Les conditions thermodynamiques régnant au sein des planètes géantes telles que Jupiter, Saturne et bon nombre des exoplanètes découvertes quotidiennement, impliquent que les interactions entre particules – atomes, ions, électrons – sont prépondérantes dans les enveloppes planétaires, principalement composées d'hydrogène et d'hélium, et déterminent les propriétés mécaniques et thermiques de ces objets. La caractérisation de ces plasmas denses est donc cruciale pour comprendre la structure et l'évolution de ces planètes géantes. Les simulations ab initio, utilisant la théorie de la fonctionnelle de la densité, ont montré leurs performances pour la caractérisation des espèces pures dans leur phase plasma dense, en reproduisant correctement les résultats des expériences de chocs par laser haute-puissance. Néanmoins, des écarts importants perdurent entre modèles planétaires et observations. Ils sont attribués à la non-idéalité du mélange H-He et de possibles transitions de phase. Dans ce travail de thèse, ces méthodes numériques ab initio ont été appliquées au cas des mélanges H-He. L'étude thermodynamique a révélé des déviations sensibles par rapport aux prédictions obtenues pour des mélanges idéaux. Par ailleurs, les calculs des propriétés de transport (conductivité électrique, thermique, propriétés optiques...) ont montré une transition isolant-conducteur du mélange, notamment par l'ionisation de l'hydrogène. Celle-ci s'accompagne, dans un certain domaine de paramètres, d'une séparation de phase entre l'hydrogène conducteur et l'hélium neutre. Ces calculs ont également permis d'établir des diagnostics pour les expériences laser, afin de pouvoir corroborer cet ensemble de résultats et obtenir, à terme, une équation d'état fiable du mélange H-He, applicable aux planètes géantes. / The thermodynamical conditions inside the giant planets - like Jupiter, Saturn or many of the daily discovered exoplanets – are such that the interactions between particles – atoms, ions, electrons – are highly dominant in the physics of giant planets envelope s, mostly made of hydrogen and helium in a plasma phase. The heat and mechanical properties of these planets are mainly determined by these interactions. Thus, it is of crucial interest to study these dense plasmas to understand the structure and the evolution of the giant planets. The dense plasma phase of the pure compounds has been successfully characterized by ab initio simulations using density functional theory. For instance, they correctly reproduced the results obtained in high-power laser chock experiments. Nevertheless, large discrepancies remain between planetary models and observations. A proposed hypothesis is a strong influence of the H-He mixture non-ideality and possible phase separations. In this work, these ab initio numerical methods have been applied to the H-He mixtures. The thermodynamical study has shown sensitive deviations from ideal mixtures. The estimates of the transport properties (electrical and heat conductivities, optical properties...) indicate an insulator-conductor transition in the mixture, associated with hydrogen ionization. In some conditions, demixing of conducting hydrogen and neutral helium has also been observed. These computations have allowed us to determine pathways to verify our results through laser experiments. This is the first step in the establishment of a reliable equation of state of H-He mixtures, usable in giant planets modeling.

La connaissance des étoiles et des planètes denses nécessite une détermination fine du comportement thermodynamique de la matière dans ces objets. L'une des approches les plus fécondes aujourd'hui est celle des simulations ab initio, utilisant le formalisme de la physique statistique et la théorie de la fonctionnelle de la densité. Cette approche a notamment montré ses performances en reproduisant avec succès un grand nombre de résultats expérimentaux.Dans la première partie de ce travail de thèse, ces méthodes sont appliquées à l'étude des« glaces », impliquées dans des planètes telles que Uranus ou Neptune. Nous avons dans un premier temps confirmé le travail pré-existant sur le cas de l'eau (équations d'état et existence d'une phase superionique), puis nos avons étendu ces résultats aux cas de planètes plus denses, telles que les exoplanètes appelées« super-Jupiters ». Nous atteignons des limites de pression auxquelles le comportement est analytiquement connu, nous permettant de proposer un ajustement numérique pour l'eau dans une gamme de pression et température extrêmement large. Les autres glaces(méthane et ammoniac) ont seulement été étudiés dans les conditions des planètes de notre système solaire.Nous nous sommes ensuite intéressés au cas des naines blanches et à leur dynamique de refroidissement ~; il s'agit des restes d'étoiles les plus courants, et ils peuvent ainsi être utilisés comme moyen de datation de la galaxie. En particulier, la composition de ces objets conduit à des transitions de phase binaires ayant de lourdes répercussions sur leur temps de refroidissement. Nous avons investigué ce diagramme binaire à l'aide d'une méthode ab initio, et nous proposons de nouvelles stratégies numériques ainsi que des résultats confirmant partiellement les récents travaux dans le domaine. / A correct knowledge of dense stars and planets need an accurate determination of the thermodynamic behavior of matter in these objects. One of the most efficient approaches nowadays is to perform ab initio simulations, using both the statistical physics formalism and the density functionnal theory. This approach has shown its capabilities by reproducing many experimental data.In the first part of this thesis project, these methods are used to study planetary``ices'', found in planets such as Uranus or Neptun. We first confirmed the existing literature on water (equations of state and existence of a superionic phase); we then extended these results to denser planets, such as the so-called ``super-Jupiter''exoplanets. We reach very high pressures, until where the behavior is analytically established; this permitted us to construct a numerical fit for water in a very large temperature and pressure range. The other planetary ices (methane and ammonia) were thenstudied in the conditions of our solar system.We then considered white dwarves, and their cooling dynamics: they are the most usualstar remnants, so that they can be used as cosmochronometers. The composition of these objects lead to binary phase transitions, which can have important consequences on their cooling time. We used ab inition methods to investigate this binary diagram, and wesuggest new numerical strategies, leading to new results which partially confirm theprevious literature.

Dans la modélisation de la matière dense, et partiellement ionisée, une question importante concerne le traitement des électrons libres. Vis-à-vis des électrons liés, la nature délocalisée et non discrète de ces électrons est responsable d’une différence de traitement, qui est souvent effectuée dans les modélisations des propriétés radiatives des plasmas. Cependant, afin d’éviter les incohérences dans le calcul des spectres d’absorption, tous les électrons devraient, en principe, être décrits dans un même formalisme.Nous utilisons deux modèles variationnels d’atome-moyen : un modèle semi-classique, et un modèle quantique, qui permettent cette égalité de traitement pour tous les électrons. Nous calculons la section-efficace de photo-extinction, en appliquant le cadre de la théorie de la réponse linéaire dynamique à chacun de ces modèles d’atome dans un plasma. Pour cette étude, nous développons et utilisons une approche auto-cohérente, de type random-phase-approximation (RPA), qui, en allant au-delà de la réponse des électrons indépendants, permet d’évaluer les effets collectifs, par l’introduction de la polarisation dynamique. Cette approche s’inscrit dans le formalisme de la théorie de la fonctionnelle de la densité dépendant du temps (TDDFT), appliquée au cas d’un système atomique immergé dans un plasma.Pour les deux modèles, semi-classique et quantique, nous dérivons, et vérifions dans nos calculs, une nouvelle règle de somme, qui permet d’évaluer le dipôle atomique à partir d’un volume fini dans le plasma. Cette règle de somme s’avère être un outil de premier ordre pour le calcul des propriétés radiatives des atomes dans les plasmas denses. / In modeling dense and partially ionized matter, the treatment of the free electrons remains an important issue. Compared to bound electrons, the delocalized and non-discrete nature of these electrons is responsible to treat them differently, which is usually adopted in the modelings of radiative properties of plasmas. However, in order to avoid inconsistencies in the calculation of absorption spectra, all the electrons should be described in the same formalism.We use two variational average-atom models: a semi-classical and a quantum model, which allow this common treatment for all the electrons. We calculate the photo-extinction cross-section, by applying the framework of the linear dynamical response theory to each of these models of an atom in a plasma. For this study, we develop and use a self-consistent approach, of random-phase-approximation (RPA) type, which, while going beyond the independent electron response, permits to evaluate the collective effects by the introduction of the dynamical polarization. This approach uses the formalism of the time dependent density functional theory (TDDFT), applied in the case of an atomic system immersed in a plasma.For both models, semi-classical and quantum, we derive and verify in our calculations, a new sum rule, which allows the evaluation of the atomic dipole from a finite volume in the plasma. This sum rule turns out to be a crucial device in the calculation of radiative properties of atoms in dense plasmas.

High-intensity, short-pulse laser-solid interactions are of great importance for a number of applications and fundamental research, such as high energy density (HED) physics, laboratory astrophysics, inertial confinement fusion (ICF), particle acceleration, and ultrafast x-ray sources. X-ray spectroscopy is a powerful diagnostic tool to investigate the extreme states of matter created by these interactions. This thesis presents the development and application of x-ray spectroscopy in relativistic laser-solid interactions. Two x-ray crystal spectrometers have been developed on the DRACO and European X-ray Free Electron Laser (XFEL) facilities for the diagnosis of dense plasmas produced by ultrashort relativistic laser pulses. A high-resolution x-ray crystal spectrometer is developed at the DRACO petawatt laser, measuring the K-shell emission spectra of Ti targets ranging from cold Kα to thermal Heα lines. This spectrometer employs a spherically bent quartz crystal and adopts Johann geometry in the dispersive plane. Geometrical analysis and ray-tracing simulations are implemented, respectively, to determine the most suitable configuration and evaluate the performance of the spectrometer, showing an excellent spectral resolution of E/δE≈15000. With the quartz spectrometer, the production and transport of hot electrons as well as the heating state in the proton acceleration Ti targets can be investigated at the DRACO petawatt laser. In addition, a multipurpose imaging x-ray crystal spectrometer is developed for the HED instrument of the European XFEL. This spectrometer is designed to measure x-rays in the energy range of 4 - 10 keV, providing high-resolution, spatially-resolved spectral measurements. A toroidally bent germanium (Ge) crystal is used, allowing x-ray diffraction from the crystal to image along a one-dimensional spatial profile while spectrally resolving along the other. A detailed geometrical analysis is performed to determine the curvature of the crystal. The theoretical performance of the spectrometer in various configurations is calculated by ray-tracing simulations. The key properties of the spectrometer, including the spectral and spatial resolution, are demonstrated experimentally on different platforms. Experimental results prove that this Ge spectrometer is a powerful tool for spatially resolved measurements of x-ray emission, scattering, or absorption spectra in high energy density physics. The enhancement effect of a microstructured surface on laser absorption and characteristic Kα emission has been investigated by measuring K-shell emission from titanium (Ti) targets irradiated with high-intensity (~ 10^20 W/cm^2), sub-picosecond (500 fs) laser pulses. The experimental results indicate a modest enhancement (1.6x) of Kα emission from microstructured targets compared to flat foils, but with similar intensity and profile of Heα and Li-like satellites. Particle-in-cell (PIC) simulations are implemented to further understand the underlying physical processes in the laser interaction with both targets, interpreting the mechanisms responsible for the Kα enhancement. The reasons for the lower-than-expected enhancement of Kα emission are discussed. The rapid heating of the bulk plasma might result in the premature shutdown of Kα emission before the thermalization of hot electrons or even the end of laser pulses, suggesting that the use of Kα emission as a diagnostic of the hot-electron yield or relaxation could lead to a misinterpretation. This work reveals that an optimized microstructured target shows promise to produce high-brightness, quasi-monochromatic laser-driven x-ray sources for many probing applications. While x-ray spectroscopy has been widely used for diagnosing the internal conditions of laser-produced plasmas, it is usually very challenging to extract reliable and accurate physical information from the raw x-ray spectra, especially for time- and space-integrated spectra emitting from a range of plasma conditions. In this thesis, a complex spatio-temporally resolved analysis of time- and space-integrated x-ray emission spectroscopy from the relativistic laser plasmas is presented. Particle-in-cell (PIC) simulations using the PICLS code are performed to investigate the laser-solid interaction within a picosecond (ps). The subsequent plasma evolution is simulated with the hydrodynamic code FLASH on a larger timescale (hundreds of ps). With the outputs of PIC and hydrodynamic simulations, atomic kinetics-spectroscopy simulations using the FLYCHK, SCFLY, and ATOMIC codes are performed to generate a series of synthetic spectra. These synthetic spectra are used to reconstruct a composite emission spectrum and then compared to the measured integrated spectra. A full-time evolution of electron density, temperature, and ionization state of laser plasmas is thus extracted, and verified by the comparison between the measured and simulated spectra. By this methodology, the dynamics of ultrafast relativistic laser-plasma systems was studied. The combination of x-ray spectroscopy, atomic physics, and multi-scale (i.e. PIC and hydro-) simulations is demonstrated to be a promising method to characterize the evolution of internal conditions of laser-produced plasmas. This method can also be used as an effective benchmark or reference for these numerical simulations.