A measurement of the equation of state of carbon envelopes of white dwarfs.

White dwarfs represent the final state of evolution for most stars1-3. Certain classes of white dwarfs pulsate4,5, leading to observable brightness variations, and analysis of these variations with theoretical stellar models probes their internal structure. Modelling of these pulsating stars provides stringent tests of white dwarf models and a detailed picture of the outcome of the late stages of stellar evolution6. However, the high-energy-density states that exist in white dwarfs are extremely difficult to reach and to measure in the laboratory, so theoretical predictions are largely untested at these conditions. Here we report measurements of the relationship between pressure and density along the principal shock Hugoniot (equations describing the state of the sample material before and after the passage of the shock derived from conservation laws) of hydrocarbon to within five per cent. The observed maximum compressibility is consistent with theoretical models that include detailed electronic structure. This is relevant for the equation of state of matter at pressures ranging from 100 million to 450 million atmospheres, where the understanding of white dwarf physics is sensitive to the equation of state and where models differ considerably. The measurements test these equation-of-state relations that are used in the modelling of white dwarfs and inertial confinement fusion experiments7,8, and we predict an increase in compressibility due to ionization of the inner-core orbitals of carbon. We also find that a detailed treatment of the electronic structure and the electron degeneracy pressure is required to capture the measured shape of the pressure-density evolution for hydrocarbon before peak compression. Our results illuminate the equation of state of the white dwarf envelope (the region surrounding the stellar core that contains partially ionized and partially degenerate non-ideal plasmas), which is a weak link in the constitutive physics informing the structure and evolution of white dwarf stars9.

In situ X-ray diffraction of silicate liquids and glasses under dynamic and static compression to megabar pressures.

Properties of liquid silicates under high-pressure and high-temperature conditions are critical for modeling the dynamics and solidification mechanisms of the magma ocean in the early Earth, as well as for constraining entrainment of melts in the mantle and in the present-day core-mantle boundary. Here we present in situ structural measurements by X-ray diffraction of selected amorphous silicates compressed statically in diamond anvil cells (up to 157 GPa at room temperature) or dynamically by laser-generated shock compression (up to 130 GPa and 6,000 K along the MgSiO3 glass Hugoniot). The X-ray diffraction patterns of silicate glasses and liquids reveal similar characteristics over a wide pressure and temperature range. Beyond the increase in Si coordination observed at 20 GPa, we find no evidence for major structural changes occurring in the silicate melts studied up to pressures and temperatures exceeding Earth's core mantle boundary conditions. This result is supported by molecular dynamics calculations. Our findings reinforce the widely used assumption that the silicate glasses studies are appropriate structural analogs for understanding the atomic arrangement of silicate liquids at these high pressures.

Structure retrieval in liquid-phase electron scattering.

Electron scattering on liquid samples has been enabled recently by the development of ultrathin liquid sheet technologies. The data treatment of liquid-phase electron scattering has been mostly reliant on methodologies developed for gas electron diffraction, in which theoretical inputs and empirical fittings are often needed to account for the atomic form factor and remove the inelastic scattering background. In this work, we present an alternative data treatment method that is able to retrieve the radial distribution of all the charged particle pairs without the need of either theoretical inputs or empirical fittings. The merits of this new method are illustrated through the retrieval of real-space molecular structure from experimental electron scattering patterns of liquid water, carbon tetrachloride, chloroform, and dichloromethane.

High-Pressure Melt Curve and Phase Diagram of Lithium.

We investigate the phase diagram of lithium at temperatures of 200 to 400 K, to pressures over 100 GPa using x-ray diffraction in diamond anvil cells, covering the region in which the melting curve is disputed. To overcome degradation of the diamond anvils by dense lithium we utilize a rapid compression scheme taking advantage of the high flux available at modern synchrotrons. Our results show the hR1 and cI16 phases to be stable to higher temperature than previously reported. The melting minima of lithium is found to be close to room temperature between 40 and 60 GPa, below which the solid is crystalline. Analysis of the stability fields of the cI16 and oC88 phases suggest the existence of a triple point between these and an undetermined solid phase at 60 GPa between 220 and 255 K.

Self-referenced single-shot THz detection.

We demonstrate a self-referencing method to reduce noise in a single-shot terahertz detection scheme. By splitting a single terahertz pulse and using a reflective echelon, both the signal and reference terahertz time-domain waveforms were measured using one laser pulse. Simultaneous acquisition of these waveforms significantly reduces noise originating from shot-to-shot fluctuations. We show that correlation function based referencing, which is not limited to polarization dependent measurements, can achieve a noise floor that is comparable to state-of-the-art polarization-gated balanced detection. Lastly, we extract the DC conductivity of a 30 nm free-standing gold film using a single THz pulse. The measured value of σ0 = 1.3 ± 0.4 × 107 S m-1 is in good agreement with the value measured by four-point probe, indicating the viability of this method for measuring dynamical changes and small signals.

Evidence for phonon hardening in laser-excited gold using x-ray diffraction at a hard x-ray free electron laser.

Studies of laser-heated materials on femtosecond timescales have shown that the interatomic potential can be perturbed at sufficiently high laser intensities. For gold, it has been postulated to undergo a strong stiffening leading to an increase of the phonon energies, known as phonon hardening. Despite efforts to investigate this behavior, only measurements at low absorbed energy density have been performed, for which the interpretation of the experimental data remains ambiguous. By using in situ single-shot x-ray diffraction at a hard x-ray free-electron laser, the evolution of diffraction line intensities of laser-excited Au to a higher energy density provides evidence for phonon hardening.

Release dynamics of nanodiamonds created by laser-driven shock-compression of polyethylene terephthalate.

Laser-driven dynamic compression experiments of plastic materials have found surprisingly fast formation of nanodiamonds (ND) via X-ray probing. This mechanism is relevant for planetary models, but could also open efficient synthesis routes for tailored NDs. We investigate the release mechanics of compressed NDs by molecular dynamics simulation of the isotropic expansion of finite size diamond from different P-T states. Analysing the structural integrity along different release paths via molecular dynamic simulations, we found substantial disintegration rates upon shock release, increasing with the on-Hugnoiot shock temperature. We also find that recrystallization can occur after the expansion and hence during the release, depending on subsequent cooling mechanisms. Our study suggests higher ND recovery rates from off-Hugoniot states, e.g., via double-shocks, due to faster cooling. Laser-driven shock compression experiments of polyethylene terephthalate (PET) samples with in situ X-ray probing at the simulated conditions found diamond signal that persists up to 11 ns after breakout. In the diffraction pattern, we observed peak shifts, which we attribute to thermal expansion of the NDs and thus a total release of pressure, which indicates the stability of the released NDs.

X-ray Thomson scattering spectra from density functional theory molecular dynamics simulations based on a modified Chihara formula.

We study ab initio approaches for calculating x-ray Thomson scattering spectra from density functional theory molecular dynamics simulations based on a modified Chihara formula that expresses the inelastic contribution in terms of the dielectric function. We study the electronic dynamic structure factor computed from the Mermin dielectric function using an ab initio electron-ion collision frequency in comparison to computations using a linear-response time-dependent density functional theory (LR-TDDFT) framework for hydrogen and beryllium and investigate the dispersion of free-free and bound-free contributions to the scattering signal. A separate treatment of these contributions, where only the free-free part follows the Mermin dispersion, shows good agreement with LR-TDDFT results for ambient-density beryllium, but breaks down for highly compressed matter where the bound states become pressure ionized. LR-TDDFT is used to reanalyze x-ray Thomson scattering experiments on beryllium demonstrating strong deviations from the plasma conditions inferred with traditional analytic models at small scattering angles.

Intense laser interaction with micro-bars.

Intense laser fields interact very differently with micrometric rough surfaces than with flat objects. The interaction features high laser energy absorption and increased emission of MeV electrons, ions, and of hard x-rays. In this work, we irradiated isolated, translationally-symmetric objects in the form of micrometric Au bars. The interaction resulted in the emission of two forward-directed electron jets having a small opening angle, a narrow energy spread in the MeV range, and a positive angle to energy correlation. Our numerical simulations show that following ionization, those electrons that are pulled into vacuum near the object's edge, remain in-phase with the laser pulse for long enough so that the Lorentz force they experience drive them around the object's edge. After these electrons pass the object, they form attosecond duration bunches and interact with the laser field over large distances in vacuum in confined volumes that trap and accelerate them within a narrow range of momentum. The selectivity in energy of the interaction, its directionality, and the preservation of the attosecond duration of the electron bunches over large distances, offer new means for designing future laser-based light sources.

Ultra-short pulse laser acceleration of protons to 80 MeV from cryogenic hydrogen jets tailored to near-critical density.

Laser plasma-based particle accelerators attract great interest in fields where conventional accelerators reach limits based on size, cost or beam parameters. Despite the fact that particle in cell simulations have predicted several advantageous ion acceleration schemes, laser accelerators have not yet reached their full potential in producing simultaneous high-radiation doses at high particle energies. The most stringent limitation is the lack of a suitable high-repetition rate target that also provides a high degree of control of the plasma conditions required to access these advanced regimes. Here, we demonstrate that the interaction of petawatt-class laser pulses with a pre-formed micrometer-sized cryogenic hydrogen jet plasma overcomes these limitations enabling tailored density scans from the solid to the underdense regime. Our proof-of-concept experiment demonstrates that the near-critical plasma density profile produces proton energies of up to 80 MeV. Based on hydrodynamic and three-dimensional particle in cell simulations, transition between different acceleration schemes are shown, suggesting enhanced proton acceleration at the relativistic transparency front for the optimal case.

The high-pressure lithium-palladium and lithium-palladium-hydrogen systems.

The lithium-palladium and lithium-palladium-hydrogen systems are investigated at high pressures at and above room temperature. Two novel lithium-palladium compounds are found below [Formula: see text]. An ambient temperature phase is tentatively assigned as [Formula: see text], with [Formula: see text] Å at 8.64 GPa, isostructural with [Formula: see text]. The other phase occurs at high-temperature and is [Formula: see text], [Formula: see text] Å at 3.88 GPa and 200 [Formula: see text], similar to [Formula: see text], which is also known at high pressure. The presence of hydrogen in the system results in an [Formula: see text] structure with [Formula: see text] Å at 9.74 GPa. This persists up to [Formula: see text], the highest pressure studied. Below [Formula: see text] an fcc phase with a large unit cell, [Formula: see text] Å at 0.39 GPa, is also observed in the presence of hydrogen. On heating the hydrogen containing system at 4 GPa the [Formula: see text] phases persists to the melting point of lithium. In both systems melting the lithium results in the loss of crystalline diffraction from palladium containing phases. This is attributed to dissolution of the palladium in the molten lithium, and on cooling the palladium remains dispersed.

Sub-micron thick liquid sheets produced by isotropically etched glass nozzles.

We report on the design and testing of glass nozzles used to produce liquid sheets. The sheet nozzles use a single converging channel chemically etched into glass wafers by standard lithographic methods. Operation in ambient air and vacuum was demonstrated. The measured sheet thickness ranges over one order of magnitude with the smallest thickness of 250 nm and the largest of 2.5 µm. Sheet thickness was shown to be independent of liquid flow rate, and dependent on the nozzle outlet area. Sheet surface roughness was dependent on nozzle surface finish and was on the order of 10 nm for polished nozzles. Electron transmission data is presented for various sheet thicknesses near the MeV mean free path and the charge pair distribution function for D2O is determined from electron scattering data.

Off-harmonic optical probing of high intensity laser plasma expansion dynamics in solid density hydrogen jets.

Due to the non-linear nature of relativistic laser induced plasma processes, the development of laser-plasma accelerators requires precise numerical modeling. Especially high intensity laser-solid interactions are sensitive to the temporal laser rising edge and the predictive capability of simulations suffers from incomplete information on the plasma state at the onset of the relativistic interaction. Experimental diagnostics utilizing ultra-fast optical backlighters can help to ease this challenge by providing temporally resolved inside into the plasma density evolution. We present the successful implementation of an off-harmonic optical probe laser setup to investigate the interaction of a high-intensity laser at [Formula: see text] peak intensity with a solid-density cylindrical cryogenic hydrogen jet target of [Formula: see text] diameter as a target test bed. The temporal synchronization of pump and probe laser, spectral filtering and spectrally resolved data of the parasitic plasma self-emission are discussed. The probing technique mitigates detector saturation by self-emission and allowed to record a temporal scan of shadowgraphy data revealing details of the target ionization and expansion dynamics that were so far not accessible for the given laser intensity. Plasma expansion speeds of up to [Formula: see text] followed by full target transparency at [Formula: see text] after the high intensity laser peak are observed. A three dimensional particle-in-cell simulation initiated with the diagnosed target pre-expansion at [Formula: see text] and post processed by ray tracing simulations supports the experimental observations and demonstrates the capability of time resolved optical diagnostics to provide quantitative input and feedback to the numerical treatment within the time frame of the relativistic laser-plasma interaction.

Diamond formation kinetics in shock-compressed C─H─O samples recorded by small-angle x-ray scattering and x-ray diffraction.

Extreme conditions inside ice giants such as Uranus and Neptune can result in peculiar chemistry and structural transitions, e.g., the precipitation of diamonds or superionic water, as so far experimentally observed only for pure C─H and H2O systems, respectively. Here, we investigate a stoichiometric mixture of C and H2O by shock-compressing polyethylene terephthalate (PET) plastics and performing in situ x-ray probing. We observe diamond formation at pressures between 72 ± 7 and 125 ± 13 GPa at temperatures ranging from ~3500 to ~6000 K. Combining x-ray diffraction and small-angle x-ray scattering, we access the kinetics of this exotic reaction. The observed demixing of C and H2O suggests that diamond precipitation inside the ice giants is enhanced by oxygen, which can lead to isolated water and thus the formation of superionic structures relevant to the planets' magnetic fields. Moreover, our measurements indicate a way of producing nanodiamonds by simple laser-driven shock compression of cheap PET plastics.

High Pressure Brillouin Spectroscopy and X-ray Diffraction of Cerium Dioxide.

Simultaneous high-pressure Brillouin spectroscopy and powder X-ray diffraction of cerium dioxide powders are presented at room temperature to a pressure of 45 GPa. Micro- and nanocrystalline powders are studied and the density, acoustic velocities and elastic moduli determined. In contrast to recent reports of anomalous compressibility and strength in nanocrystalline cerium dioxide, the acoustic velocities are found to be insensitive to grain size and enhanced strength is not observed in nanocrystalline CeO2. Discrepancies in the bulk moduli derived from Brillouin and powder X-ray diffraction studies suggest that the properties of CeO2 are sensitive to the hydrostaticity of its environment. Our Brillouin data give the shear modulus, G0 = 63 (3) GPa, and adiabatic bulk modulus, KS0 = 142 (9) GPa, which is considerably lower than the isothermal bulk modulus, KT0∼ 230 GPa, determined by high-pressure X-ray diffraction experiments.

Cryogenic Liquid Jets for High Repetition Rate Discovery Science.

This protocol presents a detailed procedure for the operation of continuous, micron-sized cryogenic cylindrical and planar liquid jets. When operated as described here, the jet exhibits high laminarity and stability for centimeters. Successful operation of a cryogenic liquid jet in the Rayleigh regime requires a basic understanding of fluid dynamics and thermodynamics at cryogenic temperatures. Theoretical calculations and typical empirical values are provided as a guide to design a comparable system. This report identifies the importance of both cleanliness during cryogenic source assembly and stability of the cryogenic source temperature once liquefied. The system can be used for high repetition rate laser-driven proton acceleration, with an envisioned application in proton therapy. Other applications include laboratory astrophysics, materials science, and next-generation particle accelerators.

Author Correction: Generation and characterization of ultrathin free-flowing liquid sheets.

The original version of this Article contained an error in Eq. (1). This has been corrected in both the PDF and HTML versions of the Article.

Development and characterization of liquid argon and methane microjets for high-rep-rate laser-plasma experiments.

A cryogenic microjet system has been used for delivering micron-scale continuous liquid hydrogen targets for laser-plasma experiments. This technique has been extended to higher-Z, higher boiling-point gases, including argon and methane. High-resolution shadowgraphy has been used to characterize the jet's morphology and pointing stability. A split and delay illumination source has also been developed for direct measurement of jet speeds without relying on assumptions of fluid flow conditions. Under typical conditions, the argon jets freeze solid due to evaporative cooling, but the methane jets remain liquid and break up to a droplet stream. A piezo driver is used to ensure the droplets are of uniform size. This jet has enabled the investigation of methane in planetary core conditions with high-rep-rate laser heating and x-ray laser probing.

Generation and characterization of ultrathin free-flowing liquid sheets.

The physics and chemistry of liquid solutions play a central role in science, and our understanding of life on Earth. Unfortunately, key tools for interrogating aqueous systems, such as infrared and soft X-ray spectroscopy, cannot readily be applied because of strong absorption in water. Here we use gas-dynamic forces to generate free-flowing, sub-micron, liquid sheets which are two orders of magnitude thinner than anything previously reported. Optical, infrared, and X-ray spectroscopies are used to characterize the sheets, which are found to be tunable in thickness from over 1 µm  down to less than 20 nm, which corresponds to fewer than 100 water molecules thick. At this thickness, aqueous sheets can readily transmit photons across the spectrum, leading to potentially transformative applications in infrared, X-ray, electron spectroscopies and beyond. The ultrathin sheets are stable for days in vacuum, and we demonstrate their use at free-electron laser and synchrotron light sources.

Author Correction: Generation and characterization of ultrathin free-flowing liquid sheets.

The original version of this article omitted the following from the Acknowledgements:'P.B. was funded by the ELI Extreme Light Infrastructure Phase 2 (CZ.02.1.01/0.0/0.0/15008/0000162) from the European Regional Development Fund and the EUCALL project funded from the EU Horizon 2020 research and innovation programme under grant agreement No 654220,' which replaces the previous 'P.B. was funded by the ELI Extreme Light Infrastructure Phase 2 (CZ.02.1.01/0.0/0.0/15008/0000162) from the European Regional Development Fund.'This has been corrected in both the PDF and HTML versions of the article.