Modeling X-Ray Thomson Scattering Spectra of Warm Dense Matter
Warm dense matter (WDM) is sometimes described as a \solid density plasma" where neither weakly coupled plasma theory nor condensed matter theory are applicable. More specifically, WDM has densities of ~ 0:1 - 50 times solid density, temperatures of ~ 1 - 100 eV, is partially ionized, globally neutral, has strongly correlated particles (due to interactions), and partial electron degeneracy. In nature, WDM may be found in the interiors of planets such as Jupiter or in the envelopes of white dwarf stars, and in man-made processes such as inertial confinement fusion (ICF), WDM exists as a transient state of matter. To model these physical systems, the equation of state as well as opacity, conductivity, and diffusion coefficients must be known. Experimentally WDM is probed with an experimental technique known as X-Ray Thomson Scattering (XRTS). In such an experiment X-rays photons are scattered off of WDM and the resulting photons are measured at a given solid angle. The resulting spectrum gives information on the density and temperature of WDM, but a model of WDM and the scattering experiment is often required to interpret the results. As a result, these experiments also serve as a method of validation for potential models of WDM. The work presented here focuses on the model of WDM proposed by Starrett and Saumon and a model for scattering based off of Chihara’s work. The model proposed by Starrett and Saumon is an average-atom model that is coupled with a two component plasma model, hereafter referred to as an AA+TCP model. The AA+TCP model is an ab initio model with no free parameters, only requiring knowledge of the element under investigation, the density, and the temperature. The outputs from the model completely determine all the input parameters needed for Chihara’s structure function (chemical potential, elastic feature, screening potential, bound-state wavefunctions, and free wavefunctions), which in turn determines the double differential scattering cross-section of the experiment. This approach to determining the outcome of an XRTS experiment parallels that of Johnson, et al., but expands the work in many respects. For example, the AA+TCP model completely determines all the input parameters to the structure function; hence no ad hoc approximations are necessary to close the system. Also, the free-electron feature and the bound-free feature are modified to include collisions and occupation of free electron states, respectively.