Proton stopping measurements at low velocity in warm dense carbon.

Ion stopping in warm dense matter is a process of fundamental importance for the understanding of the properties of dense plasmas, the realization and the interpretation of experiments involving ion-beam-heated warm dense matter samples, and for inertial confinement fusion research. The theoretical description of the ion stopping power in warm dense matter is difficult notably due to electron coupling and degeneracy, and measurements are still largely missing. In particular, the low-velocity stopping range, that features the largest modelling uncertainties, remains virtually unexplored. Here, we report proton energy-loss measurements in warm dense plasma at unprecedented low projectile velocities. Our energy-loss data, combined with a precise target characterization based on plasma-emission measurements using two independent spectroscopy diagnostics, demonstrate a significant deviation of the stopping power from classical models in this regime. In particular, we show that our results are in closest agreement with recent first-principles simulations based on time-dependent density functional theory.

Systematic Study of L-Shell Opacity at Stellar Interior Temperatures.

The first systematic study of opacity dependence on atomic number at stellar interior temperatures is used to evaluate discrepancies between measured and modeled iron opacity [J. E. Bailey et al., Nature (London) 517, 56 (2015)NATUAS0028-083610.1038/nature14048]. High-temperature (>180 eV) chromium and nickel opacities are measured with ±6%-10% uncertainty, using the same methods employed in the previous iron experiments. The 10%-20% experiment reproducibility demonstrates experiment reliability. The overall model-data disagreements are smaller than for iron. However, the systematic study reveals shortcomings in models for density effects, excited states, and open L-shell configurations. The 30%-45% underestimate in the modeled quasicontinuum opacity at short wavelengths was observed only from iron and only at temperature above 180 eV. Thus, either opacity theories are missing physics that has nonmonotonic dependence on the number of bound electrons or there is an experimental flaw unique to the iron measurement at temperatures above 180 eV.

A higher-than-predicted measurement of iron opacity at solar interior temperatures.

Nearly a century ago it was recognized that radiation absorption by stellar matter controls the internal temperature profiles within stars. Laboratory opacity measurements, however, have never been performed at stellar interior conditions, introducing uncertainties in stellar models. A particular problem arose when refined photosphere spectral analysis led to reductions of 30-50 per cent in the inferred amounts of carbon, nitrogen and oxygen in the Sun. Standard solar models using the revised element abundances disagree with helioseismic observations that determine the internal solar structure using acoustic oscillations. This could be resolved if the true mean opacity for the solar interior matter were roughly 15 per cent higher than predicted, because increased opacity compensates for the decreased element abundances. Iron accounts for a quarter of the total opacity at the solar radiation/convection zone boundary. Here we report measurements of wavelength-resolved iron opacity at electron temperatures of 1.9-2.3 million kelvin and electron densities of (0.7-4.0) × 10(22) per cubic centimetre, conditions very similar to those in the solar region that affects the discrepancy the most: the radiation/convection zone boundary. The measured wavelength-dependent opacity is 30-400 per cent higher than predicted. This represents roughly half the change in the mean opacity needed to resolve the solar discrepancy, even though iron is only one of many elements that contribute to opacity.

Charge equilibrium of a laser-generated carbon-ion beam in warm dense matter.

Using ion carbon beams generated by high intensity short pulse lasers we perform measurements of single shot mean charge equilibration in cold or isochorically heated solid density aluminum matter. We demonstrate that plasma effects in such matter heated up to 1 eV do not significantly impact the equilibration of carbon ions with energies 0.045-0.5 MeV/nucleon. Furthermore, these measurements allow for a first evaluation of semiempirical formulas or ab initio models that are being used to predict the mean of the equilibrium charge state distribution for light ions passing through warm dense matter.

Diagnosis of x-ray heated Mg/Fe opacity research plasmas.

Understanding stellar interiors, inertial confinement fusion, and Z pinches depends on opacity models for mid-Z plasmas in the 100-300 eV temperature range. These models are complex and experimental validation is crucial. In this paper we describe the diagnosis of the first experiments to measure iron plasma opacity at a temperature high enough to produce the charge states and electron configurations that exist in the solar interior. The dynamic Hohlraum x-ray source at Sandia National Laboratories' Z facility was used to both heat and backlight Mg/Fe CH tamped foils. The backlighter equivalent brightness temperature was estimated to be T(r) approximately 314 eV+/-8% using time-resolved x-ray power and imaging diagnostics. This high brightness is significant because it overwhelms the sample self-emission. The sample transmission in the 7-15.5 A range was measured using two convex potassium acid phthalate crystal spectrometers that view the backlighter through the sample. The average spectral resolution over this range was estimated to be lambda/deltalambda approximately 700 by comparing theoretical crystal resolution calculations with measurements at 7.126, 8.340, and 12.254 A. The electron density was determined to be n(e)=6.9+/-1.7 x 10(21) cm(-3) using the Stark-broadened Mg Hebeta, Hegamma, and Hedelta lines. The temperature inferred from the H-like to He-like Mg line ratios was T(e)=156+/-6 eV. Comparisons with three different spectral synthesis models all have normalized chi(2) that is close to unity, indicating quantitative consistency in the inferred plasma conditions. This supports the reliability of the results and implies the experiments are suitable for testing iron opacity models.

Nonequilibrium thermodynamics of highly charged ion plasmas.

Thermodynamics of irreversible processes is applied to study the interaction of matter and radiation field in nonlocal thermodynamic equilibrium. The rate of entropy production of matter and radiation field, in contact with a free electron reservoir in local thermodynamic equilibrium, is obtained using the conjugate variables of the state variables. When approximating the electronic configuration populations by an effective Boltzmann law, the corresponding effective temperature is determined by minimizing the rate of entropy production at fixed electronic density, electronic temperature, and radiation field. Numerical results and comparisons with recent experiment for photoionized iron plasma are presented and discussed.

Description of strongly coupled Yukawa fluids using the variational modified hypernetted chain approach.

The variational modified hypernetted chain approach as proposed by J. Stat. Phys. 42, 437 (1986)] is used to describe strongly coupled Yukawa fluids. The integral equations of interest can be solved using the spherical harmonic oscillator wave functions as a seed. Comparisons are done with simulation results for equation of state and transport coefficients over the entire fluid domain for a wide range of the system parameters.

Equation of state and transport coefficients for dense plasmas.

We hereby present a model to describe the thermodynamic and transport properties of dense plasmas. The electronic and ionic structures are determined self-consistently using finite-temperature density functional theory and Gibbs-Bogolyubov inequality. The main thermodynamic quantities, i.e., internal energy, pressure, entropy, and sound speed, are obtained by numerical differentiation of the plasma total Helmholtz free energy. Electronic electrical and thermal conductivities are calculated from the Ziman approach. Ionic transport coefficients are estimated using those of hard-sphere system and the Rosenfeld semiempirical "universal" correspondence between excess entropy and dimensionless transport coefficients of dense fluids. Numerical results and comparisons with experiments are presented and discussed.

Aluminum equation-of-state data in the warm dense matter regime.

Isochore measurements were performed in the warm dense matter regime. Pressure and internal energy variation of aluminum plasma (density 0.1 g/cm(3) and 0.3 g/cm(3)) are measured using a homogeneous and thermally equilibrated media produced inside an isochoric plasma closed vessel in the internal energy range 20-50 MJ/kg. These data are compared to detailed calculations obtained from ab initio quantum molecular dynamics, average atom model within the framework of the density functional theory, and standard theories. A dispersion between theoretical isochore equation of state is found in the studied experimental thermodynamic regime.

Gibbs-Bogolyubov inequality and transport properties for strongly coupled Yukawa fluids.

The Gibbs-Bogolyubov inequality is used to establish a mapping between the Yukawa system and both the hard-sphere and the one-component reference systems. The transport coefficients of self-diffusion, shear viscosity, and thermal conductivity are computed for the Yukawa fluid using known properties of the reference systems. Comparisons are made with simulation results. For sufficiently strong screening, the hard-sphere reference system yields a lower upper bound of the Yukawa Helmholtz free energy and a better estimate of the Yukawa transport coefficients.

Combined pressure and electrical-resistivity measurements of warm dense aluminum and titanium plasmas.

Electrical resistivity, pressure, and internal energy variation of warm dense correlated titanium (density 0.2 g/cm(3)) and aluminum (density 0.1 g/cm(3)) plasmas are measured using a homogeneous and thermally equilibrated media produced inside an isochoric closed-vessel plasma. These data are compared to detailed calculations based on the density functional theory. In the studied temperature range (15,000-30,000 K), it appears that both exchange-correlation and ion-ion interaction treatments are of great importance to calculate accurate theoretical values.

Generalization of super-transition-array methods to hot dense plasmas by using optimum independent particle reference systems.

The computation of superconfiguration partition functions relies upon independent electron statistics, with electron-electron contributions included as an average first-order correction factor. The decomposition into a first-order correction and reference independent electron system has degrees of freedom not exploited by current methods. We present a derivation for the conventional choice of decomposition and propose a different method for obtaining an optimal decomposition for each superconfiguration. This constitutes an alternative procedure to recomputing self-consistent fields for the refinement of superconfiguration partition functions. Numerical results are presented and discussed.

Nonlocal thermodynamic equilibrium self-consistent average-atom model for plasma physics.

A time-dependent collisional-radiative average-atom model is presented to study statistical properties of highly charged ion plasmas in off-equilibrium conditions. The time evolution of electron populations and the electron covariance matrix is obtained as approximate solutions of a master equation. Atomic structure is described either with a screened-hydrogenic model including l splitting, or by calculating one-electron states in a self-consistent average-atom potential. Collisional and radiative excitation/deexcitation and ionization/recombination rates, as well as autoionization and dielectronic recombination rates, are formulated within the average-configuration framework. Local thermodynamic equilibrium is obtained as a specific steady-state solution. The influence of atomic structure and the role of autoionization and dielectronic recombination processes are studied by calculating steady-state average ionization and ionization variance of hot plasmas with or without radiation field.

Superconfiguration accounting approach versus average-atom model in local-thermodynamic-equilibrium highly ionized plasmas.

Statistical methods of describing and simulating complex ionized plasmas requires the development of reliable and computationally tractable models. In that spirit, we propose the screened-hydrogenic average atom, augmented with corrections resulting from fluctuations of the occupation probabilities around the mean-field equilibrium, as an approximation to calculate the grand potential and related statistical properties. Our main objective is to check the validity of this approach by comparing its predictions with those given by the superconfiguration accounting method. The latter is well-suited to this purpose. In effect, this method makes it possible to go beyond the mean-field model by using nonperturbative, analytic, and systematic techniques. Besides, it allows us to establish the relationship between the detailed configuration accounting and the average-atom methods. To our knowledge, this is the first time that the superconfiguration description has been used in this context. Finally, this study is also the occasion for presenting a powerful technique from analytic number theory to calculate superconfiguration averaged quantities.