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The electronic structure of warm dense matter has been investigated using absorption spectroscopy by looking at shifts in the K-edge position of shocked compressed parylene-C and potassium chloride. The Vulcan laser facility was used to drive double sided shocks into the embedded chlorine samples creating a warm dense matter state with compressions greater than four times solid density and temperatures of around 10 eV. This resulted in red-shifts of the K-edge energy on the order of 10 eV. Also measured are differences in the edge energy with increasing density between the two types of chlorine samples, demonstrating how the embedded environment can effect the electronic structure of the plasma under warm dense conditions. The experimental results have been reproduced well by a reformulated version of the Stewart-Pyatt model that takes into consideration dynamical processes by including an additional relaxation energy exchange between the atom and its surrounding plasma when an electron is photo-ionised from the K-shell. In addition to this good agreement with the experimental results is also observed with simulations carried out using density functional theory.

Experiments were conducted to test models of free-free absorption in warm dense aluminium by Iglesias, Shaffer et al. and Hollebon et al., Radiative heating using L-shell x-rays from a high temperature palladium plasma was used to heat an aluminium foil to a temperature of 0.9±0.23eV. Before the sample could significantly decompress, it was then probed using an XUV beam generated by HHG from a 1.5ps optical laser, with photon energies of 21eV, 26eV and 31eV. This XUV beam propagated to a grating spectrometer, which allowed the opacity of each sample foil to be measured at multiple photon energies simultaneously. A modelling code was created to simulate the diffraction of the XUV beam around the sample, which allowed both the transmission and refraction-induced phase shift to be measured very precisely for each sample. From these, the real refractive index and attenuation coefficient can be measured, along with estimates of the experimental error. The opacity of the WDM was found to be closest to the predictions by Iglesias and Hollebon, and followed a similar trend with photon energy, though was still lower than predicted by 2 error bars. The measurements were significantly higher than the predictions by Shaffer et al, and were not consistent with the predictions of a weak dependence on photon energy in this range. Refractive index measurements were inconclusive due to ambiguity in the measurements of the phase shift, though this proved valuable as a proof-of-concept for future work. The analysis methods used here are a significant advancement over those used in previous work. One of these is to the diffraction modelling code; the ability to model phase shift of the light passing through the sample has been developed and allows the real part of the sample's refractive index to be measured for the first time. The error analysis methods are now done in a more systematic manner, allowing for more confidence in the error estimates at each stage of the process. The experiment design was also improved, resulting in additional data being collected that was not possible previously, more samples being measured, and more confidence in some of the assumptions that were required for the analysis. These factors allow for higher confidence in the final bulk property measurements than in the previous work on this project by Kettle et al., despite the similar error estimates.

Quantum plasmas arise in a range of physical contexts, from planetary interiors to Inertial Confinement Fusion experiments. We require sophisticated numerical approaches to find the structural and dynamic properties of these complex, many-body quantum systems; diverse in accuracy and applicability, these computational approaches each have their own strengths and (often ignored) weaknesses. By combining existing techniques with newly developed algorithms, this thesis addresses some weaknesses that are common to many state-of-the-art calculation methods for quantum plasmas, and opens up paths to calculating properties that were not previously accessible. The focus of the thesis is a method based on Bohmian mechanics for dynamic structure calculations; alongside this, stochastic gradient Markov Chain Monte Carlo methods are developed for inferring plasma properties from experimental data.

The warm dense matter regime (WDM), defined by temperatures of a few electron volts and densities comparable with solids, is a complex state of matter where multi-body particle correlations and quantum effects play an important role in determining the overall structure and equation of state. The study of WDM states represents the laboratory analogue of the astrophysical environments found in the cores of planets and in the crusts of old stars, but also has practical applications for controlled thermonuclear fusion. Time resolved X-ray diffraction is used to study the temporal evolution of a sample from solid state towards WDM, either after irradiation with an intense proton/electron beam, in carbon samples, or direct laser illumination, in thin gold nanofoils. The electron-ion equilibration time is extracted through the use of the two-temperature model and in highly excited carbon shown to be longer than previously thought, this is attributed to strong ion-ion coupling screening the interaction (coupled mode theory). Calculation of the dynamic ion-ion structure factor is performed using orbital-free density functional theory (OF-DFT) and shown to compare well with Kohn-Sham DFT in both the static and dynamic cases. Experimental verification of these results is vital and measurement of the microscopic dynamics of warm dense aluminium have been successfully demonstrated through inelastic X-ray scattering. Using the self-seeded beam at the linear coherent light source (LCLS) scattering at a small momentum exchange allowed the first direct measurement of ion acoustic waves in WDM. This data provides the basis for a direct experimental test of many dense plasma theories through direct comparison with the ion-ion dynamic structure factor.

Detailed understanding of the equation of state of light elements such as the hydrogen isotopes in the warm dense matter (WDM) regime is essential for the modeling of the inner structure of many astrophysical objects, in particular Jovian planets as well as inertial confinement fusion (ICF) research. In these systems quantum degeneracy and strong inter-particle forces play an important role making its theoretical description extremely challenging. The Omega laser was used to drive a planar shock wave in cryogenically cooled deuterium creating WDM conditions. We used a set of independent diagnostics to measure the thermodynamic conditions of WDM including velocity interferometry (VISAR), streaked optical pyrometry (SOP) and x-ray Thomson scattering (XRTS). With a narrow-band x-ray backlighter probe at backscattering geometry the spectrally resolved XRTS accessed the boundary of collective and non-collective regimes making our measurement sensitive to both electron temperature and density. This work presents a full set of measurements of the thermodynamic properties for different laser intensity drives creating warm dense deuterium at various degrees of degeneracy and coupling. The measured electron densities and temperatures ranged between 0.2 and 2.15x1023 cm−3 and 0.6 − 20 eV respectively. The scattering measurement confirmed the findings from the VISAR and SOP data and together densityfunctional molecular dynamics (DFT-MD) simulations provides a novel self-consistent approach for an accurate characterization of the microscopic structure of WDM. Complementary to the laser compression work, findings from project employing static compression hydrogen with the use of diamond anvil cells is also be presented. The first direct measurement of the local field correction to the Coulomb interactions in degenerate plasma was obtained from inelastic scattering (20 keV probe) at the Diamond Light Source synchrotron facility.

Warm dense matter (WDM) is characterized as having temperatures above about 11 605 K and roughly solid densities. Occupying a region in phase space somewhere between hot, sparse plasmas and cool, condensed matter, WDM conditions exist within astrophysical objects, and are created for fractions of a second in inertial confinement fusion (ICF) and laboratory astrophysics experiments. Furthermore, designing and interpreting results from high energy density (HED) laboratory experiments often relies on simulating the complex plasma and material evolution with sophisticated radiation- or magneto- hydrodynamics (R/MHD) codes. In turn, the accuracy of R/MHD simulations rely on detailed descriptions of the material properties like transport coefficients, stopping powers, scattering and absorption spectra, and many other quantities in the WDM regime. However, competing physical effects, like partial ionization, correlated ion behavior, and quantum degeneracy makes model- ing WDM challenging and often computationally expensive. In this thesis, we develop efficient approximate-physics models to describe the unbound, free-electron behavior for WDM. We rely on the dielectric formalism, an approach that has historically been used in this field and show how it can be modified by incorporating electron-ion collision rates from a self-consistent average atom model (AA). We focus on two quantities of interest in the WDM and HED communities: the plasmon peak in the dynamic structure factor (DSF), which can be observed in x-ray Thomson scattering experiments; and the electronic stopping power, which is important for self-heating in ICF. Our results indicate that using collision rates that account for inelastic and strong scattering interactions, ion-ion correlations, and a non-ideal density of states greatly improves agreement with experiments and ab initio theories versus the commonly used Born-based collision theories. Finally, we explore the use of Bayesian statistics to infer dynamic collision rates based on first-principles DSF data, which can qualitatively inform the collisional theories implemented in the AA model. We also show how these methods can use DSF data to bound fundamental transport quantities that are difficult to measure experimentally, like the zero-frequency (DC) electrical conductivity, but find that even in a noise-free case, these bounds are over an order-of-magnitude wide.

Warm Dense Matter (WDM) can be found in a myriad of useful and worthwhile applications, whether it be in the ongoing study of inertial confinement fusion, novel shock experiments, or planetary interiors. One crucial tool that has revolutionized our understanding of WDM over the last few decades has been Finite-Temperature Density Functional Theory (FT-DFT), which has enabled various groundbreaking simulations in the field (often when experimental studies were too difficult and costly to be performed). Although successful, modern implementations of FT-DFT suffer from significant drawbacks, namely the large computational burden inherent to studying high-temperature materials, and the lack of sophisticated approximations describing temperature-dependent exchange-correlation interactions. The research contained in this dissertation works to address these fundamental challenges both directly and indirectly.Chapter 2 serves as an introduction to the underlying theorems of ground-state DFT, all of which extend to nonzero temperatures, and are depicted through illustrative examples using the Hubbard dimer. Chapter 3 introduces Density-Corrected DFT, a novel theory studying the origin of errors in functional approximations, and a means of analysis for approximations in both the ground state and at finite temperatures.Chapter 4 derives exact conditions for Ensemble Density Functional Theory, all of which provide insight into the behavior of temperature-dependent exact conditions for FT-DFT. Chapter 5 proposes a novel temperature-dependent generalized gradient approximation, the locally thermal Perdew–Burke–Ernzerhof (ltPBE) approximation, for FT-DFT calculations of WDM. This temperature-dependent approximation is the first of its kind, with its origin rooted entirely in a model of the PBE gradient-dependent exchange-correlation hole density at nonzero temperatures.Lastly, Chapter 6 discusses how Tensor Processing Units (hardware that was originally designed to perform machine-learning tasks) has been repurposed to perform highly efficient Kohn-Sham DFT calculations. This in particular has significant impact on future studies of WDM, where high temperatures greatly increase the computational cost of calculations.

Recent experiments observing the development of extreme-density plasmas led to a more careful and detailed look at assumptions made for low-density plasmas. As plasma approaches the warm dense matter regime, the physics change significantly, which necessitates novel computational methods that relax some preliminary assumptions made for low-density plasmas. One such example is the ideal plasma approximation, which is not adequately accurate at high pressures. In this dissertation, the development of a particle-in-cell Monte Carlo-collision (PIC-MCC) computational model for strongly ionized non-ideal plasmas is presented. The model is established to investigate the interaction of electromagnetic waves and dense plasmas at high pressures, and study the second-stage wave-heating that results from this interaction. The main focus is on establishing a valid plasma chemistry for extreme-density, non-ideal, strongly ionized plasmas; which differs drastically from established chemistry mechanisms for low-density plasmas. Plasma non-ideality resulting from Coulomb coupling at high plasma densities is manifested as a depression in the effective ionization potential of atoms and enhanced collision cross sections. Using a one-dimensional PIC-MCC model, full ionization of the plasma is found to occur on the picosecond timescale, with the plasma non-ideality resulting in more rapid ionization compared to an ideal plasma, especially at higher pressures. Moreover, the significance of excited states is reflected in the ionization process with a stepwise ionization reaction. This additional pathway is revealed as a very important mechanism for plasma generation that speeds up the process to reach full ionization. Next, the one-dimensional PIC-MCC model is parallelized using the shared-memory parallelization library OpenMP to increase the code performance by decreasing the run time by ~60%. Finally, the one-dimensional model is extended to two dimensions to capture geometrically more complicated discharges and their interactions with generalized electromagnetic waves.

Quantitative electron beam-target interaction studies on the Dual-Axis Radiographic Hydrodynamic Test (DARHT) electron linear induction accelerators have only been performed recently. This includes characterization of the temperature, density, pressure, extent, and expansion velocity of the plasma plume. The results presented in this dissertation present a detailed and unified overview of the accelerator systems, target heating physics, beam transport, and diagnostic tools. Additional information includes calibration sources, radiation hydrodynamics, spectroscopic-qual-ity radiation transport modeling, experimental measurements, and analyses of electron beam driven aluminum experiments. The first set of spatially and temporally resolved spectroscopic measurements of electron beam driven aluminum are presented. Contamination quantification analyses are used to understand the origin of the strong Na-I 3p-3s lines that are observed in absorption within the aluminum plasma continuum. These results inform the creation of the first spectroscopic-quality radiation transport model that links several atomic physics codes to interpret the conditions from which the Na-I lines originate. A good agreement is found between the surface analysis results and the model which confirms the concentration of the sodium present within the aluminum alloy foil material. It also demonstrates, for the first time on electron beam-driven target experiments, the ability to interpret plasma conditions from measured absorption lines. In a second experimental campaign which focuses on pure aluminum, the Al-I 3p-4s and 3p-3d doublets are both measured in emission. A detailed analysis of the Al-I 3p-4s doublet reveals that the lines undergo moderate self-absorption. A simple model of the self-absorption effect is successfully used to match measured spectra at various temperature/density/plasma scale length combinations. These measurements led to the realization of the minimum density that can be resolved by the spectrometers for the Al-I 3p-4s lines due to the large slit width required to observe a signal on aluminum. These measurements also demonstrate the sensitivity of visible and long wave UV spectroscopy to minor changes in both temperature and density. The simple self-absorption model will be useful for analysis of other beam-target interaction experiments with spectra exhibiting either self-absorption or full self-reversal. Substantial headway has been made on the modeling front by linking together several codes needed to model both the energy deposition, hydrodynamic motion, and atomic kinetics to produce synthetic spectral calculations that are compared with experimental measurements. There exists ample space for improvement, especially with benchmarking the hydrodynamics codes and equation-of-state tables with experimental measurements. The X-ray diagnostics required to make these new measurements along with the simulation capabilities required to interpret the results are under development and will be the subject of future studies.

This dissertation is an accumulation of my contribution to the fundamental understanding of ensemble Density Functional Theory and finite temperature Density Functional Theory, through the use of quantum model systems. Ensemble DFT is a time-independent method to extracting excitation energies, and provides a way to extract multiple excitations. Currently this is not possible with the common approximations used in time-dependent DFT. Chapter 3 of this thesis covers ensemble DFT and verifies an exact exchange approximation that can accurately capture multiple excitations using the Hubbard model. Finite temperature DFT is often incorrectly confused with ensemble DFT, and refers to DFT at non zero temperatures. Its value comes from its applications to warm dense matter simulations. The last three chapters of this dissertation contain several projects in the hopes of improving the understanding of finite temperature DFT. In particular it generalizes the PPLB derivative discontinuity model to finite temperatures, and discusses the construction of an exact finite temperature approximation. These contributions are done with the intention on enhancing warm dense simulations.

The hydrodynamic motion of warm dense matter produced by intense electrons is being experimentally studied on the Dual-Axis Radiographic Hydrodynamic Test Facility (DARHT). Experimental results are compared to hydrodynamic simulation codes for verification. Copper and titanium foils of varying thickness are heated in two stages, the first being isochoric, by an electron bunch with ~100 ns pulse length, energy of 19.8 MeV, current of 1.7 kA, and beam spot size of 2 mm. Aluminum, nickel, and carbon are heated in a similar fashion, but with a current of ~1.44 kA and beam spot size of 1 mm. The corresponding hydrodynamic motion of the foils during energy deposition is measured instantaneously with photonic Doppler velocimetry (PDV). The PDV diagnostic provides time-resolved measurement of the foil velocity, inferred pressure in the foil, and hydrodynamic disassembly time. The 1-D hydrodynamic HELIOS-CR code models the electron energy deposition on these foils. Calculated results of foil velocity and plasma pressure profiles are then compared to experimental results and 2-D hydrodynamics simulations with LASNEX. These parametric studies are crucial in understanding the evolution of warm dense matter during energy deposition, and optimizing electron-target interactions that improve the Bremsstrahlung targets and radiographic spot size capabilities on DARHT.

High energy density physics (HEDP) is an emerging field that seeks to investigate the properties of matter at extreme conditions. High energy density conditions occur in materials with pressures exceeding 1 Mbar, or pressures that exceed Earth’s atmospheric pressure by a factor of more than a million. A regime of HEDP of particular interest is warm dense matter (WDM) physics, which describes the behavior of materials at near solid densities and 10’s of eV temperatures. WDM occurs in astrophysical objects, such as giant planets and brown dwarfs, and is also generated in inertial confinement fusion (ICF) experiments. X-ray Thomson scattering (XRTS) offers a powerful tool to probe the equation of state of WDM. XRTS spectra consist of two components: elastically scattered photons with the frequency of the original x-ray source and inelastically scattered photons that are down- shifted in frequency. The Compton-shifted profile of inelastically scattered x-rays can be analyzed to return the sample’s electron density and electron temperature. The ratio of elastically to inelastically scattered x-rays relates to the number of tightly bound versus free electrons, and thus reflects the ionization state.This thesis discusses the results of XRTS experiments on WDM performed at the OMEGA Laser facility. The first experiment presents and discusses XRTS results from 1 mm diamond spheres. The scattering spectra show evidence of higher ionization than predicted by several commonly-applied ionization models. A second experiment analyzed the contributions to elastic scattering from a small argon impurity in imploding beryllium capsules. The exper- iment found that less than 1 at.% of argon significantly affects the elastic scattering signal strength, and concluded that impurities in a sample should be considered before drawing conclusions from elastic scattering signals. The final experiment uses XRTS to measure the electron temperature and ionization state in isochorically heated materials used in ion stopping power experiments. The results from these experiments demonstrate the power of XRTS to measure ionization in WDM to benchmark theoretical modeling.

In this dissertation, I introduce both ground-state and thermal density functional theory. Throughout I use the asymmetric two-site Hubbard model, called the Hubbard dimer for short, to better understand and/or develop these theories. This model is used because it can be solved analytically and it contains all the necessary physics while still being conceptually simple enough to tease apart the various aspects of density functional theory. Ground-statedensity functional theory has seen broad use in many disciplines including physics, chemistry, geology, and material science and has led to a number of important physical and technological successes. In the first two chapters I elucidate the behavior of the ground-state theory using the Hubbard dimer. The simplicity of the model allows me to showcase aspects of the theory that are common points of confusion within the electronic structure community, e.g. the fundamental gap problem. The next two chapters focus on thermal density functional theory which has been coming to prominence as the study of warm dense matter has becomea growing interest at the national laboratories and in the astronomical body community. The Hubbard dimer allows me to do the first ever exact thermal density functional theory calculation. In this work I am better able to understand the approximations used in thermal density functional theory and can point to why they succeed and fail. This also allows me to illustrate old conditions and derive new ones. I conclude with an overview of the work and a few different directions in which the asymmetric Hubbard dimer could be used further.

High intensity lasers interacting with an overdense target can accelerate high energy (“hot”) electrons at currents that would far exceed the Alfven limit. Hot electron propagation can be inhibited when bulk electron motion is unable to provide a return current such that the total current is nearly zero. The ability of the material to generate a sufficient return current, and permit propagation of the non-collisional hot electrons, is strongly affected by the material conductivity. Here we present an experimental study of the interplay between the conductivity of strongly heated solid density matter and the propagation of laser accelerated hot electrons. We diagnose the hot electrons by imaging the coherent transition radiation(CTR) generated from the target’s back surface into vacuum. The 1ω and 2ω harmonics of the CTR were imaged using a 10x microscope objective to CCD cameras. The spatial profile and energy emitted at the rear surface were evaluated, showing marked differences between high and low conductive materials. The conductivity is changed through both target temperature and material selection. CTR images of electrons propagating in high conductive targets, aluminum, displayed a high degree of collimation and a spot size 2.5x smaller than the focal spot. In contrast, CTR images from low conductive target exhibited significant expansion of the electron beam. Electron propagation through the dielectric experienced 2x divergence on average compared to the aluminum. The 1ω and 2ω CTR images of heated aluminum were both 1.2 times greater area on average than the corresponding unheated spot sizes. Evaluating the energy contained in a 7.5 x 7.5 micron square, the unheated targets have 1.6x more energy for 1ω and 2x greater for 2ω on average. The reduction in material conductivity produces an electrostatic field opposing the hot electron beam leading to a reduction in energy and increased divergence of the electron beam.

Warm dense matter (WDM) is a high energy phase between solids and plasmas, with characteristics of both. It is present in the centers of giant planets, within the earth's core, and on the path to ignition of inertial confinement fusion. The high temperatures and pressures of warm dense matter lead to complications in its simulation, as both classical and quantum effects must be included. One of the most successful simulation methods is density functional theory-molecular dynamics (DFT-MD). Despite great success in a diverse array of applications, DFT-MD remains computationally expensive and it neglects the explicit temperature dependence of electron-electron interactions known to exist within exact DFT.Finite-temperature density functional theory (FT DFT) is an extension of the wildly successful ground-state DFT formalism via thermal ensembles, broadening its quantum mechanical treatment of electrons to include systems at non-zero temperatures. Exact mathematical conditions have been used to predict the behavior of approximations in limiting conditions and to connect FT DFT to the ground-state theory. An introduction to FT DFT is given within the context of ensemble DFT and the larger field of DFT is discussed for context.Ensemble DFT is used to describe ensembles of ground-state and excited systems. Exact conditions in ensemble DFT and the performance of approximations depend on ensemble weights. Using an inversion method, exact Kohn-Sham ensemble potentials are found and compared to approximations. The symmetry eigenstate Hartree-exchange approximation is in good agreement with exact calculations because of its inclusion of an ensemble derivative discontinuity. Since ensemble weights in FT DFT are temperature-dependent Fermi weights, this insight may help develop approximations well-suited to both ground-state and FT DFT.A novel, highly efficient approach to free energy calculations, finite-temperature potential functional theory, is derived, which has the potential to transform the simulation of warm dense matter. As a semiclassical method, it connects the normally disparate regimes of cold condensed matter physics and hot plasma physics. This orbital-free approach captures the smooth classical density envelope and quantum density oscillations that are both crucial to accurate modeling of materials where temperature and pressure effects are influential.

Abstract: Femtosecond (fs, 1fs=10^(-15)s) laser pulses are used in a variety of fields from nano-machining to the quest for fusion energy. However, knowledge of quantitative details for femtosecond laser material interaction processes is still insufficient, and many unique applications remain unexplored. The first part of this thesis describes the quantitative study of the fundamental processes in early stages of femtosecond laser excited gold. The second part discusses the investigation of a unique application using femtosecond laser to tune the silicon microring resonators. In the fundamental investigation, a single state warm dense gold was generated by isochorically heating a free standing gold thin foil of 30nm thickness with a 45fs laser pulse at 400nm. The uniform heating of such a target was confirmed by simultaneous measurement of the reflectivity from its front and rear sides with two frequency chirped probe pulses, at energy density up to ~5MJ/kg. The frequency chirped pulse probe single shot technique was developed so that the evolutions of the reflectivities from front and rear surfaces of the heated foil were mapped in frequency domain. Optical pump-probe technique was then used to study the optical properties of gold in the first several picoseconds after laser excitation. The reflectivity (R) and transmissivity (T) of the excited target were measured simultaneously, and its AC conductivity was calculated from measured R and T. Experimental results were used to benchmark the first principle calculations based Density Functional Theory (DFT) and Quantum Molecular Dynamic (QMD) simulations. In the application study, the feasibility of using femtosecond laser pulses for tuning frequency in silicon microring resonators (SMR) was investigated. Due to fabrication imperfection, the designed resonant frequencies of SMRs are difficult to achieve accurately (e.g. 1nm variation in height can result in an SMR out of tune). It has been demonstrated that femtosecond laser pulses can tune the resonant frequency of SMRs permanently to either shorter or longer wavelengths, and controllable tuning is also possible.

This thesis examines the equation of state of copper at Warm Dense Matter states, between 1-100 eV and .1-10 times solid density. Protons accelerated off a thin metal foil irradiated with a high intensity laser beam flash heat solid density copper to between 5-10 eV before significant expansion occurs. The measured temperature and expansion are compared against simulations using various equations of states. The production and characterization of the laser system and proton beam used to heat the matter is also presented.