Theory of X-ray Thomson scattering in warm dense matter

This thesis presents the theoretical framework required to apply spectrally resolved x-ray Thomson scattering (XRTS) as a diagnostic method for warm dense matter. In particular, the theory is generalised to allow for the description of systems with multiple ion species where all mutual correlations are taken into account within the new approach. Supplemented with the theory presented, XRTS is now a promising diagnostics for high-energy-density matter containing different chemical elements or mixtures of different materials. The signal measured at XRTS contains the unshifted Rayleigh peak and frequency-shifted features. The first is related to elastic scattering from electrons co-moving with the ions whilst the second occurs due to scattering from free electrons and excitation/ionisation events. The focus of this thesis lies on the elastic scattering feature which requires the ion structure and the electron density around the ion as input for the theoretical modelling. The ion structure is obtained from quantum simulations (DFT-MD) and classical hypernetted-chain (HNC) equations. The analysis of the DTF-MD simulation data reveals that partial ionisation yields strong modifications of the ion-ion interactions. Similar effects are found for the form of the electron screening cloud around an ion. On the basis of the newly developed theory and structural models, multicomponent effects on the XRTS signal are studied. It is shown that the Rayleigh feature is very sensitive to the ratio of the elements in the scattering volume and their mutual correlations. These results indicate that XRTS is well-suited to probe the properties of complex materials and the process of mixing in the WDM regime. The advanced theories are finally applied to experimental spectra. The procedure allows for both extracting the basic plasma parameters and assessing the quality of the theoretical models applied. Comparisons with several experiments demonstrated that the non-collective regime (large scattering angle) is reasonably well understood whereas the collective regime (small scattering angle/long wavelength limit) still holds challenges. The collective regime is problematic as here strong correlations and screening are highly relevant and, thus, a yet unknown description for fully coupled quantum systems needs to be applied