A two-dimensional axisymmetric implementation of the smoothed particle hydrodynamics (SPH) technique, called for short AxisSPH, has been described in this thesis, along with a number of basic tests and realistic applications. The main goal of this work was to fill a gap on a topic which has been scarcely addressed in the published literature concerning SPH. Although the application of AxisSPH to the simulation of real problems is restricted to those systems which display the appropriate symmetry there are, however, many interesting examples of physical systems which evolve following the axisymmetric premise. These examples belong to a variety of scientific and technological areas such as, for example, astrophysics, laboratory astrophysics or inertial confinement fusion. Additionally AxisSPH can be also useful in convergence studies of the standard 3D-SPH technique because the higher resolution achieved in 2D can be used to benchmark the three-dimensional codes. The main improvements implemented in AxisSPH with respect existing axisymmetric SPH formulations are summarized as follows: 1) We have derived simple analytical expressions for correction factors which largely improves the calculation of density and velocity in the vicinity of the z-axis. These expressions and their derivatives were given as a function of an adimensional parameter and do not increase the computational load of the scheme. 2) We have obtained the appropriate expression of the fluid Euler equations containing the new correction functions and their derivatives. Far enough from the singular axis, the scheme reduces to the standard formulation discussed by Brookshaw (2003). 3) A novel expression for the heat conduction term, which has to be added to the energy equation was devised and checked. This new term improves the description of the heat flux for those particles located at the axis neighborhoods. 4) Until now axisymmetric SPH hydrocodes handle artificial viscosity using a crude approach because it was treated as a simple restriction of the standard 3D Cartesian viscosity to 2D. Here we propose to calculate the viscous pressure as a combination of two terms, the first one is the (standard) Cartesian part and the second is the axis-converging part of the viscosity respectively. As expected this last term is of special relevance to simulate implosions. 5) We have developed an original method to incorporate gravity into AxisSPH. First the direct ring to ring force was found as a function of the Euclidean distance between the 2D particles. In second place the gravitational force on a given particle was obtained by summing the contributions of all N particles. We have also developed a more efficient scheme to obtain the gravitational force calculating the potential of the ring, instead the force because it involves lesser algebraic operations. The scheme has been checked using a large number of tests cases. These tests range from very specific oriented to check a particular algorithm or a piece of physics, to rather complex ones intended to analyze the behavior of the scheme in potential real applications (ICF, jets, astrophysics). At least in one case, the head on collision of a pair of white dwarfs, the result of the simulations carried out using AxisSPH brings new, unpublished, scientific material. / En esta tesis se ha desarrollado un código, que hemos llamado AxisSPH, en dos dimensiones axisimétrico a partir de la técnica conocida como SPH (“smooothed particle hydrodynamics”). AxisSPH ha sido validado después de realizar una serie de tests básicos y algunas simulaciones de situaciones reales. El objetivo principal de este trabajo ha sido llenar, en parte, el vacío existente al respecto en la literatura sobre SPH. Aunque sólo se puede aplicar AxisSPH en problemas reales que presenten la apropiada simetría, existen muchos ejemplos interesantes de sistemas físicos que presentan la simetría axial demandada. Existen ejemplos en campos de aplicación tanto científica como tecnológica, por ejemplo en astrofísica, en el llamado laboratorio de astrofísica o en fusión por confinamiento inercial (ICF). Otra interesante aplicación de AxisSPH puede ser su utilización en estudios de convergencia con otros códigos 3D-SPH debido a su mayor resolución, al tratarse de un código 2D. Las mejoras implementadas en el código AxisSPH en comparación con otros códigos axisimétricos SPH existentes se pueden resumir en los siguientes puntos: 1) Hemos deducido expresiones analíticas simples para unos factores de corrección que mejoran el cálculo de la densidad y la velocidad en las proximidades del eje z. Dichas expresiones y sus derivadas dependen de un parámetro adimensional que no incrementa mucho el peso computacional del esquema propuesto. 2) Hemos obtenido las expresiones adecuadas de las ecuaciones de Euler que contienen estas nuevas funciones correctoras y sus derivadas. Lejos del eje de singularidad estas ecuaciones se transforman en las de la formulación estándar propuesta por Brookshaw (2003). 3) Una expresión novedosa del término de conducción, que debe de añadirse a la ecuación de la energía, se ha propuesto y validado. Este nuevo término mejora la evolución del flujo de calor de las partículas situadas en las proximidades del eje z. 4) Hasta el momento los códigos hidrodinámicos SPH axisimétricos existentes trabajaban con una aproximación poco elaborada de la viscosidad artificial ya que consistían en una restricción a dos dimensiones de la viscosidad estándar 3D. En este trabajo proponemos el cálculo de la presión debida a la viscosidad como combinación de dos términos, el primero reflejo de la parte cartesiana y la segunda da cuenta de la parte relacionada con la convergencia en el eje. Como era de esperar este último término es de relevante importancia en la simulación de implosiones. 5) Hemos desarrollado un método original para incorporar el cálculo de la gravedad en el código AxisSPH. En primer lugar la fuerza directa de anillo a anillo y en segundo lugar la fuerza de la gravedad que sufre una determinada partícula a partir de la contribución del resto de las N partículas existentes. También hemos desarrollado un esquema más eficiente para calcular la gravedad a partir del cálculo del potencial del anillo en lugar del cálculo directo de la fuerza ya que implica un menor número de operaciones algebraicas. El método ha sido verificado con un gran número de test numéricos. Desde los más específicos orientados a comprobar la validez de un algoritmo particular o la capacidad para simular un fenómeno físico en particular, hasta simulaciones bastante más complejas, con la intención de validar la capacidad de simular aplicaciones potencialmente más reales (ICF, jets, astrofísica). Así, en al menos un caso, en la colisión frontal de dos enanas blancas, los resultados de la simulación utilizando AxisSPH pueden aportar material científico publicable.

This thesis focuses on the propagation of charged particle beams in plasmas, and is divided into two main parts. In the second chapter, a novel theoretical model for underdense electron beam propagation during the nonlinear stage of the resistive Weibel instability (WI) is presented and is used to calculate the stopping time of the beam. The model and supporting simulation results lead to the conclusion that the WI initially enhances beam deceleration but then reduces it when compared to a filamentation-suppressed beam (without WI), so that the overall stopping time of the beam is essentially unaffected by the instability. Using the theoretical model, a criterion is derived that determines when deceleration is no longer enhanced by the instability. We also demonstrate that exotic plasma return current distributions can be obtained within and outside of beam filaments that sharply contrast those observed in collisionless systems. For example, the plasma return current is reversed in selected areas. In the next chapter, a new method for initiating the modulation instability (MI) of a proton beam in a proton driver plasma wakefield accelerator using a short laser pulse preceding the beam is presented. A diffracting laser pulse is used to produce a plasma wave that provides a seeding modulation of the proton bunch with the period equal to that of the plasma wave. Using the envelope description of the proton beam, this method of seeding the MI is analytically compared with the earlier suggested seeding technique that involves an abrupt truncation of the proton bunch. The full kinetic simulation of a realistic proton bunch is used to validate the analytic results. It is further used to demonstrate that a plasma density ramp placed in the early stages of the laser-seeded MI leads to its stabilization, resulting in sustained accelerating electric fields (of order several hundred MV/m) over long propagation distances (100-1000 m). The final chapter describes a harmonic expansion formalism that attempts to explain the post-linear stage of the MI. The formalism is developed first, and then several crippling problems with it are identified. / text

This master thesis deals with the optimal initial perturbation problem for a 1D unsteady self-similar ablation flow in an inertial confinement fusion context. The physical modelling consists of the compressible Euler equations with nonlinear heat conduction. The base flow and linear 3D perturbations are computed using a multidomain Chebyshev collocation method. Longitudinal optimal initial perturbations are computed by means of a non-modal analysis method for stationary perturbation evolution operators (Schmid, 2001 & 2007) after transformation of the time-dependent perturbation problem. Results of optimal gain and initial perturbation differ significantly from those produced by a non-stationary direct-adjoint method (Varillon, 2019). This discrepancy is analyzed to be a consequence of a diagonalization failure of the discrete perturbation evolution operator.

Experimental results and simulations of imploding fusion concepts have identified the Rayleigh-Taylor (RT) instability as one of the largest inhibitors to achieving fusion. Understanding the origin and development of the RT instability will allow for the development of mitigating measures to dampen the instability growth, thus improving the chance that fusion concepts such as inertial confinement fusion (ICF) are successful. A study of 1D and 2D simulations are presented for investigating RT instability growth in deceleration stage of imploding geometries. Two cases of laser-driven implosion geometry, Cartesian and cylindrical, are used to study late stage deceleration-phase RT instability development on the interior surface of imploding targets. FLASH's hydrodynamic (HD) and magnetohydrodynamic (MHD) modeling capabilities are used for different laser and target parameters in order to study the RT instability and the impact of externally applied magnetic fields on their evolution. Several simulation regimes have been identified that provide novel insight into the impact that a seeded magnetic field can have on RT instability growth and the conditions under which magnetic field stabilization of the RT instability is observable. Finally, future work and recommendations are made. / Master of Science / The direction for the future of renewable energy is uncertain at this time; however, it is known that the future of human energy consumption must be green in order to be sustainable. Fusion energy presents an opportunity for an unlimited clean renewable energy source that has yet to be realized. Fusion is achieved only by overcoming the earthly limitations presented by trying to replicate conditions at the interior of stellar structures. The pressures, temperature, and densities seen in the interior of stars are not easily reproduced, and thus human technology must be developed to reach these difficult stellar conditions in order to harvest fusion energy. There are two main branches of developmental technology geared towards achieving the difficult conditions controlled nuclear fusion presents, magnetic confinement fusion (MCF) and inertial confinement fusion (ICF)[17]. Yet in both approaches barriers exist which have thwarted the efforts toward reaching fusion ignition which must be addressed through scientific discovery. Successfully reaching ignition is only the first step in the ultimate pursuit of a self sustaining fusion reactor. This work will focus on the experimental ICF configuration, and on one such inhibitor toward achieving ignition, the Rayleigh-Taylor (RT) instability. The RT instability develops on the surfaces of the fusion fuel capsules, targets, and causes nonuniform compression of the target. This nonuniform compression of the target leads to lower pressures and densities through the material mixing of fusion fuel and the capsule shell, which ultimately leads to challenges with reaching fusion ignition. The work presented here was performed utilizing the University of Chicago's FLASH code, which is a state-of-the-art open source radiation magneto-hydrodynamic (MHD) code used for plasma and astrophysics computational modeling [11]. Simulations of the RT instability are performed using FLASH in planar and cylindrical geometries to explore fundamental Rayleigh-Taylor instability evolution for these two different geometries. These geometries provide easier access for experimental diagnostics to probe RT dynamics. Additionally, the impact of externally applied magnetic fields are explored in an effort to examine if and how the detrimental instability can be controlled.

Z-Pinch IFE (Inertial Fusion Energy) reactor designs will likely utilize high yield targets (~ 3 GJ) at low repetition rates (~ 0.1 Hz). Appropriately arranged thick liquid jets can protect the cavity walls from the target x-rays, ions, and neutrons. However, the shock waves and mechanical loadings produced by rapid heating and evaporation of incompressible liquid jets may be challenging to accommodate within a small reactor cavity. This investigation examines the possibility of using two-phase compressible (liquid/gas) jets to protect the cavity walls in high yield IFE systems, thereby mitigating the mechanical consequences of rapid energy deposition within the jets. Two-phase, free, vertical jets with different cross sections (planar, circular, and annular) were examined over wide ranges of liquid velocities and void fractions. The void fraction and bubble size distributions within the jets were measured; correlations to predict variations of the slip ratio and the Sauter mean diameter were developed. An exploding wire system was used to generate a shock wave at the center of the annular jets. Attenuation of the shock by the surrounding single- or two-phase medium was measured. The results show that stable coherent jets can be established and steadily maintained over a wide range of inlet void fractions and liquid velocities, and that significant attenuation in shock strength can be attained with relatively modest void fractions (~ 1%); the compressible two-phase jets effectively convert and dissipate mechanical energy into thermal energy within the gas bubbles. The experimental characteristics of single- and two-phase jets were compared against predictions of a state-of-art CFD code (FLUENT®). The data obtained in this investigation will allow reactor system designers to predict the behavior of single- and two-phase jets and quantify their effectiveness in mitigating the consequences of shock waves on the cavity walls in high yield IFE systems.

Recent missions to solar system comets, such as ESA's Rosetta mission, raise interest for models and descriptions of their plasma environment. The interaction with various space phenomena such as stellar wind make the construction of an analytical description difficult. Instead, a simplified view of the comet environment is considered where the effects of magnetism and departures from radial symmetry are neglected. This is done in an effort to construct an approximation of the comet plasma behaviour later to be compared against observational accounts to find which plasma features are dependent on more complex phenomena and which plasma features arise as a result of the simpler comet view. Several attempts are made to construct an analytical description of comet plasma as based on the description within another branch of plasma physics: fusion. Previous work regarding the vacuum expansion of plasma after a stationary target is rapidly ablated via high-intensity lasers appears promising for adaptation to the comet environment. Before the comet environment can be considered the different natures of the two problems have to be considered. For example, the comet case is a stationary expansion problem as opposed to fast-ignition fusion where the expansion is treated as an initial value problem. Having accounted for the problems' inherent differences, a few methods are proposed to convert solutions of lab fusion distribution functions to the comet case. Additionally, a numerical approach to calculate the distribution function of comet electrons is presented employing ergodic invariance. Lastly, a toy-model simulation of the timescale for variations in the potential show that the error in the ergodic invariance may in practice have a faster convergent timescale dependence than theoretical bounds suggest. Optimistically, this suggest the possibility of future use in numerical attempts at modelling comet plasma.

L'étude de la fusion par confinement inertiel du mélange deutérium + tritium (DT) est une problématique depuis longtemps abordée par le CEA. Les expérimentations liées à cette thématique, effectuées prochainement au sein du laser mégajoule (LMJ), nécessitent l'utilisation de matériaux aux propriétés particulières. Cela concerne entre autres les mousses de polymères (aérogels organiques) composant les cibles de pré-ignition. De tels matériaux doivent notamment associer une importante porosité à une forte teneur métallique (1% atomique de Ti), tout en étant compatible avec les procédés de préparation utilisés. Dans ce contexte, un nouveau complexe polymérisable de titane a été préparé et caractérisé par plusieurs techniques d'analyses. Ce monomère dispose d'une forte teneur métallique tout en présentant une bonne stabilité vis-à-vis l'air et l'humidité. Sa copolymérisation radicalaire selon différentes conditions suivie d'un séchage en condition supercritique a permis l'obtention d'une série d'aérogels organiques. Les caractérisations chimiques (RMN, infrarouge et analyses élémentaires) ainsi que les caractérisations structurales (MEB-EDS, MET, mesure des isothermes d'adsorption/désorption de l'azote et SAXS) de ces polymères ont permis de valider les critères mentionnés dans notre cahier des charges. En outre, ces données ont permis de déterminer les mécanismes de formation de la nanostructure des mousses. / Inertial Confinement Fusion (ICF) is a technique widely studied by the French atomic commission (CEA). Experiments will be performed within the Laser Megajoule (LMJ). They require innovative materials like organic aerogels that constitute laser targets. Such polymeric material must provide both a high porosity and a significant titanium percentage (1 atom %). Moreover, the monomers developed must be compatible with the synthesis procedure already in use. According to these specifications, a new polymerizable titanium complex was synthesized and fully characterized. This air and moisture-stable monomer provides a high metal percentage. Its free-radical cross-linked copolymerization affords several titanium-containing polymers. These gels were dried under supercritical conditions and organic aerogels were obtained. The chemical compositions of these materials were investigated by NMR, IR and elemental analysis while their structure was characterized by MEB-EDS, MET, N2 adsorption/desorption isotherms measurements and SAXS. The data collected fit the specification requirements. Moreover, the mechanisms responsible of the foam nanostructure formation were discussed.

Le contrôle de l’instabilité de Rayleigh-Taylor (RT) est crucial pour la fusion par confinement inertiel (FCI) puisque son développement peut compromettre l’implosion et la correcte compression de la cible. En attaque directe, l’énergie fournie par l’irradiation de nombreux faisceaux laser provoque l’ablation de la couche externe de la cible (ablateur) et l’apparition résultante d’un plasma de basse densité en expansion. De ce fait, une très haute pression apparait autour de cette surface, ce qui conduit à l’accélération de la cible vers l’intérieur. On se trouve alors en présence d’un fluide de basse densité qui pousse et accélère le fluide plus dense. C’est une des situations typiques qui favorisent le développement de l’instabilité de RT. Cette thèse développe pour la première fois, dans le contexte de la FCI, une théorie linéaire de stabilité pour des structures à double front d’ablation, qui apparaissent quand des matériaux de nombre atomique modéré sont utilisés comme ablateurs. / The Rayleigh-Taylor instability is a major issue in inertial confinement fusion capable to prevent appropriate target implosions. In the direct-drive approach, the energy deposited by directed laser irradiation ablates off the external shell of the capsule (ablator) into a low-density expanding plasma. This induces a high pressure around the ablating target surface (ablation region) that accelerates the capsule radially inwards. This situation, a low density fluid pushing and accelerating a higher density one, is the standard situation for the development of the Rayleigh-Taylor instability, and therefore a potential source of target compression degradation. For moderate-Z materials, the hydrodynamic structure of the ablation region is made up of two ablation fronts (double ablation front) due to the increasing importance of radiation effects. This thesis develops for the first time a linear stability theory of double ablation fronts for direct-drive inertial confinement fusion targets.

Ce travail de thèse porte sur l’étude de la dynamique et de la stabilité de structures présentant deux fronts d’ablation dans le cadre de la fusion par confinement inertiel (FCI) en attaque directe. Dans un premier temps, des simulations 1D réalisées avec le code d’hydrodynamique CHIC ont permis d’obtenir ces structures. Pour cela, des plaques planes de matériaux de Z modéré, comme l’aluminium, la silice, le plastique dopé au brome, ainsi que le plastique sont éclairées par laser, à des intensités proches de celles requises pour la FCI. Les effets radiatifs, de par leur contribution dans le bilan d’énergie, modifient alors l’hydrodynamique de la cible : deux fronts d’ablation séparés par un plateau de densité quasi-constante sont observés. La dynamique de telles structures est alors caractérisée de manière qualitative. Une étude du préchauffage du combustible (DT) induit par le rayonnement de ces ablateurs de Z modéré est alors réalisée. Un nouveau modèle théorique, basé sur une hypothèse d’isobaricité au front d’ablation, prend en compte deux mécanismes de transport de l’énergie (transport d’électrons et de photons) et permet de reproduire ces structures en supposant un traitement analytique des opacités de la matière. De plus, ce modèle permet de comprendre les mécanismes physiques qui interviennent dans la formation des structures à double front d’ablation. Le code PERLE, dédié à l’étude de la stabilité hydrodynamique d’écoulements en phase linéaire, est alors modifié pour prendre en compte le transport de photons en utilisant les simplifications du modèle théorique. La deuxième partie de cette thèse porte sur la stabilité hydrodynamique de ces structures à double front d’ablation. Les modèles existants pour les problèmes de stabilité au front d’ablation sont insuffisants : les limites de ces modèles sont montrées, mais des premières informations sur le front d’ablation principal sont néanmoins obtenues. Le code PERLE permet alors de calculer les perturbations linéaires au front d’ablation quand la structure à double front d’ablation entière est considérée. Des taux de croissance pour l’instabilité Rayleigh-Taylor ablative sont obtenus et présentent une nouvelle forme non connue, associée directement à la structure à double front d’ablation. Les calculs 2D réalisés avec le code CHIC et une physique plus réaliste confirment ces résultats. L’étude de la localisation spatiale des perturbations montrent la relation entre la structure à deux fronts d’ablation et la forme caractéristique des taux de croissance. Finalement, l’utilisation d’ablateurs de Z modéré peut être une alternative intéressante pour réduire l’instabilité de Rayleigh-Taylor au front d’ablation en FCI par attaque directe. / This PhD thesis adresses the dynamics and the stability of double ablation fronts structures in direct-drive inertial confinement fusion (ICF). In the first part, these structures have been obtained using the hydrodynamic code CHIC calculations. By irradiating solid targets of moderate Z such as aluminium, silicium, brominated doped plastic, and plastic with ICF like laser intensities, radiative effects become non negligibles and modify the target hydrodynamics. Two ablation fronts separated by a quasi-constant density plateau are then observed. The dynamic of such structures is then qualitatively characterized. The fuel (DT) preheat due to self-emitted radition of such ablators is then studied. A new theoretical model, based on an isobaric approximation in the ablation region allows us to understand the complex physical mecanisms involved in the formation and the dynamics of these structures, using analytical expressions for the opacities. The PERLE code, dedicated to the calculation of linear perturbations of unsteady flows, is then modified to take into account the radiative energy transport, using the hypothesis of the new theoretical model. In the second part of this work, a study of the stability of double ablation fronts structures is carried out. The existing models for the ablation front stability problems are no longer sufficient in this case: their limitations are shown, but, nevertheless, firsts informations on the main ablation front are obtained. Then, the PERLE code is used when the whole double ablation fronts structure is considered. The growth rates for the ablative Rayleigh-Taylor instability are estimated, and show a new shape, unknown up to now. The 2D calculations made with the CHIC code using a more realistic physics confirm these results. The study of the spatial localization of perturbations in the structure shows the relation between the two ablation fronts and the characteristic shape of the growth rates obtained. Finally, the use of such moderate Z ablators is an interesting alternative to reduce the Rayleigh-Taylor instability at the ablation front in direct-drive ICF.

Cette thèse s’inscrit dans le cadre de recherches menées sur la fusion par confinement inertiel (FCI). En particulier, l’étude proposée ici s’est concentrée sur les équations d’état tabulées de deux matériaux ablateurs synthétisés sur les capsules du Laser Mégajoule. Le but est alors de tester la modélisation théorique implémentée dans ces tables. Nous avons concentré notre étude sur un domaine restreint du diagramme de phase caractérisé par des pressions de quelques mégabars et de températures de quelques électronvolts qui peut être atteint sur des installations laser de tailles moyennes.Pour ce faire, nous nous sommes basés sur le modèle QEOS, car il est simple d’utilisation, paramétrable et donc facilement modifiable.Nous avons ensuite appliqué les méthodes de la dynamique moléculaire quantique pour générer la courbe froide et les courbes d’Hugoniot des deux matériaux étudiés. Ces calculs ont notamment mis en avant l’influence de la dissociation chimique sur la forme de ces courbes. Une comparaison avec le modèle QEOS a montré un écart important sur l’Hugoniot. Une modification de ce modèle, à travers le coefficient de Grüneisen, nous a ensuite permis de restituer les effets observés et d’étudier leurs impacts sur la chronométrie des chocs dans une capsule de FCI.Parallèlement à cette étude numérique, nous avons mesuré des états thermodynamiques le long de l’Hugoniot lors de trois campagnes sur les installations laser LULI2000 et GEKKO XII. L’utilisation de diagnostics VISAR et d’un diagnostic d’émission propre, nous a alors permis de sonder la matière sous choc. En outre, les données expérimentales ont confirmé les précédents résultats.En outre, cette étude a été réalisée sur deux matériaux ablateurs différents parmi lesquels on distingue le polymère non dopé CHO et le polymère dopé au silicium CHOSi. Elle montre un comportement universel de ces matériaux le long de l’Hugoniot. / This PhD thesis enters the field of inertial confinement fusion studies. In particular, it focuses on the equation of state tables of ablator materials synthetized on LMJ capsules. This work is indeed aims at improving the theoretical models introduced into the equation of state tables. We focused in the Mbar-eV pressure-temperature range because it can be access on kJ-scale laser facilities.In order to achieve this, we used the QEOS model, which is simple to use, configurable, and easily modifiable.First, quantum molecular dynamics (QMD) simulations were performed to generate cold compression curve as well as shock compression curves along the principal Hugoniot. Simulations were compared to QEOS model and showed that atomic bond dissociation has an effect on the compressibility. Results from these simulations are then used to parametrize the Grüneisen parameter in order to generate a tabulated equation of state that includes dissociation. It allowed us to show its influence on shock timing in a hydrodynamic simulation.Second, thermodynamic states along the Hugoniot were measured during three experimental campaigns upon the LULI2000 and GEKKO XII laser facilities. Experimental data confirm QMD simulations.This study was performed on two ablator materials which are an undoped polymer CHO, and a silicon-doped polymer CHOSi. Results showed universal shock compression properties.