Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 157-163). Available also in a digital version from Dissertation Abstracts.

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Thesis (Ph. D.)--University of Texas at Austin, 2004. / Supervisor: Herbert L. Berk. Vita. Includes bibliographical references.

The mechanisms of acceleration and transport of collisionless plasma in the presence of electromagnetic turbulence (EMT) still remains not fully understood. The particle-EMT interaction can be modelled as the interaction of the particle with a particular wave in the presence of random noise. It has been shown that in such a model the acceleration of the charged particles can be almost free. This effect is known as resonance, which can be explained by the so-called “surfatron” mechanism. We have conducted several numerical simulations for the models with and without the presence of EMT. The turbulence has been modeled as small random fluctuations on the background magnetic field. Particles dynamics consist of two regimes of motion: (i) almost free (Larmor) rotation and (ii) captured (resonance) propagation, which are given by two different sets of invariants. We have determined the necessary conditions for capture and release from resonance for the model without fluctuations, as well as the intrinsic structure of the initial conditions domain for particles in order to be captured. We observed a difference in the orders of magnitude of the dispersion of adiabatic invariant due to the effects of the added fluctuations at the resonance. These results are important to describe the mixing of the different energy levels in the presence of EMT. To understand the impact of the EMT on the system dynamics, we have performed statistical analysis of the effects that different characteristics of the random fluctuations have on the system. The particles' energy gain can be viewed as a random walk over the energy levels, which can be described in terms of the diffusion partial differential equation for the probability distribution function. This problem can be reverse-engineered to understand the nature and structure of the EMT, knowing beforehand the energy distribution of a set of particles. / Mechanical Engineering

<p>Thermonuclear fusion is a promising energy source for the future. If an economically efficient thermonuclear reactor would be built it has to be a cheap, safe, and highly productive electric power plant, or, a heating plant.</p><p>The emphasis of this thesis is on the single cell mirror trap with a marginally stable minimum B vacuum magnetic field, the straight field line mirror field, which provides MHD stability of the system, absence of the radial drift even to the first order in plasma β , and a reduced magnetic flux tube ellipticity. Strong density depletion at the mirrors is proposed as a mean to build up a strong potential barrier for the electrons and thereby increase the electron temperature. Conditions to obtain an energy gain factor Q>10 are briefly analyzed. Current coils which could generate the derived magnetic field are proposed. A sloshing ion distribution function is constructed for the three dimensional ‘straight line mirror field’. The gyro centre Clebsch coordinates are found to be a new pair of motional invariants for this magnetic field. The gyro centre Clebsch coordinate invariants can be used to obtain complete solutions of the Vlasov equation, including the diamagnetic drift. These solutions show that the equilibria satisfy the locally omniginuity criterion to the first order in β .</p><p>Contributions of the plasma diamagnetism to the magnetic flux tube ellipticity are studied for the straight field line mirror vacuum magnetic field and a sloshing ion distribution. Computations employing ray tracing have shown that there is a modest increase in the ellipticity, but the effect is small if β <0.2 .</p><p>Adiabatic charged particle motion in general field geometry has been studied. A set of four independent stationary invariants, the energy, the magnetic moment, the radial drift invariant, and the bounce average parallel velocity is proposed to describe adiabatic equilibria. </p>

Thermonuclear fusion is a promising energy source for the future. If an economically efficient thermonuclear reactor would be built it has to be a cheap, safe, and highly productive electric power plant, or, a heating plant. The emphasis of this thesis is on the single cell mirror trap with a marginally stable minimum B vacuum magnetic field, the straight field line mirror field, which provides MHD stability of the system, absence of the radial drift even to the first order in plasma β , and a reduced magnetic flux tube ellipticity. Strong density depletion at the mirrors is proposed as a mean to build up a strong potential barrier for the electrons and thereby increase the electron temperature. Conditions to obtain an energy gain factor Q&gt;10 are briefly analyzed. Current coils which could generate the derived magnetic field are proposed. A sloshing ion distribution function is constructed for the three dimensional ‘straight line mirror field’. The gyro centre Clebsch coordinates are found to be a new pair of motional invariants for this magnetic field. The gyro centre Clebsch coordinate invariants can be used to obtain complete solutions of the Vlasov equation, including the diamagnetic drift. These solutions show that the equilibria satisfy the locally omniginuity criterion to the first order in β . Contributions of the plasma diamagnetism to the magnetic flux tube ellipticity are studied for the straight field line mirror vacuum magnetic field and a sloshing ion distribution. Computations employing ray tracing have shown that there is a modest increase in the ellipticity, but the effect is small if β &lt;0.2 . Adiabatic charged particle motion in general field geometry has been studied. A set of four independent stationary invariants, the energy, the magnetic moment, the radial drift invariant, and the bounce average parallel velocity is proposed to describe adiabatic equilibria.

Cette étude s’inscrit dans le domaine de la description de la dynamique des ceintures deradiation terrestres. Elle consiste à modéliser le phénomène de diffusion radiale en travaillantavec une résolution spatio-temporelle plus fine que celle utilisée pour décrire la dynamiquedes ceintures par le biais d’une équation de diffusion. La démarche s’est organisée en troistemps. Tout d’abord, l’objectif a été d’étudier le phénomène de diffusion radiale d’un point devue théorique afin de mettre en lumière les principaux pilotes du processus et d’expliciter uneformulation des coefficients de diffusion radiale. Une fois l’expression de ces coefficientsétablie, l’objectif a ensuite été de les quantifier. Pour cela, nous avons développé desprotocoles analytiques et numériques puis des protocoles expérimentaux. Nous avons discutéles résultats obtenus ainsi que les atouts et les limites de ces protocoles. Cette étude met enévidence le rôle central de l’asymétrie des variations du champ électromagnétique et deschamps électriques induits dans le processus de diffusion radiale. Elle propose des pistes pourla quantification numérique et expérimentale de ces deux pilotes. Elle apporte également unregard critique sur les travaux de la littérature. Elle ouvre la voie pour une nouvellequantification des coefficients de diffusion basée sur une modélisation adéquate de ladynamique de l’environnement électromagnétique / This study falls within the field of the Earth’s radiation belt dynamics. It consists of modelingthe radial diffusion process based on a spatiotemporal resolution higher than the resolution atwhich radiation belt dynamics are described in terms of a diffusion equation. The approachhas been organized in three parts. First, we described radial diffusion theoretically,highlighting the main drivers of the phenomenon and giving a ready-made formula of theradial diffusion coefficients. Then, based on this formula, we aimed to quantify the radialdiffusion coefficients. In order to reach this goal, we developed analytical and numericalprocedures, and then, observational procedures. Finally, we discussed the results and the prosand cons of each method. This study highlights the central role of asymmetric variations ofthe electromagnetic fields and induced electric fields in the driving of the intensity of theradial diffusion process. It provides tracks for numerical and experimental quantification ofthese two drivers. It also provides tools for a critical review of the literature. It paves the wayfor a more accurate determination of radial diffusion coefficients based on a more precisedescription of the electromagnetic environment and its variations.

Les satellites sont vulnérables aux particules de forte énergie piégées dans les ceintures de Van Allen. Afin d’en assurer la protection, il est nécessaire de prédire avec précision la dynamique des électrons au sein de la magnétosphère. Dans un premier temps nous proposons une méthode originale de résolution analytique de l’équation de Fokker-Planck réduite qui modélise le transport et les pertes des électrons de la magnétosphère interne. La résolution repose sur une technique de décomposition spectrale. Si la solution analytique s’avère utile pour mettre en exergue certaines propriétés physiques des ceintures de radiation, elle est également pertinente pour valider le code numérique de résolution de l’équation de Fokker-Planck réduite, développé durant la thèse. Ce dernier nous amène à généraliser l’étude précédente en illustrant l’évolution des flux d’électrons pour diverses énergies et positions. Nous prouvons notamment que la structure des ceintures de radiation ainsi que leur temps d’évolution ne dépendent que de quelques facteurs bien choisis. Dans la perspective de reproduire un événement particulier de retour au calme après un orage magnétique, mesuré par les satellites de la NASA dédiés aux ceintures de radiation, nous sommes en mesure de simuler la précipitation des électrons dans l’atmosphère terrestre causée par les interactions avec les ondes électromagnétiques de la magnétosphère. L’utilisation de conditions bâties sur des données empiriques et spécifiques à la période en question nous permet de corroborer les flux observés. Enfin, l’influence du champ magnétique terrestre sur la dynamique des ceintures de radiation est étudiée sous divers aspects. Nous nous concentrons sur la ceinture externe pour comprendre comment les asymétries du champ magnétique, considérablement façonnées par l’activité solaire, affectent notre manière de concilier théorie et observations. Nous explorons également l’importance de certains processus diffusifs nouveaux et cachés, qui émergent à cause de l’irrégularité naturelle du champ magnétique au plus proche voisinage de la Terre. / Satellites are vulnerable to high-energy particles trapped in the Van Allen belts. To ensure their protection, it is necessary to predict properly the electron dynamics in the magnetosphere. We first propose an original method to find the analytical solution of the reduced Fokker-Planck equation that models the transport and loss of electrons in the inner magnetosphere. The resolution relies on an eigenfunction expansion approach. If the analytical solution is proven to be useful at uncovering some of the physical properties of the radiation belts, it is also relevant to validate the numerical code that solves the reduced Fokker-Planck equation, which has been developed during the PhD. The latter code is used to generalize the previous study in illustrating the evolution of the electron fluxes for various energies and locations. We demonstrate that the structure of the radiation belts as well as their dynamical timescales only depend on a few well-chosen parameters. In the perspective of reproducing a specific storm-recovery event reported by the NASA Van Allen Probes, we are able to simulate the electron scattering in the Earth’s atmosphere due to the interaction with magnetospheric electromagnetic waves. The consideration of data-driven and event-specific conditions enables us to corroborate the observed fluxes. Finally, various influences of the Earth’s magnetic field on the dynamics of the radiation belts are investigated. We focus on the outer belt to see how the magnetic field asymmetries, which are strongly shaped by solar activity, affect the way of conciliating theory and observations. We also explore the importance of new hidden diffusive processes that emerge due to the natural irregularity of the magnetic field in the closest vicinity of the Earth.