Deterministic-Kinetic Computational Analyses of Expansion Flows and Current-Carrying Plasmas

Spacecraft electric propulsion (EP) takes advantage of the ability of electric and magnetic fields to accelerate plasmas to high velocities to generate efficient thrust. The thermionic hollow cathode is a critical component to both gridded-ion and Hall-effect thrusters, the state-of-the-art devices of the EP discipline. However, experiments demonstrate that the hollow cathode is plagued by erosion of its surfaces by the plasma, which may eventually cause premature failure of the device. This erosion has been linked to the ion-acoustic instability (IAI), a kinetic plasma instability which operates in the cathode plume. Existence of this kinetic instability has prevented numerical simulation from predicting the operating characteristics and lifetime of the hollow cathode device. Therefore, this thesis utilizes deterministic-kinetic (DK) simulation of gas and plasma flows to further the understanding of the IAI as it relates to the hollow cathode plume and to ultimately develop a predictive hollow cathode simulation platform. Towards these goals, two approaches to applying the DK simulation method to the hollow cathode plasma are undertaken: hybrid-kinetic simulation and fully-kinetic simulation. Hybrid-kinetic simulations utilize a kinetic description of the heavy propellant particles while using a reduced-order, fluid approach for the light electrons. Two unique two-dimensional, axisymmetric kinetic schemes are developed, one for neutral particles and one for ions; the schemes are verified by comparison with solutions obtained using the direct-simulation Monte Carlo method and with an analytic solution for a rarefied neutral jet flow. Assuming quasi-neutrality in the hollow cathode plasma and using the Boltzmann relation for the plasma potential, the hybrid-kinetic solver is applied to the problem of NASA's NSTAR discharge hollow cathode. Partial validation is achieved through agreement with experimental Langmuir probe data in the near-orifice region, while shortcomings of the solver such as use of a simplified electron model are discussed. Fully-kinetic simulations, where all species are considered kinetically, are carried out to study the IAI. The anomalous resistivity generated by the IAI is measured from one-dimensional fully-kinetic simulations and compared with a closure model commonly used in hollow cathode fluid codes, finding that the agreement with the closure model varies based on simulation domain size and electron Mach number. Further, the formation of high-energy tails in the ion velocity distribution function is observed near the transition to the Buneman instability, another instability of current-carrying plasmas. Two-dimensional kinetic simulations of current-carrying instabilities are carried out, finding that the nature of nonlinear saturation of the IAI differs significantly from that shown in one-dimensional simulations. A phenomenon known as the off-axis instability generates waves propagating normal to the current direction which eventually reach energy levels close to that of the waves along the current direction. Further fully-kinetic simulations demonstrate the formation of weak plasma double layers, regions of plasma which sustain a potential gradient, in the nonlinear saturation stage of the IAI. These double layers are found to be ubiquitous in all plasma species considered, even the heavy xenon ions commonly used in hollow cathodes. Phase space analysis suggests the double layers form from ion-acoustic wave packets which grow into ion phase space holes. Spectral analysis demonstrates a shift towards smaller wavenumbers which marks this transition. An electron two-stream instability is spawned due to the potential well of the double layer, where spectral analyses demonstrate that a simple theoretical expression well-predicts the resulting wave phase velocity.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/169806/1/vazsonyi_1.pd

Turbulent transport in rotating tokamak plasmas

Small scale turbulence in a magnetically confined fusion plasma drives energy and particle transport which determine the confinement. The plasma in a tokamak experiment has a toroidal rotation which may be driven externally, but can also arise spontaneously from turbulent momentum transport. This thesis investigates the interaction between turbulence and rotation via nonlinear numerical simulations, which use the gyrokinetic description in the frame that corotates with the plasma. A local gyrokinetic code is extended to include both the centrifugal force, and the stabilising effect of sheared equilibrium flow. Sheared flow perpendicular to the magnetic field suppresses the turbulence, and also breaks a symmetry of the local model. The resulting asymmetry creates a turbulent residual stress which can counteract diffusive momentum transport and contribute to spontaneous rotation. The competition between symmetry breaking and turbulence suppression results in a maximum in the nondiffusive momentum flux at intermediate shearing rates. Whilst this component of the momentum transport is driven by the sheared flow, it is also found to be suppressed by the shearing more strongly than the thermal transport. The direction of the residual stress reverses for negative magnetic shear, but also persists at zero magnetic shear. The parallel component of the centrifugal force traps particles on the outboard side of the plasma, which destabilises trapped particle driven modes. The perpendicular component of the centrifugal force appears as a centrifugal drift which modifies the phase relation between density and electric field perturbations, and is stabilising for both electron and ion driven instabilities. For ion temperature gradient dominated turbulence, an increased fraction of slow trapped electrons enhances the convective particle pinch, suggesting increased density peaking for strongly rotating plasmas. Heavy impurities feel the centrifugal force more strongly, therefore the effects of rotation are significant for impurities even when the bulk ion Mach number is low. For ion driven modes, rotation results in a strong impurity convection inward, whilst a more moderate convection outward is found for electron driven modes.EThOS - Electronic Theses Online ServiceEngineering and Physical Sciences Research Council (EPSRC)Culham Centre for Fusion Energy (CCFE)GBUnited Kingdo

Computational and Numerical Simulations

Computational and Numerical Simulations is an edited book including 20 chapters. Book handles the recent research devoted to numerical simulations of physical and engineering systems. It presents both new theories and their applications, showing bridge between theoretical investigations and possibility to apply them by engineers of different branches of science. Numerical simulations play a key role in both theoretical and application oriented research

Conservative fourth-order finite-volume Vlasov–Poisson solver for axisymmetric plasmas in cylindrical (r,vr,vθ) phase space coordinates

A fourth-order finite-volume Vlasov–Poisson algorithm is developed for simulating axisymmetric plasma configurations in (r,vr,vθ) phase space coordinates. The Vlasov equation for cylindrical phase space coordinates is cast into conservation-law form and is discretized on a structured grid. The conservative finite-volume discretization is based on fifth-order upwind reconstructions of the distribution function and a fourth-order quadrature rule that accounts for transverse variations of fluxes along control volume surfaces. High-order specular reflection boundary conditions enable high-fidelity treatment of plasma distribution functions at the axis and at wall boundaries. The numerical method is applied to simulate a confined uniform neutral gas to assess convergence properties for an equilibrium system in which effects of finite-temperature and acceleration due to centrifugal and Coriolis forces are present. The discretization is also applied to a Z-pinch configuration to study electrostatic ion confinement and the dynamics of the associated breathing mode. Simulations show that the ion distribution function exhibits non-Maxwellian features and that a temperature anisotropy develops and is sustained. The finite-volume implementation is demonstrated to converge at fourth-order for both applications

Exploring gravity theories with gravitational waves and compact objects

This thesis is devoted to the study of tests of General Relativitywhich could be performed using astrophysical observations of stars or compact objects. The thesis consists of two parts. In the first one, I have investigated how the future gravitational wave observations by the space-based detector LISA will permit mapping the spacetime of the supermassive black holes which are thought to reside in galactic centres. In particular, I have analysed the dynamics of a stellar black hole orbiting around a supermassive black hole and have investigated under which conditions the gravitational wave signal emitted by such a system can allow one to detect the presence of an accretion torus around the supermassive black hole. I have also studied the motion of a stellar black hole in the very strong field region of a nearly extreme supermassive black hole: contrary to our expectations and to suggestions present in the literature, we have found that although the motion presents peculiar characteristics, the emitted gravitational waves do not retain an observable imprint of the almost maximal rotation of the supermassive black hole. Also, I considered black hole binaries with arbitrary masses and spins. Although the coalescence of such systems can be studied only with numerical simulations, I have derived a compact analytic formula for the spin of the final remnant. This formula is in agreement with all the numerical simulations available to date

De la cosmologie à la formation des galaxies : que nous apprennent les grandes structures de l'Univers ?

This thesis by publication is devoted to the theoretical understanding of the large-scale structure of the Universe and its role in the context of cosmology and galaxy formation. The birth and evolution of galaxies occur within the large cosmic highways drawn by the cosmic web and the natural question which arises is whether galaxies retain a memory of the large-scale cosmic flows from which they emerge. To address this key question, we will first show that in cosmological simulations, the spin of galaxies and the direction of their host filament are correlated in a mass-dependent way. This signal will be shown to be qualitatively understood in the context of hierarchical structure formation. An analytic model which explicitly takes into account the anisotropy of the cosmic web will complement this qualitative understanding by reproducing the measured correlations. Those ideas are important to understand the evolution of galaxy morphology but also to understand the intrinsic alignments of galaxies that contaminate cosmological probes like cosmic shear experiments. We will in particular measure this contamination directly from a state-of-the-art hydrodynamical simulation. In a second part, we will address the question of how to efficiently use large-scale structure data to probe the cosmological model describing our Universe by measuring its topology and geometry and using perturbation theory in the weakly and even mildly non-linear regime. The major contribution of this work is to analytically study the effect of redshift space distortions and non-linear collapse of structures on the topology, geometry and statistics of the cosmic density field.Dans cette thèse sur articles, nous nous intéressons aux grandes structures de l’Univers et à leur rôle fondamental pour la cosmologie et la formation des galaxies. Les galaxies naissent et grandissent au sein des filaments de la toile cosmique soulevant la question de l’impact de ces filaments sur les propriétés galactiques telles que la morphologie. Pour étudier cette question fondamentale, nous allons dans un premier temps montrer que dans les simulations numériques de l’Univers, le spin des galaxies est fortement lié à la direction de leur filament hôte avec un comportement qui dépend de leur masse. Ces corrélations spin-filament seront expliquées qualitativement dans le contexte de la formation hiérarchique des structures cosmologiques. Un modèle analytique tenant compte de l’anisotropie de la toile cosmique complètera ce tableau en reproduisant les corrélations observées. Ces idées sont importantes pour comprendre la morphologie des galaxies mais aussi les alignements intrinsèques qui peuvent certaines sondes cosmologiques basées sur la mesure de l’astigmatisme cosmique. Nous allons en particulier mesurer cette contamination dans une simulation hydrodynamique. Dans la seconde partie de ce manuscrit, nous nous poserons la question de comment extraire efficacement de l’information de la toile cosmique en mesurant sa topologie et sa géométrie et en utilisant la théorie perturbative dans un régime quasi-linéaire, la pierre angulaire de ce travail reposant sur l’étude analytique de l’impact de l’effondrement non-linéaire des structures et des distorsions en espace des redshifts sur la statistique du champ de densité cosmique