Dielectronic satellite emission from a solid-density Mg plasma: Relationship to models of ionization potential depression.

We report on experiments where solid-density Mg plasmas are created by heating with the focused output of the Linac Coherent Light Source x-ray free-electron laser. We study the K-shell emission from the helium- and lithium-like ions using Bragg crystal spectroscopy. Observation of the dielectronic satellites in lithium-like ions confirms that the M-shell electrons appear bound for these high charge states. An analysis of the intensity of these satellites indicates that when modeled with an atomic-kinetics code, the ionization potential depression model employed needs to produce depressions for these ions which lie between those predicted by the well known Stewart-Pyatt and Ecker-Kroll models. These results are largely consistent with recent density functional theory calculations.

Learning the Exchange-Correlation Functional from Nature with Fully Differentiable Density Functional Theory.

Improving the predictive capability of molecular properties in ab initio simulations is essential for advanced material discovery. Despite recent progress making use of machine learning, utilizing deep neural networks to improve quantum chemistry modeling remains severely limited by the scarcity and heterogeneity of appropriate experimental data. Here we show how training a neural network to replace the exchange-correlation functional within a fully differentiable three-dimensional Kohn-Sham density functional theory framework can greatly improve simulation accuracy. Using only eight experimental data points on diatomic molecules, our trained exchange-correlation networks enable improved prediction accuracy of atomization energies across a collection of 104 molecules containing new bonds, and atoms, that are not present in the training dataset.

Probing the Electronic Structure of Warm Dense Nickel via Resonant Inelastic X-Ray Scattering.

The development of bright free-electron lasers (FEL) has revolutionized our ability to create and study matter in the high-energy-density (HED) regime. Current diagnostic techniques have been successful in yielding information on fundamental thermodynamic plasma properties, but provide only limited or indirect information on the detailed quantum structure of these systems, and on how it is affected by ionization dynamics. Here we show how the valence electronic structure of solid-density nickel, heated to temperatures of around 10 of eV on femtosecond timescales, can be probed by single-shot resonant inelastic x-ray scattering (RIXS) at the Linac Coherent Light Source FEL. The RIXS spectrum provides a wealth of information on the HED system that goes well beyond what can be extracted from x-ray absorption or emission spectroscopy alone, and is particularly well suited to time-resolved studies of electronic-structure dynamics.

Time-Resolved XUV Opacity Measurements of Warm Dense Aluminum.

The free-free opacity in plasmas is fundamental to our understanding of energy transport in stellar interiors and for inertial confinement fusion research. However, theoretical predictions in the challenging dense plasma regime are conflicting and there is a dearth of accurate experimental data to allow for direct model validation. Here we present time-resolved transmission measurements in solid-density Al heated by an XUV free-electron laser. We use a novel functional optimization approach to extract the temperature-dependent absorption coefficient directly from an oversampled pool of single-shot measurements, and find a pronounced enhancement of the opacity as the plasma is heated to temperatures of order of the Fermi energy. Plasma heating and opacity enhancement are observed on ultrafast timescales, within the duration of the femtosecond XUV pulse. We attribute further rises in the opacity on ps timescales to melt and the formation of warm dense matter.

Ab initio simulations and measurements of the free-free opacity in aluminum.

The free-free opacity in dense systems is a property that both tests our fundamental understanding of correlated many-body systems, and is needed to understand the radiative properties of high energy-density plasmas. Despite its importance, predictive calculations of the free-free opacity remain challenging even in the condensed matter phase for simple metals. Here we show how the free-free opacity can be modelled at finite-temperatures via time-dependent density functional theory, and illustrate the importance of including local field corrections, core polarization, and self-energy corrections. Our calculations for ground-state Al are shown to agree well with experimental opacity measurements performed on the Artemis laser facility across a wide range of extreme ultraviolet wavelengths. We extend our calculations across the melt to the warm-dense matter regime, finding good agreement with advanced plasma models based on inverse bremsstrahlung at temperatures above 10 eV.

Retrieving fields from proton radiography without source profiles.

Proton radiography is a technique in high-energy density science to diagnose magnetic and/or electric fields in a plasma by firing a proton beam and detecting its modulated intensity profile on a screen. Current approaches to retrieve the integrated field from the modulated intensity profile require the unmodulated beam intensity profile before the interaction, which is rarely available experimentally due to shot-to-shot variability. In this paper, we present a statistical method to retrieve the integrated field without needing to know the exact source profile. We apply our method to experimental data, showing the robustness of our approach. Our proposed technique allows for the retrieval not only of the path-integrated fields, but also of the statistical properties of the fields.

Validating Continuum Lowering Models via Multi-Wavelength Measurements of Integrated X-ray Emission.

X-ray emission spectroscopy is a well-established technique used to study continuum lowering in dense plasmas. It relies on accurate atomic physics models to robustly reproduce high-resolution emission spectra, and depends on our ability to identify spectroscopic signatures such as emission lines or ionization edges of individual charge states within the plasma. Here we describe a method that forgoes these requirements, enabling the validation of different continuum lowering models based solely on the total intensity of plasma emission in systems driven by narrow-bandwidth x-ray pulses across a range of wavelengths. The method is tested on published Al spectroscopy data and applied to the new case of solid-density partially-ionized Fe plasmas, where extracting ionization edges directly is precluded by the significant overlap of emission from a wide range of charge states.

Clocking Femtosecond Collisional Dynamics via Resonant X-Ray Spectroscopy.

Electron-ion collisional dynamics is of fundamental importance in determining plasma transport properties, nonequilibrium plasma evolution, and electron damage in diffraction imaging applications using bright x-ray free-electron lasers (FELs). Here we describe the first experimental measurements of ultrafast electron impact collisional ionization dynamics using resonant core-hole spectroscopy in a solid-density magnesium plasma, created and diagnosed with the Linac Coherent Light Source x-ray FEL. By resonantly pumping the 1s→2p transition in highly charged ions within an optically thin plasma, we have measured how off-resonance charge states are populated via collisional processes on femtosecond time scales. We present a collisional cross section model that matches our results and demonstrates how the cross sections are enhanced by dense-plasma effects including continuum lowering. Nonlocal thermodynamic equilibrium collisional radiative simulations show excellent agreement with the experimental results and provide new insight on collisional ionization and three-body-recombination processes in the dense-plasma regime.

Short-wavelength free-electron laser sources and science: a review.

This review is focused on free-electron lasers (FELs) in the hard to soft x-ray regime. The aim is to provide newcomers to the area with insights into: the basic physics of FELs, the qualities of the radiation they produce, the challenges of transmitting that radiation to end users and the diversity of current scientific applications. Initial consideration is given to FEL theory in order to provide the foundation for discussion of FEL output properties and the technical challenges of short-wavelength FELs. This is followed by an overview of existing x-ray FEL facilities, future facilities and FEL frontiers. To provide a context for information in the above sections, a detailed comparison of the photon pulse characteristics of FEL sources with those of other sources of high brightness x-rays is made. A brief summary of FEL beamline design and photon diagnostics then precedes an overview of FEL scientific applications. Recent highlights are covered in sections on structural biology, atomic and molecular physics, photochemistry, non-linear spectroscopy, shock physics, solid density plasmas. A short industrial perspective is also included to emphasise potential in this area.

Observation of Reverse Saturable Absorption of an X-ray Laser.

A nonlinear absorber in which the excited state absorption is larger than the ground state can undergo a process called reverse saturable absorption. It is a well-known phenomenon in laser physics in the optical regime, but is more difficult to generate in the x-ray regime, where fast nonradiative core electron transitions typically dominate the population kinetics during light matter interactions. Here, we report the first observation of decreasing x-ray transmission in a solid target pumped by intense x-ray free electron laser pulses. The measurement has been made below the K-absorption edge of aluminum, and the x-ray intensity ranges are 10^{16} -10^{17} W/cm^{2}. It has been confirmed by collisional radiative population kinetic calculations, underscoring the fast spectral modulation of the x-ray pulses and charge states relevant to the absorption and transmission of x-ray photons. The processes shown through detailed simulations are consistent with reverse saturable absorption, which would be the first observation of this phenomena in the x-ray regime. These light matter interactions provide a unique opportunity to investigate optical transport properties in the extreme state of matters, as well as affording the potential to regulate ultrafast x-ray free-electron laser pulses.

Measurements of the K-Shell Opacity of a Solid-Density Magnesium Plasma Heated by an X-Ray Free-Electron Laser.

We present measurements of the spectrally resolved x rays emitted from solid-density magnesium targets of varying sub-µm thicknesses isochorically heated by an x-ray laser. The data exhibit a largely thickness-independent source function, allowing the extraction of a measure of the opacity to K-shell x rays within well-defined regimes of electron density and temperature, extremely close to local thermodynamic equilibrium conditions. The deduced opacities at the peak of the Kα transitions of the ions are consistent with those predicted by detailed atomic-kinetics calculations.

Measurements of continuum lowering in solid-density plasmas created from elements and compounds.

The effect of a dense plasma environment on the energy levels of an embedded ion is usually described in terms of the lowering of its continuum level. For strongly coupled plasmas, the phenomenon is intimately related to the equation of state; hence, an accurate treatment is crucial for most astrophysical and inertial-fusion applications, where the case of plasma mixtures is of particular interest. Here we present an experiment showing that the standard density-dependent analytical models are inadequate to describe solid-density plasmas at the temperatures studied, where the reduction of the binding energies for a given species is unaffected by the different plasma environment (ion density) in either the element or compounds of that species, and can be accurately estimated by calculations only involving the energy levels of an isolated neutral atom. The results have implications for the standard approaches to the equation of state calculations.

Investigation of femtosecond collisional ionization rates in a solid-density aluminium plasma.

The rate at which atoms and ions within a plasma are further ionized by collisions with the free electrons is a fundamental parameter that dictates the dynamics of plasma systems at intermediate and high densities. While collision rates are well known experimentally in a few dilute systems, similar measurements for nonideal plasmas at densities approaching or exceeding those of solids remain elusive. Here we describe a spectroscopic method to study collision rates in solid-density aluminium plasmas created and diagnosed using the Linac Coherent light Source free-electron X-ray laser, tuned to specific interaction pathways around the absorption edges of ionic charge states. We estimate the rate of collisional ionization in solid-density aluminium plasmas at temperatures ~30 eV to be several times higher than that predicted by standard semiempirical models.

Saturable absorption of an x-ray free-electron-laser heated solid-density aluminum plasma.

High-intensity x-ray pulses from an x-ray free-electron laser are used to heat and probe a solid-density aluminum sample. The photon-energy-dependent transmission of the heating beam is studied through the use of a photodiode. Saturable absorption is observed, with the resulting transmission differing significantly from the cold case, in good agreement with atomic-kinetics simulations.

Evidence for a glassy state in strongly driven carbon.

Here, we report results of an experiment creating a transient, highly correlated carbon state using a combination of optical and x-ray lasers. Scattered x-rays reveal a highly ordered state with an electrostatic energy significantly exceeding the thermal energy of the ions. Strong Coulomb forces are predicted to induce nucleation into a crystalline ion structure within a few picoseconds. However, we observe no evidence of such phase transition after several tens of picoseconds but strong indications for an over-correlated fluid state. The experiment suggests a much slower nucleation and points to an intermediate glassy state where the ions are frozen close to their original positions in the fluid.

Density functional theory calculations of continuum lowering in strongly coupled plasmas.

An accurate description of the ionization potential depression of ions in plasmas due to their interaction with the environment is a fundamental problem in plasma physics, playing a key role in determining the ionization balance, charge state distribution, opacity and plasma equation of state. Here we present a method to study the structure and position of the continuum of highly ionized dense plasmas using finite-temperature density functional theory in combination with excited-state projector augmented-wave potentials. The method is applied to aluminium plasmas created by intense X-ray irradiation, and shows excellent agreement with recently obtained experimental results. We find that the continuum lowering for ions in dense plasmas at intermediate temperatures is larger than predicted by standard plasma models and explain this effect through the electronic structure of the valence states in these strong-coupling conditions.

Direct measurements of the ionization potential depression in a dense plasma.

We have used the Linac Coherent Light Source to generate solid-density aluminum plasmas at temperatures of up to 180 eV. By varying the photon energy of the x rays that both create and probe the plasma, and observing the K-α fluorescence, we can directly measure the position of the K edge of the highly charged ions within the system. The results are found to disagree with the predictions of the extensively used Stewart-Pyatt model, but are consistent with the earlier model of Ecker and Kröll, which predicts significantly greater depression of the ionization potential.

Creation and diagnosis of a solid-density plasma with an X-ray free-electron laser.

Matter with a high energy density (>10(5) joules per cm(3)) is prevalent throughout the Universe, being present in all types of stars and towards the centre of the giant planets; it is also relevant for inertial confinement fusion. Its thermodynamic and transport properties are challenging to measure, requiring the creation of sufficiently long-lived samples at homogeneous temperatures and densities. With the advent of the Linac Coherent Light Source (LCLS) X-ray laser, high-intensity radiation (>10(17) watts per cm(2), previously the domain of optical lasers) can be produced at X-ray wavelengths. The interaction of single atoms with such intense X-rays has recently been investigated. An understanding of the contrasting case of intense X-ray interaction with dense systems is important from a fundamental viewpoint and for applications. Here we report the experimental creation of a solid-density plasma at temperatures in excess of 10(6) kelvin on inertial-confinement timescales using an X-ray free-electron laser. We discuss the pertinent physics of the intense X-ray-matter interactions, and illustrate the importance of electron-ion collisions. Detailed simulations of the interaction process conducted with a radiative-collisional code show good qualitative agreement with the experimental results. We obtain insights into the evolution of the charge state distribution of the system, the electron density and temperature, and the timescales of collisional processes. Our results should inform future high-intensity X-ray experiments involving dense samples, such as X-ray diffractive imaging of biological systems, material science investigations, and the study of matter in extreme conditions.

Resonant Kα spectroscopy of solid-density aluminum plasmas.

The x-ray intensities made available by x-ray free electron lasers (FEL) open up new x-ray matter interaction channels not accessible with previous sources. We report here on the resonant generation of Kα emission, that is to say the production of copious Kα radiation by tuning the x-ray FEL pulse to photon energies below that of the K edge of a solid aluminum sample. The sequential absorption of multiple photons in the same atom during the 80 fs pulse, with photons creating L-shell holes and then one resonantly exciting a K-shell electron into one of these holes, opens up a channel for the Kα production, as well as the absorption of further photons. We demonstrate rich spectra of such channels, and investigate the emission produced by tuning the FEL energy to the K-L transitions of those highly charged ions that have transition energies below the K edge of the cold material. The spectra are sensitive to x-ray intensity dependent opacity effects, with ions containing L-shell holes readily reabsorbing the Kα radiation.

Decay of cystalline order and equilibration during the solid-to-plasma transition induced by 20-fs microfocused 92-eV free-electron-laser pulses.

We have studied a solid-to-plasma transition by irradiating Al foils with the FLASH free electron laser at intensities up to 10(16) W/cm(2). Intense XUV self-emission shows spectral features that are consistent with emission from regions of high density, which go beyond single inner-shell photoionization of solids. Characteristic features of intrashell transitions allowed us to identify Auger heating of the electrons in the conduction band occurring immediately after the absorption of the XUV laser energy as the dominant mechanism. A simple model of a multicharge state inverse Auger effect is proposed to explain the target emission when the conduction band at solid density becomes more atomiclike as energy is transferred from the electrons to the ions. This allows one to determine, independent of plasma simulations, the electron temperature and density just after the decay of crystalline order and to characterize the early time evolution.