Warm Dense Matter Studies Research Articles

On-the-fly machine learned force fields for the study of warm dense matter: Application to diffusion and viscosity of CH

We develop a framework for on-the-fly machine learned force field (MLFF) molecular dynamics (MD) simulations of warm dense matter (WDM). In particular, we employ an MLFF scheme based on the kernel method and Bayesian linear regression, with the training data generated from the Kohn–Sham density functional theory (DFT) using the Gauss spectral quadrature method, within which we calculate energies, atomic forces, and stresses. We verify the accuracy of the formalism by comparing the predicted properties of warm dense carbon with recent Kohn–Sham DFT results in the literature. In so doing, we demonstrate that ab initio MD simulations of WDM can be accelerated by up to three orders of magnitude, while retaining ab initio accuracy. We apply this framework to calculate the diffusion coefficients and shear viscosity of CH at a density of 1 g/cm3 and temperatures in the range of 75 000–750 000 K. We find that the self- and inter-diffusion coefficients and the viscosity obey a power law with temperature, and that the diffusion coefficient results suggest a weak coupling between C and H in CH. In addition, we find agreement within standard deviation with previous results for C and CH but disagreement for H, demonstrating the need for ab initio calculations as presented here.

DC electrical conductivity measurements of warm dense matter using ultrafast THz radiation

We describe measurements of the DC electrical conductivity of warm dense matter using ultrafast terahertz (THz) pulses. THz fields are sufficiently slowly varying that they behave like DC fields on the timescale of electron–electron and electron–ion interactions and hence probe DC-like responses. Using a novel single-shot electro-optic sampling technique, the electrical conductivity of the laser-generated warm dense matter was determined with <1 ps temporal resolution. We present the details of the single-shot THz detection methodology as well as considerations for warm dense matter experiments. We, then, provide proof-of-concept studies on aluminum driven to the warm dense matter regime through isochoric heating and shock compression. Our results indicate a decrease in the conductivity when driven to warm dense matter conditions and provide a platform for future warm dense matter studies.

Enhancement of K-shell spectroscopy for temperature measuring of isochorically heated matter in the sub-keV range

Both K-shell x-ray emission spectroscopy and fluorescence spectroscopy are well-accepted diagnostics for experimental studies of warm dense matter and hot dense matter (HDM). Until now, however, this diagnosis has been used for the study of dense matter with temperatures lower than 100 eV or with temperatures above 1 keV. In this work, we have demonstrated the possibility of using K-shell emission spectroscopy for an intermediate temperature range of 100s eV to study dense plasma. Here, we discuss an analysis of the HDM emission spectra of a solid-state copper with temperatures up to a few hundreds of electronvolts heated by laser-accelerated charged particles.

Electronic pair alignment and roton feature in the warm dense electron gas

The study of matter under extreme densities and temperatures as they occur, for example, in astrophysical objects and nuclear fusion applications has emerged as one of the most active frontiers in physics, material science, and related disciplines. In this context, a key quantity is given by the dynamic structure factor S(q, ω), which is probed in scattering experiments—the most widely used method of diagnostics at these extreme conditions. In addition to its importance for the study of warm dense matter, the modelling of such dynamic properties of correlated quantum many-body systems constitutes an important theoretical challenge. Here, we report a roton feature in the dynamic structure factor S(q, ω) of the warm dense electron gas, and introduce a microscopic explanation in terms of an electronic pair alignment model. Our results will have direct impact on the interpretation of scattering experiments and may provide insights into the dynamics of a number of correlated quantum many-body systems such as ultracold helium, dipolar supersolids, and bilayer heterostructures.

Exchange-correlation effect in the charge response of a warm dense electron gas

The study of warm dense matter, widely existing in nature and laboratories, is challenging due to the interplay of quantum and classical fluctuations. We develop a variational diagrammatic Monte Carlo method and determine the exchange-correlation kernel ${K}_{\mathrm{XC}}(q;T)$ of a warm dense electron gas for a broad range of temperature $T$ and momentum $q$. We observe several interesting physics, including the $T$-dependent evolution of the hump structure and the large-$q$ tail and the emergence of a scaling relation. Particularly, by deriving an analytical form for $q\ensuremath{\rightarrow}\ensuremath{\infty}$, we obtain large-$q$ tails of ${K}_{\mathrm{XC}}$ with high precision. It is shown that the ${K}_{\mathrm{XC}}$ data can be reliably transformed into real space, which can be directly used in density-functional-theory calculations of real warm dense matter.

Femtosecond laser-induced sub-wavelength plasma inside dielectrics: I. Field enhancement

The creation of high-energy-density (≳106 joules per cm3) over-critical plasmas in a large volume has essential applications in the study of warm dense matter, being present in the hot cores of stars and planets. It was recently shown that femtosecond Bessel beams enable creating over-critical plasmas inside sapphire with sub-wavelength radius and several tens of micrometers in length. Here, the dependence of field structure and absorption mechanism on the plasma density transverse profile are investigated by performing self-consistent Particle-In-Cell (PIC) simulations. Two limiting cases are considered: one is a homogeneous step-like profile that can sustain plasmon formation, and the second is an inhomogeneous Gaussian profile, where resonance absorption occurs. Comparing experimental absorption measures to analytical predictions allows determining the plasma parameters used in PIC simulations. The PIC simulation results are in good agreement with experimental diagnostics of total absorption, near-field fluence distribution, and far-field radiation pattern. We show that in each case, an ambipolar field forms at the plasma surface due to the expansion of the hot electrons and that electron sound waves propagate into the over-critical region.

An Investigation into the Approximations Used in Wave Packet Molecular Dynamics for the Study of Warm Dense Matter

Wave packet molecular dynamics (WPMD) has recently received a lot of attention as a computationally fast tool with which to study dynamical processes in warm dense matter beyond the Born–Oppenheimer approximation. These techniques, typically, employ many approximations to achieve computational efficiency while implementing semi-empirical scaling parameters to retain accuracy. We investigated three of the main approximations ubiquitous to WPMD: a restricted basis set, approximations to exchange, and the lack of correlation. We examined each of these approximations in regard to atomic and molecular hydrogen in addition to a dense hydrogen plasma. We found that the biggest improvement to WPMD comes from combining a two-Gaussian basis with a semi-empirical correction based on the valence-bond wave function. A single parameter scales this correction to match experimental pressures of dense hydrogen. Ultimately, we found that semi-empirical scaling parameters are necessary to correct for the main approximations in WPMD. However, reducing the scaling parameters for more ab-initio terms gives more accurate results and displays the underlying physics more readily.

Investigation of plasma states formed under the interaction of high-power laser pulses with wire-shape Al–Cu target

Study of warm dense matter remains a very important task for understanding of many unique phenomena observing as in astrophysical research as in inertial fusion and fast ignition. In this work, we studied the parameters of plasma created by 1.7 ps laser pulses of relativistic intensity of 7 × 1018 W/cm2 in a specially designed Al–Cu wire-shape target, in comparison with a flat Cu and Al foil targets. We observed the strong emission of neutral or virtually neutral Cu Kα line from both Cu foil and Cu wire part of targets, which indicates the creation of a dense state exposed to the intense flow of hot electrons. Parameters of the plasma were evaluated by comparison of experimental spectra with the results of modeling by collisional-radiative kinetic code PrismSpec under the plasma zone approach. The using of Al foil in front of Cu wire part of target allowed avoiding the direct heating of Cu-wire and acquiring spectra of Cu K-shell emission evidently belonging to emission of warm dense matter (WDM) state. The upper estimate for the electron temperature in WDM region was found to be below 80 eV.

Compact high-current pulse generator for laboratory studies of high energy density matter.

We present the design and parameters of a compact and mobile high-current pulse generator, which can be applied in the study of warm dense matter in university laboratories. The generator dimensions are 550 × 570 × 590mm3, the weight is ∼70kg, and it consists of four "bricks" connected in parallel. Each brick, made up of 2 × 40 nF, 100 kV low-inductance capacitors connected in parallel, has its own multi-gap and multichannel ball gas spark switch, triggered via a capacitively coupled triggering by a positive polarity pulse of ∼80 kV amplitude and ∼15ns rise time. At a charging voltage of ∼70 kV, the generator produces a ∼155 kA current pulse with a rise time of ∼220ns on a ∼15 nH inductive short-circuit load and a ∼90 kA amplitude current pulse in the underwater electrical explosion of a copper wire.

Influence of different charge-state ion distribution on elastic X-ray scattering in warm dense matter

The study of warm dense matter is very important for the evolution of celestial bodies and inertial confinement fusion, which often contains a mixture of multiple elements and different charge-state ions. The ionic structure and distribution of different charge-states directly affect the diagnosis and physical properties of warm dense matter. At the same time, the influence of high-temperature dense plasma on the ionic structure should be considered when we study the physical properties from the first-principle calculation of electron structure. In the present work, the radial distribution functions of multiple charge-state ions (gold, carbon-hydrogen mixture, and aluminum) are developed in the hypernetted-chain approximation, and elastic x-ray scattering of different charge-state ions are calculated in the warm dense matter regime. Firstly, the electron structure of different charge-state ions is self-consistently computed in the ionic sphere, in which the ion-sphere radii are determined by the plasma density and their charges. And then the ionic fraction is obtained by solving the modified Saha equation, with the interactions among different charge-state ions taken into account, and ion-ion pair potentials are obtained by Yukawa model. Finally, the ion features of x-ray elastic scattering for Al are calculated on the basis of electronic distribution around the nuclei and ionic radial distribution function. By comparing the results of different charge-sate ions with the result of mean charge-sate ion, it is shown that different statistical methods can affect the physical properties which are dependent on the electronic and ionic structure.

Optimization of a laser plasma-based x-ray source according to WDM absorption spectroscopy requirements

X-ray absorption spectroscopy is a well-accepted diagnostic for experimental studies of warm dense matter. It requires a short-lived X-ray source of sufficiently high emissivity and without characteristic lines in the spectral range of interest. In the present work, we discuss how to choose an optimum material and thickness to get a bright source in the wavelength range 2 Å–6 Å (∼2 keV to 6 keV) by considering relatively low-Z elements. We demonstrate that the highest emissivity of solid aluminum and silicon foil targets irradiated with a 1-ps high-contrast sub-kJ laser pulse is achieved when the target thickness is close to 10 µm. An outer plastic layer can increase the emissivity even further.

Fast collisional electron heating and relaxation in thin foils driven by a circularly polarized ultraintense short-pulse laser

The creation of well-thermalized, hot and dense plasmas is attractive for warm dense matter studies. We investigate collisionally induced energy absorption of an ultraintense and ultrashort laser pulse in a solid copper target using particle-in-cell simulations. We find that, upon irradiation by a$2\times 10^{20}~\text{W}\,\text{cm}^{-2}$intensity, 60 fs duration, circularly polarized laser pulse, the electrons in the collisional simulation rapidly reach a well-thermalized distribution with${\sim}3.5~\text{keV}$temperature, while in the collisionless simulation the absorption is several orders of magnitude weaker. Circular polarization inhibits the generation of suprathermal electrons, while ensuring efficient bulk heating through inverse bremsstrahlung, a mechanism usually overlooked at relativistic laser intensity. An additional simulation, taking account of both collisional and field ionization, yields similar results: the bulk electrons are heated to${\sim}2.5~\text{keV}$, but with a somewhat lower degree of thermalization than in the pre-set, fixed-ionization case. The collisional absorption mechanism is found to be robust against variations in the laser parameters. At fixed laser pulse energy, increasing the pulse duration rather than the intensity leads to a higher electron temperature.

X-ray phase-contrast imaging for laser-induced shock waves

X-ray phase-contrast imaging (XPCI) is a versatile technique with applications in many fields, including fundamental physics, biology and medicine. Where X-ray absorption radiography requires high density ratios for effective imaging, the image contrast for XPCI is a function of the density gradient. In this letter, we apply XPCI to the study of laser-driven shock waves. Our experiment was conducted at the Petawatt High-Energy Laser for Heavy Ion EXperiments (PHELIX) at GSI. Two laser beams were used: one to launch a shock wave and the other to generate an X-ray source for phase-contrast imaging. Our results suggest that this technique is suitable for the study of warm dense matter (WDM), inertial confinement fusion (ICF) and laboratory astrophysics.

Fluorescence and absorption spectroscopy for warm dense matter studies and ICF plasma diagnostics

The burning core of an inertial confinement fusion (ICF) plasma produces bright x-rays at stagnation that can directly diagnose core conditions essential for comparison to simulations and understanding fusion yields. These x-rays also backlight the surrounding shell of warm, dense matter, whose properties are critical to understanding the efficacy of the inertial confinement and global morphology. We show that the absorption and fluorescence spectra of mid-Z impurities or dopants in the warm dense shell can reveal the optical depth, temperature, and density of the shell and help constrain models of warm, dense matter. This is illustrated by the example of a high-resolution spectrum collected from an ICF plasma with a beryllium shell containing native iron impurities. Analysis of the iron K-edge provides model-independent diagnostics of the shell density (2.3 × 1024 e/cm3) and temperature (10 eV), while a 12-eV red shift in Kβ and 5-eV blue shift in the K-edge discriminate among models of warm dense matter: Both shifts are well described by a self-consistent field model based on density functional theory but are not fully consistent with isolated-atom models using ad-hoc density effects.

A sensitive EUV Schwarzschild microscope for plasma studies with sub-micrometer resolution

We present an extreme ultraviolet (EUV) microscope using a Schwarzschild objective which is optimized for single-shot sub-micrometer imaging of laser-plasma targets. The microscope has been designed and constructed for imaging the scattering from an EUV-heated solid-density hydrogen jet. Imaging of a cryogenic hydrogen target was demonstrated using single pulses of the free-electron laser in Hamburg (FLASH) free-electron laser at a wavelength of 13.5 nm. In a single exposure, we observe a hydrogen jet with ice fragments with a spatial resolution in the sub-micrometer range. In situ EUV imaging is expected to enable novel experimental capabilities for warm dense matter studies of micrometer-sized samples in laser-plasma experiments.

Single-shot mega-electronvolt ultrafast electron diffraction for structure dynamic studies of warm dense matter.

We have developed a single-shot mega-electronvolt ultrafast-electron-diffraction system to measure the structural dynamics of warm dense matter. The electron probe in this system is featured by a kinetic energy of 3.2 MeV and a total charge of 20 fC, with the FWHM pulse duration and spot size at sample of 350 fs and 120 μm respectively. We demonstrate its unique capability by visualizing the atomic structural changes of warm dense gold formed from a laser-excited 35-nm freestanding single-crystal gold foil. The temporal evolution of the Bragg peak intensity and of the liquid signal during solid-liquid phase transition are quantitatively determined. This experimental capability opens up an exciting opportunity to unravel the atomic dynamics of structural phase transitions in warm dense matter regime.

Development and testing of a pulsed helium ion source for probing materials and warm dense matter studies.

The neutralized drift compression experiment was designed and commissioned as a pulsed, linear induction accelerator to drive thin targets to warm dense matter (WDM) states with peak temperatures of ∼1 eV using intense, short pulses (∼1 ns) of 1.2 MeV lithium ions. At that kinetic energy, heating a thin target foil near the Bragg peak energy using He(+) ions leads to more uniform energy deposition of the target material than Li(+) ions. Experiments show that a higher current density of helium ions can be delivered from a plasma source compared to Li(+) ions from a hot plate type ion source. He(+) beam pulses as high as 200 mA at the peak and 4 μs long were measured from a multi-aperture 7-cm-diameter emission area. Within ±5% variation, the uniform beam area is approximately 6 cm across. The accelerated and compressed pulsed ion beams can be used for materials studies and isochoric heating of target materials for high energy density physics experiments and WDM studies.

Reflectivity and imaging capabilities of spherically bent crystals studied by ray-tracing simulations

Spherically bent crystals are widely used in focusing monochromators, spectrometers and other x-ray optical systems. In particular, they are used in focusing spectrometers with spatial resolution, applied in high energy density diagnostics and warm dense matter studies. In this case, plasma parameters are obtained via measurements of relative intensities of characteristic spectral emission lines for multiply charged ions, which are affected by an instrumental function. Here we develop and use the ray-tracing computer simulations to study reflectivity properties of spherically bent crystals in a particular experimental conditions and to provide the method to adjust and validate the measured spectral line intensities on quantitative basis.

Analysis and implementation of a space resolving spherical crystal spectrometer for x-ray Thomson scattering experiments.

The application of a space-resolving spectrometer to X-ray Thomson Scattering (XRTS) experiments has the potential to advance the study of warm dense matter. This has motivated the design of a spherical crystal spectrometer, which is a doubly focusing geometry with an overall high sensitivity and the capability of providing high-resolution, space-resolved spectra. A detailed analysis of the image fluence and crystal throughput in this geometry is carried out and analytical estimates of these quantities are presented. This analysis informed the design of a new spectrometer intended for future XRTS experiments on the Z-machine. The new spectrometer collects 6 keV x-rays with a spherically bent Ge (422) crystal and focuses the collected x-rays onto the Rowland circle. The spectrometer was built and then tested with a foam target. The resulting high-quality spectra prove that a spherical spectrometer is a viable diagnostic for XRTS experiments.

Exploring Mbar shock conditions and isochorically heated aluminum at the Matter in Extreme Conditions end station of the Linac Coherent Light Source (invited).

Recent experiments performed at the Matter in Extreme Conditions end station of the Linac Coherent Light Source (LCLS) have demonstrated the first spectrally resolved measurements of plasmons from isochorically heated aluminum. The experiments have been performed using a seeded 8-keV x-ray laser beam as a pump and probe to both volumetrically heat and scatter x-rays from aluminum. Collective x-ray Thomson scattering spectra show a well-resolved plasmon feature that is down-shifted in energy by 19 eV. In addition, Mbar shock pressures from laser-compressed aluminum foils using velocity interferometer system for any reflector have been measured. The combination of experiments fully demonstrates the possibility to perform warm dense matter studies at the LCLS with unprecedented accuracy and precision.