Equation of state measurements in liquid deuterium to 70 GPa

A pulsed power facility for studying the warm dense matter regime

A pulsed power facility has been designed for studying the warm dense matter regime. It is based on the pulsed Joule heating technique, originally proposed by Korobenko and Rakhel [Int. J. Thermophy. 20, 1257 (1999)], where a 3.96 µF capacitor bench is used for inducing a solid to plasma phase transition to metallic foils confined into a sapphire cell. The first experiments have been conducted on pure aluminum. Experimental data have been collected using electrical and optical diagnostics. Direct measurements of tension, current, pressure, and particle velocity allow us to evaluate the equation of state (EOS) and the DC conductivity of expanded aluminum. The results are compared to hydrodynamic simulations performed with various EOS models. As a result, collected data on aluminum highlight the relevance of our experimental procedure for improving EOS modeling in the warm dense matter regime.

Multishock to Quasi-Isentropic Compression of Dense Gaseous Deuterium-Helium Mixtures up to 120 GPa: Probing the Sound Velocities Relevant to Planetary Interiors

Shock reverberation compression experiments on dense gaseous deuterium-helium mixtures are carried out to provide thermodynamic parameters relevant to the conditions in planetary interiors. The multishock pressures are determined up to 120 GPa and reshock temperatures to 7400 K. Furthermore, the unique compression path from shock-adiabatic to quasi-isentropic compressions enables a direct estimation of the high-pressure sound velocities in the unexplored range of 50-120 GPa. The equation of state and sound velocity provide particular dual perspectives to validate the theoretical models. Our experimental data are found to agree with several equation of state models widely used in astrophysics within the probed pressure range. The current data improve the experimental constraints on sound velocities in the Jovian insulating-to-metallic transition layer.

Confirmation of the PPLB Derivative Discontinuity: Exact Chemical Potential at Finite Temperatures of a Model System

The landmark 1982 work of Perdew, Parr, Levy, and Balduz (often called PPLB) laid the foundation for our modern understanding of the role of the derivative discontinuity in density functional theory, which drives much development to account for its effects. A simple model for the chemical potential at vanishing temperature played a crucial role in their argument. We investigate the validity of this model in the simplest nontrivial system to which it can be applied and which can be easily solved exactly, the Hubbard dimer. We find exact agreement in the crucial zero-temperature limit and show the model remains accurate for a significant range of temperatures. We identify how this range depends on the strength of correlations. We extend the model to approximate free energies accounting for the derivative discontinuity, a feature missing in standard semilocal approximations. We provide a correction to this approximation to yield even more accurate free energies. We discuss the relevance of these results for warm dense matter.

Experimental determination of shock speed versus exciter speed in a two-dimensional dusty plasma

A shock that is continuously driven by a moving exciter will propagate at a speed that depends on the exciter speed. We obtained this dependence experimentally, in a strongly coupled dusty plasma that was prepared as a single two-dimensional layer of charged microparticles. Attaining this result required an experimental advance, developing a method of driving a shock continuously, which we did using an exciter moving at a constant supersonic speed, analogous to a piston in a cylinder. The resulting compressional pulse was a shock that propagated steadily without weakening, ahead of the moving exciter. We compare our experimental results to an empirical form M_{shock}=1+sM_{exciter}, and to the prediction of a recent simulation.

Studies of equation of state properties of high-energy-density matter generated by intense ion beams at the facility for antiprotons and ion research

The work presented in this paper shows with the help of two-dimensional hydrodynamic simulations that intense heavy-ion beams are a very efficient tool to induce high energy density (HED) states in solid matter. These simulations have been carried out using a computer code BIG2 that is based on a Godunov-type numerical algorithm. This code includes ion beam energy deposition using the cold stopping model, which is a valid approximation for the temperature range accessed in these simulations. Different phases of matter achieved due to the beam heating are treated using a semiempirical equation-of-state (EOS) model. To take care of the solid material properties, the Prandl-Reuss model is used. The high specific power deposited by the projectile particles in the target leads to phase transitions on a timescale of the order of tens of nanosecond, which means that the sample material achieves thermodynamic equilibrium during the heating process. In these calculations we use Pb as the sample material that is irradiated by an intense uranium beam. The beam parameters including particle energy, focal spot size, bunch length, and bunch intensity are considered to be the same as the design parameters of the ion beam to be generated by the SIS100 heavy-ion synchrotron at the Facility for Antiprotons and Ion Research (FAIR), at Darmstadt. The purpose of this work is to propose experiments to measure the EOS properties of HED matter including studies of the processes of phase transitions at the FAIR facility. Our simulations have shown that depending on the specific energy deposition, solid lead will undergo phase transitions leading to an expanded hot liquid state, two-phase liquid-gas state, or the critical parameter regime. In a similar manner, other materials can be studied in such experiments, which will be a very useful addition to the knowledge in this important field of research.

Pressure and energy of compressional shocks in two-dimensional Yukawa systems

The propagation of compressional shocks in two-dimensional (2D) dusty plasmas is investigated using MD simulations under various conditions. The shock Hugoniot curves of the relationship between the shock front speed D and the mean particle speed v[over ¯] after shocks are obtained and analytically fit to parabolic expressions. As the screening parameter increases, the weaker Yukawa interparticle interaction cause the shock Hugoniot curves to be more linear. Combining the obtained shock Hugoniot curves with the Rankine-Hugoniot jump relations, analytic expressions of pressure and energy after the shocks in 2D Yukawa systems are obtained, which are functions of the observable quantities, like the shock front speed D or the mean particle speed v[over ¯] or the specific volume.

Shock Compression of Liquid Deuterium up to 1 TPa

We present laser-driven shock compression experiments on cryogenic liquid deuterium to 550 GPa along the principal Hugoniot and reflected-shock data up to 1 TPa. High-precision interferometric Doppler velocimetry and impedance-matching analysis were used to determine the compression accurately enough to reveal a significant difference as compared to state-of-the-art ab initio calculations and thus, no single equation of state model fully matches the principal Hugoniot of deuterium over the observed pressure range. In the molecular-to-atomic transition pressure range, models based on density functional theory calculations predict the maximum compression accurately. However, beyond 250 GPa along the principal Hugoniot, first-principles models exhibit a stiffer response than the experimental data. Similarly, above 500 GPa the reflected shock data show 5%-7% higher compression than predicted by all current models.

Breakdown of Fermi Degeneracy in the Simplest Liquid Metal

We are reporting the observation of the breakdown of electrons' degeneracy and emergence of classical statistics in the simplest element: metallic deuterium. We have studied the optical reflectance, shock velocity, and temperature of dynamically compressed liquid deuterium up to its Fermi temperature T_{F}. Above the insulator-metal transition, the optical reflectance shows the distinctive temperature-independent resistivity saturation, which is prescribed by Mott's minimum metallic limit, in agreement with previous experiments. At T>0.4 T_{F}, however, the reflectance of metallic deuterium starts to rise with a temperature-dependent slope, consistent with the breakdown of the Fermi surface. The experimentally inferred electron-ion collisional time in this region exhibits the characteristic temperature dependence expected for a classical Landau-Spitzer plasma. Our observation of electron degeneracy lifting extends studies of degeneracy to new fermionic species-electron Fermi systems-and offers an invaluable benchmark for quantum statistical models of Coulomb systems over a wide range of temperatures relevant to dense astrophysical objects and ignition physics.

Molecular dynamics simulation of strong shock waves propagating in dense deuterium, taking into consideration effects of excited electrons

We present a molecular dynamics simulation of shock waves propagating in dense deuterium with the electron force field method [J. T. Su and W. A. Goddard, Phys. Rev. Lett. 99, 185003 (2007)PRLTAO0031-900710.1103/PhysRevLett.99.185003], which explicitly takes the excitation of electrons into consideration. Nonequilibrium features associated with the excitation of electrons are systematically investigated. We show that chemical bonds in D_{2} molecules lead to a more complicated shock wave structure near the shock front, compared with the results of classical molecular dynamics simulation. Charge separation can bring about accumulation of net charges on large scales, instead of the formation of a localized dipole layer, which might cause extra energy for the shock wave to propagate. In addition, the simulations also display that molecular dissociation at the shock front is the major factor that accounts for the "bump" structure in the principal Hugoniot. These results could help to build a more realistic picture of shock wave propagation in fuel materials commonly used in the inertial confinement fusion.

Thermodynamic and Kinetic Properties of Shocks in Two-Dimensional Yukawa Systems

Particle-level simulations of shocked plasmas are carried out to examine kinetic properties not captured by hydrodynamic models. In particular, molecular dynamics simulations of 2D Yukawa plasmas with variable couplings and screening lengths are used to examine shock features unique to plasmas, including the presence of dispersive shock structures for weak shocks. A phase-space analysis reveals several kinetic properties, including anisotropic velocity distributions, non-Maxwellian tails, and the presence of fast particles ahead of the shock, even for moderately low Mach numbers. We also examine the thermodynamics (Rankine-Hugoniot relations) of recent experiments [Phys. Rev. Lett. 111, 015002 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.015002] and find no anomalies in their equations of state.

High-pressure structural changes in liquid silica

The structural properties of liquid silica at high pressure and moderate temperature conditions, also referred to as the warm dense matter regime, were investigated using time-resolved K-edge x-ray absorption spectroscopy and ab initio calculations. We used a nanosecond laser beam to compress uniformly a solid SiO_{2} target and a picosecond laser beam to generate a broadband x-ray source. We obtained x-ray absorption spectra at the Si K edge over a large pressure-temperature domain to probe the liquid phase up to 3.6 times the normal solid density. Using ab initio simulations, we are able to interpret the changes in the x-ray absorption near-edge structure with increasing densities as an increase in the coordination number of silicon by oxygen atoms from 4 to 9. This indicates that, up to significant temperatures, the liquid structure becomes akin to what is found in the solid SiO_{2} phases.

X-ray scattering measurements of dissociation-induced metallization of dynamically compressed deuterium

Hydrogen, the simplest element in the universe, has a surprisingly complex phase diagram. Because of applications to planetary science, inertial confinement fusion and fundamental physics, its high-pressure properties have been the subject of intense study over the past two decades. While sophisticated static experiments have probed hydrogen's structure at ever higher pressures, studies examining the higher-temperature regime using dynamic compression have mostly been limited to optical measurement techniques. Here we present spectrally resolved x-ray scattering measurements from plasmons in dynamically compressed deuterium. Combined with Compton scattering, and velocity interferometry to determine shock pressure and mass density, this allows us to extract ionization state as a function of compression. The onset of ionization occurs close in pressure to where density functional theory-molecular dynamics (DFT-MD) simulations show molecular dissociation, suggesting hydrogen transitions from a molecular and insulating fluid to a conducting state without passing through an intermediate atomic phase.

Simulations of beam-matter interaction experiments at the CERN HiRadMat facility and prospects of high-energy-density physics research

In a recent publication [Schmidt et al., Phys. Plasmas 21, 080701 (2014)], we reported results on beam-target interaction experiments that have been carried out at the CERN HiRadMat (High Radiation to Materials) facility using extended solid copper cylindrical targets that were irradiated with a 440-GeV proton beam delivered by the Super Proton Synchrotron (SPS). On the one hand, these experiments confirmed the existence of hydrodynamic tunneling of the protons that leads to substantial increase in the range of the protons and the corresponding hadron shower in the target, a phenomenon predicted by our previous theoretical investigations [Tahir et al., Phys. Rev. ST Accel. Beams 25, 051003 (2012)]. On the other hand, these experiments demonstrated that the beam heated part of the target is severely damaged and is converted into different phases of high energy density (HED) matter, as suggested by our previous theoretical studies [Tahir et al., Phys. Rev. E 79, 046410 (2009)]. The latter confirms that the HiRadMat facility can be used to study HED physics. In the present paper, we give details of the numerical simulations carried out to understand the experimental measurements. These include the evolution of the physical parameters, for example, density, temperature, pressure, and the internal energy in the target, during and after the irradiation. This information is important in order to determine the region of the HED phase diagram that can be accessed in such experiments. These simulations have been done using the energy deposition code fluka and a two-dimensional hydrodynamic code, big2, iteratively.

Metallization of warm dense SiO(2) studied by XANES spectroscopy

We investigate the evolution of the electronic structure of fused silica in a dense plasma regime using time-resolved x-ray absorption spectroscopy. We use a nanosecond (ns) laser beam to generate a strong uniform shock wave in the sample and a picosecond (ps) pulse to produce a broadband x-ray source near the Si K edge. By varying the delay between the two laser beams and the intensity of the ns beam, we explore a large thermodynamical domain with densities varying from 1 to 5  g/cm^{3} and temperatures up to 5 eV. In contrast to normal conditions where silica is a well-known insulator with a wide band gap of 8.9 eV, we find that shocked silica exhibits a pseudogap as a semimetal throughout this thermodynamical domain. This is in quantitative agreement with density functional theory predictions performed using the generalized gradient approximation.

Temperature measurements of shocked silica aerogel foam

We present recent results of equation-of-state (EOS) measurements of shocked silica (SiO_{2}) aerogel foam at the OMEGA laser facility. Silica aerogel is an important low-density pressure standard used in many high energy density experiments, including the novel technique of shock and release. Due to its many applications, it has been a heavily studied material and has a well-known Hugoniot curve. This work then complements the velocity and pressure measurements with additional temperature data providing the full EOS information within the warm dense matter regime for the temperature interval of 1-15 eV and shock velocities between 10 and 40 km/s corresponding to shock pressures of 0.3-2 Mbar. The experimental results were compared with hydrodynamic simulations and EOS models. We found that the measured temperature was systematically lower than suggested by theoretical calculations. Simulations provide a possible explanation that the emission measured by optical pyrometry comes from a radiative precursor rather than from the shock front, which could have important implications for such measurements.

First-principles opacity table of warm dense deuterium for inertial-confinement-fusion applications

Accurate knowledge of the optical properties of a warm dense deuterium-tritium (DT) mixture is important for reliable design of inertial confinement fusion (ICF) implosions using radiation-hydrodynamics simulations. The opacity of a warm dense DT shell essentially determines how much radiation from hot coronal plasmas can be deposited in the DT fuel of an imploding capsule. Even for the simplest species of hydrogen, the accurate calculation of their opacities remains a challenge in the warm-dense matter regime because strong-coupling and quantum effects play an important role in such plasmas. With quantum-molecular-dynamics (QMD) simulations, we have derived a first-principles opacity table (FPOT) of deuterium (and the DT mixture by mass scaling) for a wide range of densities from ρ(D)=0.5 to 673.518g/cm(3) and temperatures from T=5000K up to the Fermi temperature T(F) for each density. Compared with results from the astrophysics opacity table (AOT) currently used in our hydrocodes, the FPOT of deuterium from our QMD calculations has shown a significant increase in opacity for strongly coupled and degenerate plasma conditions by a factor of 3-100 in the ICF-relevant photon-energy range. As conditions approach those of classical plasma, the opacity from the FPOT converges to the corresponding values of the AOT. By implementing the FPOT of deuterium and the DT mixture into our hydrocodes, we have performed radiation-hydrodynamics simulations for low-adiabat cryogenic DT implosions on the OMEGA laser and for direct-drive-ignition designs for the National Ignition Facility. The simulation results using the FPOT show that the target performance (in terms of neutron yield and energy gain) could vary from ∼10% up to a factor of ∼2 depending on the adiabat of the imploding DT capsule; the lower the adiabat, the more variation is seen in the prediction of target performance when compared to the AOT modeling.

A density functional tight binding model with an extended basis set and three-body repulsion for hydrogen under extreme thermodynamic conditions

We present a new DFTB-p3b density functional tight binding model for hydrogen at extremely high pressures and temperatures, which includes a polarizable basis set (p) and a three-body environmentally dependent repulsive potential (3b). We find that use of an extended basis set is necessary under dissociated liquid conditions to account for the substantial p-orbital character of the electronic states around the Fermi energy. The repulsive energy is determined through comparison to cold curve pressures computed from density functional theory (DFT) for the hexagonal close-packed solid, as well as pressures from thermally equilibrated DFT-MD simulations of the liquid phase. In particular, we observe improved agreement in our DFTB-p3b model with previous theoretical and experimental results for the shock Hugoniot of hydrogen up to 100 GPa and 25000 K, compared to a standard DFTB model using pairwise interactions and an s-orbital basis set, only. The DFTB-p3b approach discussed here provides a general method to extend the DFTB method for a wide variety of materials over a significantly larger range of thermodynamic conditions than previously possible.

K-shell photoabsorption edge of strongly coupled matter driven by laser-converted radiation

The first observation of the K-shell photoabsorption edge of strongly coupled matter with an ion-ion coupling parameter of about 65 generated by intense x-ray radiation-driven shocks is reported. The soft x-ray radiation generated by laser interaction with a "dog bone" high-Z hohlraum is used to ablate two thick CH layers, which cover a KCl sample, to create symmetrical inward shocks. While the two shocks impact at the central KCl sample, a highly compressed KCl is obtained with a density of 3-5 times solid density and a temperature of about 2-4 eV. The photoabsorption spectra of chlorine near the K-shell edge are measured with a crystal spectrometer using a short x-ray backlighter. The redshift of the K edge up to 11.7 eV and broadening of 15.2 eV are obtained for the maximum compression. A comparison of the measured redshifts and broadenings with dense plasma calculations are made, and it indicates potential improvements in the theoretical description.

Electronic structure investigation of highly compressed aluminum with K edge absorption spectroscopy

The electronic structure evolution of highly compressed aluminum has been investigated using time resolved K edge x-ray absorption spectroscopy. A long laser pulse (500 ps, I(L)≈8×10(13) W/cm(2)) was used to create a uniform shock. A second ps pulse (I(L)≈10(17)  W/cm(2)) generated an ultrashort broadband x-ray source near the Al K edge. The main target was designed to probe aluminum at reshocked conditions up to now unexplored (3 times the solid density and temperatures around 8 eV). The hydrodynamical conditions were obtained using rear side visible diagnostics. Data were compared to ab initio and dense plasma calculations, indicating potential improvements in either description. This comparison shows that x-ray-absorption near-edge structure measurements provide a unique capability to probe matter at these extreme conditions and severally constrains theoretical approaches currently used.

Shock compression of a fifth period element: liquid xenon to 840 GPa

Current equation of state (EOS) models for xenon show substantial differences in the Hugoniot above 100 GPa, prompting the need for an improved understanding of xenon's behavior at extreme conditions. We performed shock compression experiments on liquid xenon to determine the Hugoniot up to 840 GPa, using these results to validate density functional theory (DFT) simulations. Despite the nearly fivefold compression, we find that the limiting Thomas-Fermi theory, exact in the high density limit, does not accurately describe the system. Combining the experimental data and DFT calculations, we developed a free-energy-based, multiphase EOS capable of describing xenon over a wide range of pressures and temperatures.

Evidence for a first-order liquid-liquid transition in high-pressure hydrogen from ab initio simulations

Using quantum simulation techniques based on either density functional theory or quantum Monte Carlo, we find clear evidence of a first-order transition in liquid hydrogen, between a low conductivity molecular state and a high conductivity atomic state. Using the temperature dependence of the discontinuity in the electronic conductivity, we estimate the critical point of the transition at temperatures near 2,000 K and pressures near 120 GPa. Furthermore, we have determined the melting curve of molecular hydrogen up to pressures of 200 GPa, finding a reentrant melting line. The melting line crosses the metalization line at 700 K and 220 GPa using density functional energetics and at 550 K and 290 GPa using quantum Monte Carlo energetics.

Unified first principles description from warm dense matter to ideal ionized gas plasma: electron-ion collisions induced friction

Electron-ion interactions are central to numerous phenomena in the warm dense matter (WDM) regime and at higher temperature. The electron-ion collisions induced friction at high temperature is introduced in the procedure of ab initio molecular dynamics using the Langevin equation based on density functional theory. In this framework, as a test for Fe and H up to 1000 eV, the equation of state and the transition of electronic structures of the materials with very wide density and temperature can be described, which covers a full range of WDM up to high energy density physics. A unified first principles description from condensed matter to ideal ionized gas plasma is constructed.

Strong coupling and degeneracy effects in inertial confinement fusion implosions

Accurate knowledge about the equation of state (EOS) of deuterium is critical to inertial confinement fusion (ICF). Low-adiabat ICF implosions routinely access strongly coupled and degenerate plasma conditions. Using the path integral Monte Carlo method, we have derived a first-principles EOS (FPEOS) table of deuterium. It is the first ab initio EOS table which completely covers typical ICF implosion trajectory in the density and temperature ranges of ρ=0.002-1596  g/cm3 and T=1.35  eV-5.5  keV. Discrepancies in internal energy and pressure have been found in strongly coupled and degenerate regimes with respect to SESAME EOS. Hydrodynamics simulations of cryogenic ICF implosions using the FPEOS table have indicated significant differences in peak density, areal density (ρR), and neutron yield relative to SESAME simulations.

Energy relaxation in dense, strongly coupled two-temperature plasmas

A quantum kinetic approach for the energy relaxation in strongly coupled plasmas with different electron and ion temperatures is presented. Based on the density operator formalism, we derive a balance equation for the energies of electrons and ions connecting kinetic, correlation, and exchange energies with a quite general expression for the electron-ion energy-transfer rate. The latter is given in terms of the correlation function of density fluctuations which allows for a derivation of increasingly realistic approximation schemes including a coupled-mode expression. The equilibration of the contributions of the total energy including the species temperatures in dense hydrogen and beryllium relevant for inertial confinement fusion is investigated as an example.

Equation of State and Electrical Conductivity of Dense Fluid Hydrogen and Helium

The equation of state of fluid hydrogen, helium, and their mixtures is determined within fluid variational theory. Reactions between the constituents such as dissociation and ionization are considered. Results are given for densities and temperatures relevant for the interior of giant planets. Furthermore, the electrical conductivity is determined within linear response theory. Comparison is performed with available experiments and other theoretical work.

Studies of plastic-ablator compressibility for direct-drive inertial confinement fusion on OMEGA

The compression of planar plastic targets was studied with x-ray radiography in the range of laser intensities of I approximately 0.5 to 1.5x10(15) W/cm2 using square (low-compression) and shaped (high-compression) pulses. Two-dimensional simulations with the radiative hydrocode DRACO show good agreement with measurements at laser intensities up to I approximately 10(15) W/cm2. These results provide the first experimental evidence for low-entropy, adiabatic compression of plastic shells in the laser intensity regime relevant to direct-drive inertial confinement fusion. A density reduction near the end of the drive at a high intensity of I approximately 1.5x10(15) W/cm2 has been correlated with the hard x-ray signal caused by hot electrons from two-plasmon-decay instability.

Density measurement of low- Z shocked material from monochromatic x-ray two-dimensional images

An experiment on LULI 2000 laser devoted to density determination of shocked plastic from a two-dimensional monochromatic x-ray radiography is presented. A spherical quartz crystal was set to select the He-alpha line of vanadium at 2.382 A and perform the image of the main target. Rear side diagnostics were implemented to validate the new diagnostic. The density experimental results given by radiography are in good agreement with rear side diagnostics data and hydrodynamical simulations. The pressure regime into the plastic is 2-3 Mbar, corresponding to a compression between 2.7-2.9.

Phase transition in a strongly nonideal deuterium plasma generated by quasi-isentropical compression at megabar pressures

High-explosive driven generators of cylindrical and plane shock waves in D2 and H2 were used for the generation of warm and dense strongly nonideal matter with an intense interparticle interaction and Fermi statistics. Highly resolved flash x-ray diagnostics were used to measure the adiabatic plasma compressibility. The thermodynamic measurements demonstrated the 20% increase of density at megabar pressure, just in the density range, where the electrical measurements indicated a sharp--5 orders of magnitude--increase of electrical conductivity due to pressure ionization in strongly coupled plasmas.

Wave packet simulation of dense hydrogen

Dense hydrogen is studied in the framework of wave packet molecular dynamics. In this semiquantal many-body simulation method the electrons are represented by wave packets which are suitably parametrized. The equilibrium properties and time evolution of the system are obtained with the help of a variational principle. At room temperature the results for the isotherms are in good agreement with anvil experiments. At higher densities beyond the range of the experimental data a transition from a molecular to a metallic state is predicted. The wave packets become delocalized and the electrical conductivity increases sharply. The phase diagram is calculated in a wide range of the pressure-density-temperature space. The observed transition from the molecular to metallic state is accompanied by an increase in density in agreement with recent reverberating shock wave experiments.

Ab initio molecular dynamics simulations of dense boron plasmas up to the semiclassical Thomas-Fermi regime

We build an "all-electron" norm-conserving pseudopotential for boron which extends the use of ab initio molecular dynamics simulations up to 50 times the normal density rho0. This allows us to perform ab initio simulations of dense plasmas from the regime where quantum mechanical effects are important to the regime where semiclassical simulations based on the Thomas-Fermi approach are, by default, the only simulation method currently available. This study first allows one to establish, for the case of boron, the density regime from which the semiclassical Thomas-Fermi approach is legitimate and sufficient. It further brings forward various issues pertaining to the construction of pseudopotentials aimed at high-pressure studies.

First principles calculations of shock compressed fluid helium

The properties of hot dense helium at megabar pressures are studied with two first principles computer simulation techniques: path integral Monte Carlo simulation and density functional molecular dynamics. The simulations predict that the compressibility of helium is substantially increased by electronic excitations that are present in the hot fluid at thermodynamic equilibrium. A maximum compression ratio of 5.24(4)-fold the initial density was predicted for 360 GPa and 150,000 K. This result distinguishes helium from deuterium, for which simulations predicted a maximum compression ratio of 4.3(1). Hugoniot curves for statically precompressed samples are also discussed.

The CERN Large Hadron Collider as a tool to study high-energy density matter

The Large Hadron Collider (LHC) at CERN will generate two extremely powerful 7 TeV proton beams. Each beam will consist of 2808 bunches with an intensity per bunch of 1.15x10(11) protons so that the total number of protons in one beam will be about 3x10(14) and the total energy will be 362 MJ. Each bunch will have a duration of 0.5 ns and two successive bunches will be separated by 25 ns, while the power distribution in the radial direction will be Gaussian with a standard deviation, sigma=0.2 mm. The total duration of the beam will be about 89 mus. Using a 2D hydrodynamic code, we have carried out numerical simulations of the thermodynamic and hydrodynamic response of a solid copper target that is irradiated with one of the LHC beams. These calculations show that only the first few hundred proton bunches will deposit a high specific energy of 400 kJ/g that will induce exotic states of high energy density in matter.

Shock wave propagation in dissociating low-Z liquids: D2

We present direct molecular dynamics simulations of shock wave propagation in liquid deuterium for a wide range of impact velocities. The calculated Hugoniot is in perfect agreement with the gas-gun data as well as with the most recent experimental data. At high impact velocities we observe a smearing of the shock wave front and propagation of fast dissociated molecules well ahead of the compressed region. This smearing occurs due to the fast deuterium dissociation at the shock wave front. The experimental results are discussed in view of this effect.

Simulations of the optical properties of warm dense aluminum

Using quantum molecular dynamics simulations, we show that the optical properties of aluminum change drastically along the nonmetal metal transition observed experimentally. As the density increases and the many-body effects become important, the optical response gradually evolves from the one characteristic of an atomic fluid to the one of a simple metal. We show that quantum molecular dynamics combined with the Kubo-Greenwood formulation naturally embodies the two limits and provides a powerful tool to calculate and benchmark the optical properties of various systems as they evolve into the warm dense matter regime.

Monte Carlo results for the hydrogen Hugoniot

We propose a theoretical Hugoniot relation obtained by combining results for the equation of state from the direct path integral Monte Carlo technique (DPIMC) and those from reaction ensemble Monte Carlo (REMC) simulations. The main idea of this proposal is based on the fact that the DPMIC technique provides first-principle results for a wide range of densities and temperatures including the region of partially ionized plasmas. On the other hand, for lower temperatures where the formation of molecules becomes dominant, DPIMC simulations become cumbersome and inefficient. For this region it is possible to use accurate REMC simulations where bound states (molecules) are treated on the Born-Oppenheimer level. The remaining interaction is then reduced to the scattering between neutral particles which is reliably treated classically by applying effective potentials. The resulting Hugoniot is located between the experimental values of Knudson et al. [Phys. Rev. Lett. 87, 225501 (2001)] and Collins et al. [Science 281, 1178 (1998)].

Reaction ensemble Monte Carlo technique and hypernetted chain approximation study of dense hydrogen

In spite of the simple structure of hydrogen, up to now there is no unified theoretical and experimental description of hydrogen at high pressures. Recent results of Z-pinch experiments show a large deviation from those obtained by laser driven ones. Theoretical investigations including ab initio computer simulations show considerable differences at such extreme conditions from each other and from experimental values. We apply the reaction ensemble Monte Carlo technique on one hand and a combination of the hypernetted chain approximation with the mass action law on the other to study the behavior of dense hydrogen at such conditions. The agreement between both methods for the equation of state and for the Hugoniot curve is excellent. Comparison to other methods and experimental results is also performed.

Equation of state for weakly coupled quantum plasmas

We calculate thermodynamic properties for a dense hydrogen plasma and a quantum electron gas using thermodynamic Green's function techniques. Our perturbation approach is appropriate to give reliable results in the weak coupling regime. In particular, the contribution of the exchange term of the order e(4) is fully included for the nondegenerate case as well as for the dense highly degenerate quantum region. We compare our results for the equation of state with data obtained by different numerical simulations.