surface. The sheath controls the loss of particles from the plasma in order to maintain neutrality. Using a fully kinetic theory, the problem of a planar sheath with a single-minimum electric potential profile is investigated. Appropriate for single charge-state ions of arbitrary temperature, the theory includes the emission of warm electrons from the surface as well as a net current through the sheath and is compared to particle-in-cell simulations. Approximate expressions are developed for estimating the sheath potential as well as the transition to space-charge saturation. The case of a space-charge limited sheath is discussed and compared to the familiar Child-Langmuir law.

The inductively coupled plasma mass spectrometer (ICP-MS) has been used in laboratories for many years. The majority of the improvements to the instrument have been done empirically through trial and error. A few fluid models have been made, which have given a general description of the flow through the mass spectrometer interface. However, due to long mean free path effects and other factors, it is very difficult to simulate the flow details well enough to predict how changing the interface design will change the formation of the ion beam. Towards this end, Spencer et al. developed FENIX, a direct simulation Monte Carlo algorithm capable of modeling this transitional flow through the mass spectrometer interface, the transitional flow from disorganized plasma to focused ion beam. Their previous work describes how FENIX simulates the neutral ion flow. While understanding the argon flow is essential to understanding the ICP-MS, the true goal is to improve its analyte detection capabilities. In this work, we develop a model for adding analyte to FENIX and compare it to previously collected experimental data. We also calculate how much ambipolar fields, plasma sheaths, and electron-ion recombination affect the ion beam formation. We find that behind the sampling interface there is no evidence of turbulent mixing. The behavior of the analyte seems to be described simply by convection and diffusion. Also, ambipolar field effects are small and do not significantly affect ion beam formation between the sampler and skimmer cones. We also find that the plasma sheath that forms around the sampling cone does not significantly affect the analyte flow downstream from the skimmer. However, it does thermally insulate the electrons from the sampling cone, which reduces ion-electron recombination. We also develop a model for electron-ion recombination. By comparing it to experimental data, we find that significant amounts of electron-ion recombination occurs just downstream from the sampling interface.