| Summary: | This thesis describes the development of a comprehensive and detailed theoretical framework for modelling x-ray Thomson scattering (XRTS) diagnostics for investigating dense plasmas. Throughout, the well-known description ubiquitously used for modelling XRTS experiments is modified in a novel way in order to meet the challenges arising from the latest experiments in the thriving fields of warm dense matter (WDM), high-energydensity (HED) plasmas and inertial confinement fusion (ICF) energy research. In particular, plasmas in which the electrons and ions are in non-equilibrium states are considered, relating to both momentum and energy relaxation and also spatial inhomogeneity. The theoretical basis for describing the spectrum of scattered radiation is given by a quantum statistical approach in order to be applicable to dense, strongly coupled and partially ionized plasmas. The correlation and response properties of the electrons and ions are treated using the techniques of non-equilibrium Green’s functions, such that the different contributions to the total scattering are generalised to experiments conducive to strongly non-equilibrium electron distributions. Of particular interest is the dynamic structure of the free electrons, especially in the collective scattering regime, where the mode spectrum provides a sensitive measurement of the properties of the electron gas. The non-equilibrium model is used to analyse recent data from the FLASH free-electron laser, and it is shown that a robust understanding of the data is only possible within this new framework. The model developed is also used to study and design experiments in which other forms of non-equilibrium may be present. Simplified simulations of temperature relaxation of isochorically heated targets are presented and coupled the bespoke XRTS analysis code developed in this work; the multicomponent scattering simulation (MCSS) model. The results show that spectrally- and angularly-resolved XRTS could potentially be used to perform such measurements and, moreover, assess the validity of electron-ion transfer models under challenging conditions. Furthermore, the code is also coupled to radiation hydrodynamics simulations of experiments in large-scale targets currently being developed for the National Ignition Facility. In this case, the strongly inhomogeneous state of the target, combined with other three-dimensional effects, requires a significant development of the standard approach to modelling XRTS. Finally, the MCSS code is use to analyse data from recent experiments using shockcompressed plastic. Here, the target is small enough and evolves sufficiently slowly for the well-understood equilibrium-based XRTS theories to be robust. Detailed statistical analysis of the data supports the breakdown of the well-known Debye-Hückel description of the screening properties of dense matter. Instead, a more general approach studied in this work is shown to provide a better fit. This result constitutes the first such experimental observation in dense plasmas, and is of significant interest to a wide range of fields in which charge screening is important.
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