In a wide variety of applications such as the Hall thruster and the tokamak, understanding the plasma-material interactions which take place at the wall is important for improving performance and preventing failure due to material degradation. In the region near a surface, the plasma sheath forms and regulates the electron and ion fluxes into the material. Emission from the material has the potential to change sheath structure drastically, and must be modeled rigorously to produce accurate predictions of the fluxes into the wall. Continuum kinetic codes offer significant advantages for the modeling of sheath physics, but the complexity of emission physics makes it difficult to implement accurately. This difficulty results in major simplifications which often neglect important energy-dependent physics. A focus of the work is on proper simulation of the sheath. The implementation of source and collision terms is discussed, alongside a brief study of the Weibel instability in the sheath demonstrating the necessity of proper collision implementation to avoid missing relevant physics. A novel implementation of semi-empirical models for electron-impact secondary electron emission into the boundary conditions of a continuum kinetic code is presented here. The features of both high and low energy regimes of emission are represented self-consistently, and the underlying algorithms are flexible and can be easily extended to other emission mechanisms, such as ion-impact secondary electron emission. The models are applied to simulations of oxidized and clean lithium for fusion-relevant plasma regimes. Oxidized lithium has a high emission coefficent and the sheath transitions into space-charge limited and inverse modes for different parameters. The breakdown of the classical sheath results in an increase of energy fluxes to the surface, with potential ramification for applications. / Doctor of Philosophy / Great advances are being made in a variety of promising applications of plasma physics, such as the development of spacecraft thrusters and fusion devices. Many of these devices constrain the flow of plasma within a material channel, leading degradation of the wall due to particle impact to be a serious concern for durability and lifespan. The plasma sheath is a region next to these material surfaces where ions are accelerated towards the wall, while electrons are repelled. As particles from the sheath impact the material, they cause the emission of secondary particles back into the sheath. This can drastically change the expected fluxes into the material and consequently the degradation expected to occur. Continuum kinetic simulations are a valuable tool for predicting and modeling the evolution of the sheath, but they are limited in their ability to rigorously do material emission physics by their inability to directly represent particle interactions with the surface. As such, past treatments of material emission in continuum kinetics tend to sacrifice valuable energy-dependent physics for simplified models.par To facilitate better understanding of the effects of emission on the sheath and the ramifications it might have for applications, the work here seeks to develop a framework for capturing the entire range of energy-dependent emission physics within a continuum kinetic framework. The implementation relies on semi-empirical models of beam emission data, focusing on simplicity and flexibility while still capturing the separate emission mechanisms which dominate in different energy regimes. The model is applied to simulations of lithium, an important material for fusion applications. Oxidized lithium has significantly enhanced emission properties over clean lithium, and is found to undergo a shift to non-monotonic sheath modes. The results show that the fundamental changes in the sheath structure due to the increased emission lead to greater energy fluxes into the surface. In this work, only secondary electron emission from the impact of electrons on a surface is examined. However, the underlying algorithms are easily extended to other energy-dependent energy mechanisms, such as ion-impact secondary electron emission.

Liquid metals (LMs) are compelling candidates for use as plasma facing components (PFCs) in fusion devices to mitigate heat loading, limit damage due to erosion, and possibly breed tritium. When used as electrodes, such as in z-pinch devices, PFCs are subject to large current and magnetic flux densities resulting in large Lorentz forces. Furthermore, if the PFCs are LM, the forces excite wave behavior that has not previously been investigated. The work presented here first characterizes the response of LMs to current pulses which peak between 50 and 200 kA and generate magnetic pressures between 0.5 and 5 MPa. High-speed videography records the liquid metal free surface during and after the current pulse and captures a fast moving, annular jet of LM emerging from the main body. The vertical velocities of the jet range from 0.6 to 5.3 m/s which is consistent with hydrodynamic predictions. Ejection of small droplets is observed from the LM immediately after the current pulse, preceding the LM jet, with velocities ranging from −3.1 to 18.9 m/s in the vertical direction and −14.3 to 6.3 m/s in the radial. A statistical model is developed to predict the likelihood of certain LM PFC material contaminating a core plasma and the severity in such an event. Lastly, effectiveness of bulk wave movement mitigation is investigated with two solid barrier designs, a cylindrical and conical baffle. These designs were fabricated after an iterative design process with assistance from hydrodynamic simulations. A cylindrical baffle design is shown to be preferable for integration into future fusion devices for the reduced likelihood of interference with plasma column formation. / Doctor of Philosophy / Liquid metals are considered for use as a coating on the interior surfaces in nuclear fusion reactors because they can remove heat, reduce damage, and generate additional fuel for the reactor. There has been very little research on what happens to the liquid metal when large amounts of electric current pass through it, as would be necessary in some designs. The work presented here first shows the liquid responds to large amounts of electric current with a fast moving, ring-shaped jet that correlates to the specific amount of current used. A theoretical relationship is used to relate the jet to hydrodynamic scenarios with solid bodies entering liquids. Small droplets are also observed sprayed from the LM earlier in time and the likelihood and severity of liquid metal contaminating the fusion core is analyzed. Finally, solid barriers are used to slow down the jet and minimize the mass it contains. To reduce the likelihood that the jet interferes with the fusion core, certain characteristics of barriers are identified as being preferable for use in plasma devices.

The plasma sheath is essential for understanding the plasma-material interaction (PMI) since it regulates the plasma particle and energy fluxes to the wall. The key concept in sheath theory is the Bohm criterion that gives the lower bound of the plasma exit flow speed, also known as the Bohm speed. Traditionally, the Bohm speed is evaluated in the asymptotic limit of an infinitely thin sheath and ignores the transport physics in the plasma-sheath transition problem. Whereas in practical applications, the sheath has a finite thickness and the transport in the neighborhood of the sheath entrance is complicated. The focus of this thesis is on performing Bohm speed analysis for different applications that are away from the asymptotic limits, with an emphasis on the critical role of transport physics on the Bohm speed formulation. The classical sheath problem with a wide range of Coulomb collisionality is revisited. Here, we derive an expression for the Bohm speed from a set of anisotropic plasma transport equations. The thermal force, temperature isotropization and heat flux enter into the eval- uation of the Bohm speed. Away from the asymptotic limit, it is shown that there exists a plasma-sheath transition region, rather than a single point at the sheath entrance. In the transition region, the quasineutrality is weakly perturbed and the Bohm speed is predicted for the entire transition region. By comparison with kinetic simulation results, the Bohm speed model in our work is shown to be accurate in the sheath transition region over a broad range of collisionality. The Bohm speed analysis developed above can be applied to plasma-sheath transition prob- lems with more complex transport physics, such as a high recycling divertor in a fusion reactor. In the high recycling regime, the plasma particles hitting on the divertor surface will be recycled through reflection or desorption and return to the plasma in the form of neutrals. The plasma will interact with the recycled neutrals through atomic collisions such as ionization, excitation, or ion charge-exchange collision, complicating the plasma transport in the transition layer. A new Bohm speed model is proposed to account for the effect of the anisotropic transport and atomic collisions in the transition layer. A first principle ki- netic code VPIC with the atomic collision package is used to investigate a 1D self-consistent slab plasma with a high recycling boundary for tungsten and carbon divertors. The results demonstrate the accuracy of the Bohm speed model in predicting the ion exit flow speed in the transition region, as well as the reduction of the Bohm speed due to the ion-neutral friction. / Doctor of Philosophy / Controlled thermal nuclear fusion is a promising candidate for future energy supply. In a fusion reactor, a vast amount of energy is created and confined in the main plasma, while the boundary plasma can carry a certain amount of energy from the main plasma and deposit it on the surface of the plasma-facing component (PFC) of the reactor. The edge plasma and the material surface are strongly coupled through the plasma-material interaction (PMI). It is widely understood that PMI is a critical issue in realizing controlled thermonuclear fusion. The PMI problem involves complex physics phenomena that cover a wide range of spatial and temporal scales, posing a significant challenge to its modeling. This work mainly focuses on physics at the intermediate scale, where sheath/presheath physics dominates. The plasma sheath is a thin, positively charged layer that forms in front of the material surface to equalize the electron and ion fluxes. In classical sheath theory, an idealized point, the sheath entrance, connects the quasineutral plasma and non-neutral sheath. The ions can be accelerated by the presheath electric field and reach the Bohm speed (equal to the sound speed in classical sheath theory) at the sheath entrance. That is the Bohm criterion, a necessary condition for a stable sheath to form. The plasma sheath in a fusion reactor is exposed to a complex environment where the atoms and molecules are abundant and can interact with the plasma inelastically. As a result, many assumptions made in the classical sheath theory may not be valid for practical applications, such as a divertor sheath. The classical sheath theory is derived in the asymptotic limit of an infinitely thin sheath. In a real plasma, a sheath transition layer, rather than a singular sheath entrance, exists, and it connects the plasma and sheath smoothly. In the transition region, the quasineutrality is weakly perturbed, and the plasma transport is significant. Previous evaluation of the Bohm speed invokes drastic simplification of the transport physics, resulting in a Bohm speed equal to the sound speed. Here, we propose a new Bohm speed model that considers the dominating transport phenomena-anisotropic transport and collisional transport. The Bohm speed analysis is performed in two cases:(i) a classical sheath problem with absorbing boundaries and (ii) a high recycling divertor where the plasma-neutral interaction is significant. In the first case, we extend the classical sheath analysis to a regime that is away from the asymptotic limit. The counterpart of important concepts in the two-scale analysis, such as the sheath entrance and Bohm speed, is established and well explained. The transport dependent Bohm speed model is derived from a set of anisotropic transport equations, where the heat flux, thermal force, and Coulomb collisional isotropization are considered. The model can predict the ion exit flow speed in the transition region over a broad range of Coulomb collisionality, as shown by comparison with the kinetic simulation results. The second case is more practical, where the Bohm speed analysis is performed at the edge of a fusion reactor. The plasma transport in the transition region is complicated by the plasma-neutral interactions. As a result, the Bohm speed model includes atomic collisions, such as ionization, excitation, and ion charge-exchange collision. Among all the collision processes, the ion charge-exchange collision has the most significant influence on the Bohm speed. It acts as a significant momentum sink for the ions and makes the Bohm speed subsonic in the transition region.

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.