Thermodynamic and transport properties of dense hydrogen plasmas

Exciton Nature of Plasma Phase Transition in Warm Dense Fluid Hydrogen: ROKS Simulation

The transition of warm dense fluid hydrogen from an insulator to a conducting state at pressures of about 20-400 GPa and temperatures of 500-5000 K has been the subject of active scientific research over the past few decades. However, various experimental and theoretical methods do not provide consistent results. In this work, we have applied the restricted open-shell Kohn-Sham (ROKS) method for first principles molecular dynamics of dense hydrogen after thermal excitation to the first singlet excited state. The Wannier localization method has allowed us to analyze the exciton dynamics in this system. The model shows that a key mechanism of the transition is associated with the dissociation of electron-hole pairs, which allows explaining several stages of the transition of fluid H₂ from molecular state to plasma. This mechanism is able to give a quantitative description of several experimental results as well as to resolve the discrepancies between experimental studies.

Transport properties of warm dense neon and krypton at high pressures

The transport properties of warm dense neon (Ne) and krypton (Kr) are studied by combining self-consistent fluid variational theory (SFVT) with linear response theory (LRT). The components are determined using the SFVT, and the transport parameters, including the electrical conductivity, thermal conductivity, and thermopower, are calculated with the LRT. The relevant scattering mechanisms, including electron-ion, electron-electron, and electron-atom scatterings, are taken into account. An effective potential model in combination with the Muffin-tin model is introduced to further improve the description for electron-atom scattering, which not only includes static, exchange, and polarization interactions but also considers the plasma environmental effects. It is found that for electron-atom scattering, the influence of the plasma density is significant at lower scattering energies but the effects are different for electron-Ne and electron-Kr scattering. For electron-Kr scattering, a plasma density-dependent Ramsauer-Townsend minimum is observed. The obtained transport parameters are compared with the available experiments and other simulations. The plasma phase transition of warm dense Kr is revisited from multiple perspectives based on the numerical simulation results for the electrical conductivity and thermopower. These observations may help one to better understand the transport properties of warm dense noble gases and are an important guide for future experimental designs and theoretical developments.

Thermodynamic and Transport Properties of Equilibrium Debye Plasmas

The thermodynamic and transport properties of weakly non-ideal, high-density partially ionized hydrogen plasma are investigated, accounting for quantum effects due to the change in the energy spectrum of atomic hydrogen when the electron-proton interaction is considered embedded in the surrounding particles. The complexity of the rigorous approach led to the development of simplified models, able to include the neighbor-effects on the isolated system while remaining consistent with the traditional thermodynamic approach. High-density conditions have been simulated assuming particle interactions described by a screened Coulomb potential.

Structural characteristics of strongly coupled ions in a dense quantum plasma

The structural properties of strongly coupled ions in dense plasmas with moderately to strongly degenerate electrons are investigated in the framework of the one-component plasma model of ions interacting through a screened pair interaction potential. Special focus is put on the description of the electronic screening in the Singwi-Tosi-Land-Sjölander (STLS) approximation. Different cross-checks and analyses using ion potentials obtained from ground-state quantum Monte Carlo data, the random phase approximation (RPA), and existing analytical models are presented for the computation of the structural properties, such as the pair distribution and the static structure factor, of strongly coupled ions. The results are highly sensitive to the features of the screened pair interaction potential. This effect is particularly visible in the static structure factor. The applicability range of the screened potential computed from STLS is identified in terms of density and temperature of the electrons. It is demonstrated that at r_{s}>1, where r_{s} is the ratio of the mean interelectronic distance to the Bohr radius, electronic correlations beyond RPA have a nonnegligible effect on the structural properties. Additionally, the applicability of the hypernetted chain approximation for the calculation of the structural properties using the screened pair interaction potential is analyzed employing the effective coupling parameter approach.

Conductivity and dissociation in liquid metallic hydrogen and implications for planetary interiors

Liquid metallic hydrogen (LMH) is the most abundant form of condensed matter in our solar planetary structure. The electronic and thermal transport properties of this metallic fluid are of fundamental interest to understanding hydrogen's mechanism of conduction, atomic or pairing structure, as well as the key input for the magnetic dynamo action and thermal models of gas giants. Here, we report spectrally resolved measurements of the optical reflectance of LMH in the pressure region of 1.4-1.7 Mbar. We analyze the data, as well as previously reported measurements, using the free-electron model. Fitting the energy dependence of the reflectance data yields a dissociation fraction of 65 ± 15%, supporting theoretical models that LMH is an atomic metallic liquid. We determine the optical conductivity of LMH and find metallic hydrogen's static electrical conductivity to be 11,000-15,000 S/cm, substantially higher than the only earlier reported experimental values. The higher electrical conductivity implies that the Jovian and Saturnian dynamo are likely to operate out to shallower depths than previously assumed, while the inferred thermal conductivity should provide a crucial experimental constraint to heat transport models.

Contribution of electron-atom collisions to the plasma conductivity of noble gases

We present an approach which allows the consistent treatment of bound states in the context of dc conductivity in dense partially ionized noble gas plasmas. Besides electron-ion and electron-electron collisions, further collision mechanisms owing to neutral constituents are taken into account. Especially at low temperatures of 10^{4}to10^{5} K, electron-atom collisions give a substantial contribution to the relevant correlation functions. We suggest an optical potential for the description of the electron-atom scattering which is applicable for all noble gases. The electron-atom momentum-transfer cross section is in agreement with experimental scattering data. In addition, the influence of the medium is analyzed, the optical potential is advanced including screening effects. The position of the Ramsauer minimum is influenced by the plasma. Alternative approaches for the electron-atom potential are discussed. Good agreement of calculated conductivity with experimental data for noble gas plasmas is obtained.

Density-functional calculations of transport properties in the nondegenerate limit and the role of electron-electron scattering

We compute electrical and thermal conductivities of hydrogen plasmas in the nondegenerate regime using Kohn-Sham density functional theory (DFT) and an application of the Kubo-Greenwood response formula, and demonstrate that for thermal conductivity, the mean-field treatment of the electron-electron (e-e) interaction therein is insufficient to reproduce the weak-coupling limit obtained by plasma kinetic theories. An explicit e-e scattering correction to the DFT is posited by appealing to Matthiessen's Rule and the results of our computations of conductivities with the quantum Lenard-Balescu (QLB) equation. Further motivation of our correction is provided by an argument arising from the Zubarev quantum kinetic theory approach. Significant emphasis is placed on our efforts to produce properly converged results for plasma transport using Kohn-Sham DFT, so that an accurate assessment of the importance and efficacy of our e-e scattering corrections to the thermal conductivity can be made.

Effective potentials of interactions and thermodynamic properties of a nonideal two-temperature dense plasma

In this article a dense nonideal, nonisothermal plasma is considered. New effective screened interaction potentials taking into account quantum-mechanical diffraction and symmetry effects have been obtained. The effective potential of the ion-ion interaction in plasmas with a strongly coupled ion subsystem and semiclassical electron subsystem is presented. Based on the obtained effective potentials the analytical expressions for internal energy and the pressure of the considered plasma were obtained.

Free-electron X-ray laser measurements of collisional-damped plasmons in isochorically heated warm dense matter

We present the first highly resolved measurements of the plasmon spectrum in an ultrafast heated solid. Multi-keV x-ray photons from the Linac Coherent Light Source have been focused to one micrometer diameter focal spots producing solid density aluminum plasmas with a known electron density of n_{e}=1.8×10^{23}  cm^{-3}. Detailed balance is observed through the intensity ratio of up- and down-shifted plasmons in x-ray forward scattering spectra measuring the electron temperature. The plasmon damping is treated by electron-ion collision models beyond the Born approximation to determine the electrical conductivity of warm dense aluminum.

Conductivity of warm dense matter including electron-electron collisions

We present an approach that can resolve the controversy with respect to the role of electron-electron collisions in calculating the dynamic conductivity of dense plasmas. In particular, the dc conductivity is analyzed in the low-density, nondegenerate limit where the Spitzer theory is valid and electron-electron collisions lead to the well-known reduction in comparison to the result considering only electron-ion collisions (Lorentz model). With increasing degeneracy, the contribution of electron-electron collisions to the dc conductivity is decreasing and can be neglected for the liquid metal domain where the Ziman theory is applicable. We give expressions for the effect of electron-electron collisions in calculating the conductivity in the warm dense matter region, i.e., for strongly coupled Coulomb systems at arbitrary degeneracy.

Equations of state, transport properties, and compositions of argon plasma: combination of self-consistent fluid variation theory and linear response theory

A consistent theoretical model that can be applied in a wide range of densities and temperatures is necessary for understanding the variation of a material's properties during compression and heating. Taking argon as an example, we show that the combination of self-consistent fluid variational theory and linear response theory is a promising route for studying warm dense matter. Following this route, the compositions, equations of state, and transport properties of argon plasma are calculated in a wide range of densities (0.001-20 g/cm(3)) and temperatures (5-100 kK). The obtained equations of state and electrical conductivities are found in good agreement with available experimental data. The plasma phase transition of argon is observed at temperatures below 30 kK and density about 2-6g/cm(3). The minimum density for the metallization of argon is found to be about 5.8 g/cm(3), occurring at 30-40 kK. The effects of many-particle correlations and dynamic screening on the electrical conductivity are also discussed through the effective potentials.

Effective potential theory for transport coefficients across coupling regimes

A plasma transport theory that spans weak to strong coupling is developed from a binary collision picture, but where the interaction potential is taken to be an effective potential that includes correlation effects and screening self-consistently. This physically motivated approach provides a practical model for evaluating transport coefficients across coupling regimes. The theory is shown to compare well with classical molecular dynamics simulations of temperature relaxation in electron-ion plasmas as well as simulations and experiments of self-diffusion in one-component plasmas. The approach is versatile and can be applied to other transport coefficients as well.

Dielectric function beyond the random-phase approximation: kinetic theory versus linear response theory

Calculating the frequency-dependent dielectric function for strongly coupled plasmas, the relations within kinetic theory and linear response theory are derived and discussed in comparison. In this context, we give a proof that the Kohler variational principle can be extended to arbitrary frequencies. It is shown to be a special case of the Zubarev method for the construction of a nonequilibrium statistical operator from the principle of the extremum of entropy production. Within kinetic theory, the commonly used energy-dependent relaxation time approach is strictly valid only for the Lorentz plasma in the static case. It is compared with the result from linear response theory that includes electron-electron interactions and applies for arbitrary frequencies, including bremsstrahlung emission. It is shown how a general approach to linear response encompasses the different approximations and opens options for systematic improvements.

Application of linear response theory to magnetotransport properties of dense plasmas

Linear response theory, as developed within the Zubarev formalism, is a quantum statistical approach for describing systems out of but close to equilibrium, which has been successfully applied to a wide variety of plasmas in an external electric field and/or containing a temperature gradient. We present here an extension of linear response theory to include the effects of an external magnetic field. General expressions for the complete set of relevant transport properties are given. In particular, the Hall effect and the influence of a magnetic field on the dc electrical conductivity are discussed. Low-density limits including electron-electron scattering are presented as well as results for arbitrary degeneracy.

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.

Local-field-correction effects on the electron response functions and on the electrical conductivity in a hydrogen plasma

In a one-component plasma constituted by electrons with a uniform positive background, the correlations are studied in the framework of the Singwi, Tosi, Land, and Sjölander (STLS) model. The local-field corrections (LFCs) are calculated with electron density ranging from 10;{19}to10;{26}cm;{-3} and with a temperature of 10;{4}K . Then, a dielectric formalism is used to deduce the potential energy of a positive test charge (a proton) imbedded in the electron medium. A significant departure of this potential from the random phase approximation (RPA) one has been found. In particular, as the density increases, the discrepancy between the two potentials grows up to reach a maximum correlated to the maximum of the electron coupling parameter. In addition, it is found that in both high and low density limits, the STLS and RPA approaches yield similar results. On the other hand, the effect of the LFC on the electrical conductivity is also estimated in hydrogen plasmas.

Ionization and equation of state of dense xenon at high pressures and high temperatures

The ionization degree and equation of state of dense xenon plasma were calculated by using self-consistent fluid variational theory for temperature of 4-30kK and density of 0.01-8.5gcm;{3} . The dense fluid xenon will be ionized at high pressures and temperatures. The ionization energy of xenon will be lowered due to the interactions among all particles of Xe, Xe+ , Xe2+ , and e . The ionization degree is obtained from nonideal ionization equilibrium, taking into account the correlative contributions to the chemical potential which is determined self-consistently by the free energy function. The composition of xenon has been calculated with given densities and temperatures in the region of partial ionization. The calculated results show a pressure softening regime at the onset of ionization. Comparison is performed with available shock-wave experiments and other theoretical calculations.

Electrical conductivity of noble gases at high pressures

Theoretical results for the electrical conductivity of noble gas plasmas are presented in comparison with experiment. The composition is determined within a partially ionized plasma model. The conductivity is then calculated using linear response theory, in which the relevant scattering mechanisms of electrons from ions, electrons, and neutral species are taken into account. In particular, the Ramsauer-Townsend effect in electron-neutral scattering is discussed and the importance of a correct description of the Coulomb logarithm in electron scattering by charged particles is shown. A detailed comparison with recent experiments on argon and xenon plasmas is given and results for helium and neon are also revisited. Excellent agreement between theory and experiment is observed, showing considerable improvement upon previous calculations.

Static and dynamic conductivity of warm dense matter within a density-functional approach: application to aluminum and gold

The conductivity sigma(omega) of dense Al and Au plasmas is considered where all the needed inputs are obtained from density-functional theory (DFT). These calculations involve a self-consistent determination of (i) the equation of state and the ionization balance, (ii) evaluation of the ion-ion and ion-electron pair-distribution functions, (iii) determination of the scattering amplitudes, and finally the conductivity. We present results for Al and Au for compressions 0.1-2.0, and in the temperature range T=0.1-10 eV. Excellent agreement with recent first-principles calculations using multi-ion density-functional molecular dynamics is obtained where the data fields overlap. We review first-principles approaches to the optical conductivity, including many-body perturbation theory, molecular-dynamics evaluations, and simplified time-dependent DFT. The modification to the Drude conductivity in the presence of shallow bound states in typical Al plasmas is examined and numerical results are given at the level of the Fermi Golden Rule and an approximate time-dependent DFT.

Analytic electrical-conductivity tensor of a nondegenerate Lorentz plasma

We have developed explicit quantum-mechanical expressions for the conductivity and resistivity tensors of a Lorentz plasma in a magnetic field. The expressions are based on a solution to the Boltzmann equation that is exact when the electric field is weak, the electron-Fermi-degeneracy parameter Theta>>1, and the electron-ion Coulomb-coupling parameter Gamma/Z<<1. (Gamma is the ion-ion coupling parameter and Z is the ion charge state.) Assuming a screened 1/r electron-ion scattering potential, we calculate the Coulomb logarithm in the second Born approximation. The ratio of the term obtained in the second approximation to that obtained in the first is used to define the parameter regime over which the calculation is valid. We find that the accuracy of the approximation is determined by Gamma/Z and not simply the temperature, and that a quantum-mechanical description can be required at temperatures orders of magnitude less than assumed by Spitzer [Physics of Fully Ionized Gases (Wiley, New York, 1962)]. When the magnetic field B=0, the conductivity is identical to the Spitzer result except the Coulomb logarithm ln Lambda(1)=(ln chi(1)-1 / 2)+[(2Ze(2)/lambdam(e)v(2)(e1))(ln chi(1)-ln 2(4/3))], where chi(1) identical with 2m(e)v(e1)lambda/ variant Planck's over 2pi, m(e) is the electron mass, v(e1) identical with (7k(B)T/m(e))(1/2), k(B) is the Boltzmann constant, T is the temperature, lambda is the screening length, variant Planck's over 2pi is Planck's constant divided by 2pi, and e is the absolute value of the electron charge. When the plasma Debye length lambda(D) is greater than the ion-sphere radius a, we assume lambda=lambda(D); otherwise we set lambda=a. The B=0 conductivity is consistent with measurements when Z greater, similar 1, Theta greater, similar 2, and Gamma/Z less, similar 1, and in this parameter regime appears to be more accurate than previous analytic models. The minimum value of ln Lambda(1) when Z> or =1, Theta> or =2, and Gamma/Z< or =1 is 1.9. The expression obtained for the resistivity tensor (B not equal 0) predicts that eta( perpendicular )/eta( parallel ) (where eta( perpendicular ) and eta( parallel ) are the resistivities perpendicular and parallel to the magnetic field) can be as much as 40% less than previous analytic calculations. The results are applied to an idealized 17-MA z pinch at stagnation.

Electrical conductivity of nonideal carbon and zinc plasmas: experimental and theoretical results

Electrical conductivities of nonideal carbon and zinc plasmas have been measured in this paper. The plasma is produced by vaporizing a wire placed in a glass capillary within some hundred nanoseconds. In the case of carbon, vaporization occurs with good reproducibility when utilizing a preheating system. The particle density is in the range of n=(1-10) x 10(21) cm(-3). The plasma temperature, which is obtained by fitting a Planck function to the measured spectrum, is between 7-15 kK. Plasma radius and behavior of the plasma expansion were studied with a streak, a framing or an intensified charge coupled device camera. We compare the measured electrical conductivities with theoretical results, which were obtained solving quantum kinetic equations for the nonideal partially ionized plasmas. In this approach, the transport cross sections are calculated on the level of a T-matrix approximation using effective potentials. The plasma composition is determined from a system of coupled mass action laws with nonideality corrections.

Transport coefficients for dense metal plasmas

Thermoelectric transport coefficients of metal plasmas are calculated within the linear response theory applied previously to determine the electrical conductivity of Al and Cu plasmas [R. Redmer, Phys. Rev. E 59, 1073 (1999)]. We consider temperatures of 1-3 eV and densities of 0.001-1 g/cm(3) as relevant in rapid wire evaporation experiments. The plasma composition is calculated considering higher ionization stages of atoms up to 5+, and solving the respective system of coupled mass action laws. Interactions between charged particles are treated on T matrix level. Results for the electrical conductivity of various metal plasmas are in reasonable agreement with experimental data. Thermal conductivity and thermopower are also given. In addition, we compare with experimental data for temperatures up to 25 eV and liquidlike densities.

Long-wavelength limit of the dynamical local-field factor and dynamical conductivity of a two-component plasma

A systematic approach to the optical conductivity is given within a dielectric function formalism. The response function as well as the dynamical local-field factor G(k-->,omega) of an electron-ion plasma can be expressed in terms of determinants of equilibrium correlation functions which allow for a perturbative treatment. The dynamical collision frequency nu(omega)=-iomega(2)(pl)G(0,omega)/omega for fully ionized weakly coupled plasmas is evaluated in the low-density limit. A renormalization function is given to describe the effects of higher moments of the distribution function, thus the Spitzer formula is reproduced in the static limit. The existence of the third moment sum rule can be shown analytically. Numerical calculations are presented for the dynamical conductivity of hydrogen plasmas at solar core conditions.

Electron density separations in nonideal plasmas: structure of Thomas-Fermi-like bound states and the Mott transition

Starting from a general free energy functional, the chemical picture for nonideal plasmas arises from a certain separation of the electron density. Defining a bound state and its electrostatically screening plasma environment as a subsystem, a simple theory for plasma-correspondent bound state structure can be formulated. This provides the possibility to derive adjustable parameters for the interactions in the chemical picture. The Mott transition corresponds to the violation of the normalization condition due to plasma influences.

Response function including collisions for an interacting fermion gas

The response function of an interacting fermion gas is considered in the entire (k-->,omega) space. Applying a generalized linear response theory, it is expressed in terms of determinants of equilibrium correlation functions, which allow for a systematic perturbative treatment. The relation to dynamical local-field factors is given. As a special case, the dielectric function is evaluated for two-component (hydrogen) plasmas at arbitrary degeneracies. Collisions are treated in Born approximation leading to a (k-->,omega)-dependent collision integral. The link to the dynamical conductivity is given in the long-wavelength limit. Sum rules are discussed.

Measurements of the equation of state of deuterium at the fluid insulator-metal transition

A high-intensity laser was used to shock-compress liquid deuterium to pressures from 22 to 340 gigapascals. In this regime deuterium is predicted to transform from an insulating molecular fluid to an atomic metallic fluid. Shock densities and pressures, determined by radiography, revealed an increase in compressibility near 100 gigapascals indicative of such a transition. Velocity interferometry measurements, obtained by reflecting a laser probe directly off the shock front in flight, demonstrated that deuterium shocked above 55 gigapascals has an electrical conductivity characteristic of a liquid metal and independently confirmed the radiography.