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<p>  </p> <p>Electron emission plays a vital role in many modern technologies, from plasma medicine to heavy ion beams for fusion. An accurate theoretical model based upon the physics involved is critical to efficient operation of devices pushing the boundaries of complexity. The interactions between different electron emission mechanisms can severely alter device performance, especially when operating in extreme conditions. This dissertation studies electron emission from the perspectives of increasing geometric and physical mechanism complexities </p> <p>One half of this dissertation derives new relations for space-charge limited emission (SCLE) in non-planar geometries. SCLE is the maximum stable current that may be produced by electron emission before the electric field of the electrons themselves self-limits further emission. In planar devices, this is modeled by the well-established Child-Langmuir (CL) equation. The Langmuir-Blodgett (LB) equations remain the most commonly accepted theory for SCLE for cylindrical and spherical geometries after nearly a century; however, they suffer from being approximations based on a polynomial series expansion fit to a nonlinear differential equation. I derive exact, fully analytic equations for these geometries by using variational calculus to transform the differential equation into a new form that is fully and exactly solvable. This variational approach may be extended to any geometry and offers a full description of the electric field, velocity, and charge density profiles in the diode. </p> <p>SCLE is also an important mechanism for characterizing the operation of devices with an external magnetic field orthogonal to the electric field. This “crossed-field” problem decreases the limiting current as electrons travel longer, curved paths, effectively storing some charge in the gap (moving parallel to the emitter). At a critical magnetic field called the Hull cutoff, electron paths become so tightly curved that the circuit can no longer be completed, a condition called magnetic insulation. Crossed-field SCLE has been accurately modeled in planar devices by Lau and Christenson. Using the variational approach, I replicate their planar results and extend the calculation to cylindrical geometry, a common choice for magnetron devices. Further, I derive additional equations with simplified assumptions that, for the first time, provide an analytic description of experimental results below the Hull cutoff field. Following this I incorporate a series resistor: device resistance (or impedance) changes non-linearly with current and voltage, so I couple Ohm’s Law (OL) to all the models of crossed-field devices. For devices just below the Hull cutoff, I predict analytically and show in simulation novel bi-modal behavior, oscillating between magnetically insulated and non-insulated modes. With crossed-field device assessment, the variational calculus approach to space-charge may be used for numerous applications, including high power microwave sources, relativistic klystron devices, heavy ion beams, Hall thrusters, and plasma processing. </p> <p>The other half of this dissertation derives analytic theories to solve for emission current with three or more electron emission mechanisms simultaneously. In addition to the CL law, SCLE may also occur in neutral, non-vacuum diodes, modeled by the Mott-Gurney (MG) equation. These are the two limiting mechanisms I study; the other major modality of electron emission is direct electron production, the source of current in the device. Electrons are ejected when impelled by high temperature or electric field at the emission surface. These mechanisms are thermionic (or thermal) emission, modeled by the Richardson-Laue-Dushman (RLD) equation, and field emission, modeled by the Fowler-Nordheim (FN) equation, respectively. Additionally, just as I calculated the impedance of devices operating in a crossed-field configuration, all these models can be similarly coupled to OL. I derive models unifying FN, MG, and CL (with an extension linking OL, mentoring an undergraduate) and RLD, FN, and CL. These models are relevant for modern device design, especially as micro- and nano-scale devices seek to eliminate vacuum requirements and as space and military applications require higher temperature tolerances.</p> <p>While multi-physics models, like the ones described above, are important, the single-physics models (FN, RLD, MG, CL, OL) are still valid (and much easier to use) in their respective asymptotic limits. For example, a circuit behaves purely according to OL for very high resistances, according to MG for very high pressures, and so forth. Importantly, when devices operate in transition regions between these asymptotic limits, <em>none </em>of the asymptotic equations match the predictions of multi-physics models. Yet, intersections between the asymptotic equations are easily found, say for a certain set of voltage, gap distance, and pressure, CL=MG. Since both asymptotic equations give the same prediction, we may conclude that both must be inaccurate for those physical parameters! This gives rise to what I term “nexus theory:” solving two or more asymptotic equations simultaneously to rapidly and accurately predict sets of physical parameters at which multi-physics models (specifically, the physics leading to the “nexus point” parameters, points or curves at which nexus conditions are satisfied) are required for accurate device predictions. In fact, I show that multi-physics models are necessary within roughly one to two orders of magnitude from a nexus. In effect, nexus theory provides a simple, powerful tool to determine how complex a model is necessary for a particular device. Both nexus theory and multi-physics results in this dissertation have been successfully used to design devices to operate in specific transition regimes and identify the resulting device behavior.  </p>

<p dir="ltr">Understanding the acceleration of particles responsible for high-energy non-thermal phenomena in astrophysical jets is a ubiquitous pursuit. A possible culprit for non-thermal particle acceleration is turbulence. Specifically in this thesis, I investigate highly magne- tized or relativistic turbulence, where the magnetic energy to enthalpy ratio of the plasma is much greater than one, as a possible high-energy accelerator inside relativistic jets. I do this through three distinct projects. </p><p dir="ltr">My first project [1] (discussed in Section 3) was built upon a recent study of relativistic turbulence from [2], which found that a non-thermal particle equilibrium can be achieved when a plasma is heated via turbulence but allowed to cool radiatively. I extrapolated these results from PIC (Particle-in-Cell) simulations to larger scales and magnetizations, allowing me to encode key microphysical results of PIC simulations into a Fokker-Planck formalism. Combining these results with a single zone model for a blazar jet, I successfully define the underlying particle distribution with the global parameters of the emission region. To test this model, I fit data from 12 sources and successfully constrain key blazar parameters such as magnetization, bulk Lorentz factor, emission region size, and distance from the central engine. </p><p dir="ltr">My second project covers the development and testing of the open-source toolkit Tleco. This code base was used to evolve the Fokker-Planck equation and solve the resultant emission in my first project. Tleco offers efficient algorithms for evolving particle distributions and solving the resultant emission. It is meant to be user-friendly and easily customizable. </p><p dir="ltr">My third project attempts to enhance our understanding of coherent structures in relativistic turbulence. I employ intermittency analysis to establish a link between statistical fluctuations within the plasma and regions of high-energy dissipation. To achieve this, we used first-principle turbulent PIC simulations across a range of magnetizations and fluctuating magnetic field values. By utilizing the statistical fluctuations to determine the fractal dimension of the structures, I then examine their filling fraction and its dependence on magnetization and the fluctuating magnetic field.</p>

An artificially structured boundary (ASB) produces a short-range, static electromagnetic field that can reflect charged particles. In the work presented, an ASB is considered to consist of a spatially periodic arrangement of electrostatically plugged magnetic cusps. When used to create an enclosed volume, an ASB may confine a non-neutral plasma that is effectively free of applied electromagnetic fields, provided the spatial period of the ASB-applied field is much smaller than any one dimension of the confinement volume. As envisioned, a non-neutral positron plasma could be confined by an ASB along its edge, and the space-charge of the positron plasma would serve to confine an antiproton plasma. If the conditions of the two-species plasma are suitable, production of antihydrogen via three-body recombination for antimatter gravity studies may be possible. A classical trajectory Monte Carlo (CTMC) simulation suite has been developed in C++ to efficiently simulate charged particle interactions with user defined electromagnetic fields. The code has been used to explore several ASB configurations, and a concept for a cylindrically symmetric ASB trap that employs a picket-fence magnetic field has been developed. Particle-in-cell (PIC) modeling has been utilized to investigate the confinement of non-neutral and partially neutralized positron plasmas in the trap.

In this thesis examples of translationally invariant one-dimensional (1D) Vlasov-Maxwell (VM) equilibria are investigated. The 1D VM equilibrium equations are equivalent to the motion of a pseudoparticle in a conservative pseudopotential, with the pseudopotential being proportional to one of the diagonal components of the plasma pressure tensor. A necessary condition on the pseudopotential (plasma pressure) to allow for force-free 1D VM equilibria is formulated. It is shown that linear force-free 1D VM solutions correspond to the case where the pseudopotential is an attractive central potential. The pseudopotential for the force-free Harris sheet is found and a Fourier transform method is used to find the corresponding distribution function. The solution is extended to include a family of equilibria that describe the transition between the Harris sheet and the force-free Harris sheet. These equilibria are used in 2.5D particle-in-cell simulations of magnetic reconnection. The structure of the diffusion region is compared for simulations starting from anti-parallel magnetic field configurations with different strengths of guide field and self-consistent linear and non-linear force-free magnetic fields. It is shown that gradients of off-diagonal components of the electron pressure tensor are the dominant terms that give rise to the reconnection electric field. The typical scale length of the electron pressure tensor components in the weak guide field case is of the order of the electron bounce widths in a field reversal. In the strong guide field case the scale length reduces to the electron Larmor radius in the guide magnetic field.

Le concept de fusion par confinement inertiel (FCI) est aujourd'hui largement étudié. Il s'agit de comprimer et chauffer brièvement une petite capsule sphérique remplie de combustible, à l'aide de lasers extrêmement énergétiques. Depuis une quinzaine d'année, la technique d'allumage rapide (AR) propose de faciliter le chauffage de ce combustible en ajoutant un faisceau de particules - des électrons générés par un laser ultra-intense - au moment exact où la compression de la capsule est maximale. La présente thèse constitue une étude expérimentale de ces faisceaux d'électrons générés par lasers picosecondes. Nous présentons des nouveaux résultats sur les caractéristiques de ces électrons après leur accélération par laser (énergie, divergence, etc.) ainsi que sur leur interaction avec la matière qu'ils traversent, qu'elle soit solide ou comprimée. Les résultats expérimentaux exposés révèlent différentes facettes de ces électrons rapides créés par laser, et leur analyse nous a permis de progresser dans la compréhension de certains mécanismes : comment ils sont injectés à l'intérieur de la matière solide, comment mesurer leur divergence, et comment ils peuvent être automatiquement collimatés à l'intérieur de la matière comprimée.

Le travail présenté a trait à la modélisation et à la simulation numérique des phénomènes physiques qui régissent le régime de préarc dans les fusibles. Le problème thermique est formulé en enthalpie pour décrire les différents états physiques du fusible et le problème électrique permet de décrire les grandeurs électriques et le terme source. Ce modèle prend en compte la dépendance des coefficients de transport avec la température. Les résultats du modèle 2D montrent que la durée du préarc est influencé par les paramètres du circuit et par la géométrie des sections réduites. Lorsque le fusible est soumis aux forts courants de défaut les échanges thermiques dans la lame deviennent négligeables, le temps de préarc est obtenu à partir d'un coefficient empirique utilisé par les industriels le coefficient de Meyer. La modélisation 3D a permis la validation des résultats obtenus avec lame d'argent en 2D et la modélisation des échanges thermiques entre la lame et le milieux poreux. Ces échanges thermiques (conduction et rayonnement) sont mis en évidence sous forme de conditions aux limites d'une part et d'autre part par une méthode d'homogénéisation des grandeurs du milieux poreux basé sur une valeur typique de la porosité

One of the most conspicuous problems in space physics for the last decades has been to theoretically describe how the large parallel electric fields on auroral field lines can be generated. There is strong observational evidence of such electric fields, and stationary theory supports the need for electric fields accelerating electrons to the ionosphere where they generate auroras. However, dynamic models have not been able to reproduce these electric fields. This thesis sheds some light on this incompatibility and shows that the missing ingredient in previous dynamic models is a correct description of the electron temperature. As the electrons accelerate towards the ionosphere, their velocity along the magnetic field line will increase. In the converging magnetic field lines, the mirror force will convert much of the parallel velocity into perpendicular velocity. The result of the acceleration and mirroring will be a velocity distribution with a significantly higher temperature in the auroral acceleration region than above. The enhanced temperature corresponds to strong electron pressure gradients that balance the parallel electric fields. Thus, in regions with electron acceleration along converging magnetic field lines, the electron temperature increase is a fundamental process and must be included in any model that aims to describe the build up of parallel electric fields. The development of such a model has been hampered by the difficulty to describe the temperature variation. This thesis shows that a local equation of state cannot be used, but the electron temperature variations must be descibed as a nonlocal response to the state of the auroral flux tube. The nonlocal response can be accomplished by the particle-fluid model presented in this thesis. This new dynamic model is a combination of a fluid model and a Particle-In-Cell (PIC) model and results in large parallel electric fields consistent with in-situ observations.

La réduction fluide des équations cinétiques est un procédé couramment utilisé en physique des plasmas qui a pour objectif de remplacer la fonction de distribution définie dans l'espace des phases par des grandeurs fluides comme la densité et la pression. Cette réduction diminue la complexité du système initial. En contrepartie, la réduction fluide s'accompagne de la nécessité d'effectuer une fermeture sur les moments d'ordre supérieur. Celle-ci est souvent construite ad hoc en se basant sur des arguments physiques (e.g., quantités conservées, existance d'un théorème H, ...). Dans ce manuscrit, on propose un procédé de réduction qui permet de préserver la structure hamiltonienne du modèle cinétique parent. Ceci est important pour assurer qu'aucune dissipation d'origine non physique est introduite dans le modèle fluide, le munissant ainsi d'une structure hamiltonienne dont l'origine peut être suivie jusqu'à celle de la dynamique microscopique des particules. On utilise cette méthode pour construire des modèles fluides non-adiabatiques pour les trois premiers moments de la fonction de distribution associée à l'équation de Vlasov-Poisson à une dimension, i.e., la densité, la vitesse fluide et la pression. Les résultats sont ensuite étendus pour inclure la dynamique du flux de chaleur en considérant des fermetures construites à partir de l'analyse dimensionnelle. On montre également, pour un nombre arbitraire de champs, la relation existant avec le modèle water-bags. L'extension à des dimensions supérieures est étudiée dans le cadre de l'équation drift-cinétique ainsi que de l'équation de Vlasov-Poisson à trois dimensions. / Fluid reduction of kinetic equations is a ubiquitous procedure in plasma physics which aims to replace the distribution function defined in phase space with more concrete fluid quantities defined solely in configuration space such as the density, the fluid velocity and the pressure. This reduction lowers the complexity of the initial system, leading to a gain of physical insight into the phenomena under investigation as well as a significant decrease of the cost of numerical simulations. On the other hand, in order for the fluid reduction to be complete, one needs to perform a closure on the higher order fluid moments. The choice of the closure usually relies on some ad hoc physical arguments (e.g., conserved quantities, existence of an H-theorem, ...). In this manuscript, we present a reduction procedure that preserves the Hamiltonian structure of the parent kinetic model. This is important in order to ensure that no non-physical dissipation is introduced in the resulting fluid model, providing it with a geometric structure that can be traced back to the microscopic dynamics of the particles. We use this procedure to derive non-adiabatic fluid models for the first three fluid moments of the distribution function of the one dimensional Vlasov-Poisson equation, namely the density, the fluid velocity and the pressure. The results are extended to include the dynamics of the heat-flux by considering a closure based on dimensional analysis. For an arbitrary number of fields, we demonstrate the relationship with the water-bags model. Finally, the extension to higher dimensions is investigated through the drift-kinetic equation and the three dimensional Vlasov-Poisson equation.

L'interaction onde-particule dans les plasma est un sujet de recherche important, pour la compréhension des phénomènes physiques fondamentaux comme pour l'opération de réacteurs à fusion tels que les tokamaks. Cette intéraction peut être responsable de l'existence de modes instables, comme l'instabilité "fishbone" dans les plasmas de tokamak. Celle-ci est causée par l'interaction résonante entre un mode vivant dans la plasma et une population de particules supra-thermiques. Cette instabilité cause l'éjection d'une partie de ces particules énergétiques. Elle est par ailleurs caractérisée par une diminution de sa fréquence durant son évolution. Dans cette thèse, un modèle pour l'instabilité "fishbone", décrivant le plasma thérmique avec un traitement fluide et les particlules énergétiques avec un traitement cinétique, est développé. Ce modèle est simplifié de manière à permettre la compréhension des mécanismes les plus basiques qui causent la destabilisation du mode, sa diminution en fréquence durant son évolution ainsi que l'éjection de particules qu'il engendre. La théorie linéaire de ce modèle est faite, montrant les conditions qui permettent l'existence de l'instabilité, et permettant la caractérisation de son comportement linéaire. Les résultats analytiques sont ensuite comparés aux résultats linéaires numériques, obtenus grâce à un code développé durant cette thèse et basé sur les hypothèses du modèle, et ils sont en accord. Enfin, ce code est utilisé pour explorer le comportement non linéaire des particules énergétiques. Le mécanisme principalement responsable du changement de fréquence du mode ainsi que de l'éjection des particules est identifié et étudié en detail. / The wave-particle interaction in plasmas is an important research subject, for fundamental physical understanding as well as for the operation of fusion devices such as tokamaks. This interaction can cause the existence of unstable modes, such as the fishbone instability that is observed in tokamak plasmas. It results from the resonant interaction between an electro-magnetic wave living in the plasma and a population of supra-thermal particles. This mode causes the ejection of a portion of these energetic particles, and is thus detrimental to the confinment of energy in a tokamak, and it is characterized by a frequency down-chirping, i.e. a decrease of frequency of the mode during its evolution. In this thesis, a model for the fishbone instability is developed, that describes the thermal plasma with fluid equations and the supra-thermal particles with the kinetic Vlasov equation. This model is highly simplified in order to understand the basic mechanisms leading to destabilization, frequency chirping, and particle ejection. The linear theory of this model is then done, showing the conditions that lead to the existence of an instability, and that allow the characterization of its linear behavior. The linear analytic results are then compared to numerical linear results obtained with a code, based on the assumptions of the model, that was developed during this PhD and the results are found to be in good agreement. Finally, the code is used to explore the nonlinear behavior of energetic particles in the later phase of the fishbone instability. The main mechanism responsible for the frequency chirping and energetic particle ejection is identified and studied in detail.