Diffusion in ionic mixtures across coupling regimes

Intrinsic bulk viscosity of the one-component plasma

The intrinsic bulk viscosity of the one-component plasma (OCP) is computed and analyzed using equilibrium molecular dynamics simulations and the Green-Kubo formalism. It is found that bulk viscosity exhibits a maximum at Γ≈1, corresponding to the condition that the average kinetic energy of particles equals the potential energy at the average interparticle spacing. The weakly coupled and strongly coupled limits are analyzed and used to construct a model that captures the full range of coupling strengths simulated: Γ≈10^{-2}-10^{2}. Simulations are also run of the Yukawa one-component plasma (YOCP) in order to understand the impact of electron screening. It is found that electron screening leads to a smaller bulk viscosity due to a reduction in the excess heat capacity of the system. Bulk viscosity is shown to be at least an order of magnitude smaller than shear viscosity in both the OCP and YOCP. The generalized frequency-dependent bulk viscosity coefficient is also analyzed. This is found to exhibit a peak near twice the plasma frequency in strongly coupled conditions, which is associated with the oscillatory decay observed in the bulk viscosity autocorrelation function. The generalized shear and bulk viscosity coefficients are found to have a similar magnitude for ω≳2ω_{p} at strongly coupled conditions.

Universal Diffusion in Coulomb Crystals

Diffusion coefficients for crystallized Coulomb plasmas are essential microphysics input for modeling white dwarf cores and neutron star crusts but are poorly understood. In this work we present a model for diffusion in Coulomb crystals. We show that melting and diffusion follow the same universal scaling such that diffusion is independent of screening. Our simulations show, contrary to prevailing wisdom, that the formation of vacancies is not suppressed by the large pressure. Rather, vacancy formation and hole diffusion is the dominant mode of self-diffusion in Coulomb crystals.

Bulk viscosity of the rigid rotor one-component plasma

Bulk viscosity of a plasma consisting of strongly coupled diatomic ions is computed using molecular dynamics simulations. The simulations are based on the rigid rotor one-component plasma, which is introduced as a model system that adds two degrees of molecular rotation to the traditional one-component plasma. It is characterized by two parameters: the Coulomb coupling parameter, Γ, and the bond length parameter, Ω. Results show that the long-range nature of the Coulomb potential can lead to long rotational relaxation times, which in turn yield large values for bulk viscosity. The bulk-to-shear viscosity ratio is found to span from small to large values depending on the values of Γ and Ω. Although bulk viscosity is often neglected in plasma modeling, these results motivate that it can be large in molecular plasmas with rotational degrees of freedom.

Numerical study of the transverse diffusion coefficient for a one component model of plasma

In this paper, we discuss the results of some molecular dynamics simulations of a magnetized one component plasma, targeted to estimate the diffusion coefficient D_⊥ in the plane orthogonal to the magnetic field lines. We find that there exists a threshold with respect to the magnetic field strength |B→|: for weak magnetic field, the diffusion coefficients scale as 1/|B→|², while a slower decay appears at high field strength. The relation of this transition with the different mixing properties of the microscopic dynamics is investigated by looking at the behavior of the velocity autocorrelation.

Excess entropy and Stokes-Einstein relation in simple fluids

The Stokes-Einstein (SE) relation between the self-diffusion and shear viscosity coefficients operates in sufficiently dense liquids not too far from the liquid-solid phase transition. By considering four simple model systems with very different pairwise interaction potentials (Lennard-Jones, Coulomb, Debye-Hückel or screened Coulomb, and the hard sphere limit) we identify where exactly on the respective phase diagrams the SE relation holds. It appears that the reduced excess entropy s_{ex} can be used as a suitable indicator of the validity of the SE relation. In all cases considered the onset of SE relation validity occurs at approximately s_{ex}≲-2. In addition, we demonstrate that the line separating gaslike and liquidlike fluid behaviours on the phase diagram is roughly characterized by s_{ex}≃-1.

Vibrational model of thermal conduction for fluids with soft interactions

A vibrational model of heat transfer in simple liquids with soft pairwise interatomic interactions is discussed. A general expression is derived, which involves an averaging over the liquid collective mode excitation spectrum. The model is applied to quantify heat transfer in a dense Lennard-Jones liquid and a strongly coupled one-component plasma. Remarkable agreement with the available numerical results is documented. A similar picture does not apply to the momentum transfer and shear viscosity of liquids.

Multiscale simulation of plasma flows using active learning

Plasma flows encountered in high-energy-density experiments display features that differ from those of equilibrium systems. Nonequilibrium approaches such as kinetic theory (KT) capture many, if not all, of these phenomena. However, KT requires closure information, which can be computed from microscale simulations and communicated to KT. We present a concurrent heterogeneous multiscale approach that couples molecular dynamics (MD) with KT in the limit of near-equilibrium flows. To reduce the cost of gathering information from MD, we use active learning to train neural networks on MD data obtained by randomly sampling a small subset of the parameter space. We apply this method to a plasma interfacial mixing problem relevant to warm dense matter, showing considerable computational gains when compared with the full kinetic-MD approach. We find that our approach enables the probing of Coulomb coupling physics across a broad range of temperatures and densities that are inaccessible with current theoretical models.

Structure of multicomponent Coulomb crystals

Coulomb plasmas crystallize in a number of physical systems, such as dusty plasmas, neutron star crusts, and white dwarf cores. The crystal structure of the one-component and binary plasma has received significant attention in the literature, though the less studied multicomponent plasma may be most relevant for many physical systems which contain a large range of particle charges. We report on molecular dynamics simulations of multicomponent plasmas near the melting temperature with mixtures taken to be realistic x-ray burst ash compositions. We quantify the structure of the crystal with the bond order parameters and radial distribution function. Consistent with past work, low charge particles form interstitial defects and we argue that they are in a quasiliquid state within the lattice. The lattice shows screening effects which preserves long-range order despite the large variance in particle charges, which may impact transport properties relevant to astrophysics.

Ion friction at small values of the Coulomb logarithm

Transport properties of high-energy-density plasmas are influenced by the ion collision rate. Traditionally, this rate involves the Coulomb logarithm, lnΛ. Typical values of lnΛ are ≈10-20 in kinetic theories where transport properties are dominated by weak-scattering events caused by long-range forces. The validity of these theories breaks down for strongly coupled plasmas, when lnΛ is of order one. We present measurements and simulations of collision data in strongly coupled plasmas when lnΛ is small. Experiments are carried out in the first dual-species ultracold neutral plasma (UNP), using Ca^{+} and Yb^{+} ions. We find strong collisional coupling between the different ion species in the bulk of the plasma. We simulate the plasma using a two-species fluid code that includes Coulomb logarithms derived from either a screened Coulomb potential or a the potential of mean force. We find generally good agreement between the experimental measurements and the simulations. With some improvements, the mixed Ca^{+} and Yb^{+} dual-species UNP will be a promising platform for testing theoretical expressions for lnΛ and collision cross-sections from kinetic theories through measurements of energy relaxation, stopping power, two-stream instabilities, and the evolution of sculpted distribution functions in an idealized environment in which the initial temperatures, densities, and charge states are accurately known.

Laser cooling of ions in a neutral plasma

Laser cooling of a neutral plasma is a challenging task because of the high temperatures typically associated with the plasma state. By using an ultracold neutral plasma created by photoionization of an ultracold atomic gas, we avoid this obstacle and demonstrate laser cooling of ions in a neutral plasma. After 135 microseconds of cooling, we observed a reduction in ion temperature by up to a factor of four, with the temperature reaching as low as 50(4) millikelvin. This pushes laboratory studies of neutral plasmas deeper into the strongly coupled regime, beyond the limits of validity of current kinetic theories for calculating transport properties. The same optical forces also retard the plasma expansion, opening avenues for neutral-plasma confinement and manipulation.

Dynamic electron-ion collisions and nuclear quantum effects in quantum simulation of warm dense matter

The structural, thermodynamic and transport properties of warm dense matter (WDM) are crucial to the fields of astrophysics and planet science, as well as inertial confinement fusion. WDM refers to the states of matter in a regime of temperature and density between cold condensed matter and hot ideal plasmas, where the density is from near-solid up to ten times solid density, and the temperature between 0.1 and 100 eV. In the WDM regime, matter exhibits moderately or strongly coupled, partially degenerate properties. Therefore, the methods used to deal with condensed matter and isolated atoms need to be properly validated for WDM. It is therefore a big challenge to understand WDM within a unified theoretical description with reliable accuracy. Here, we review the progress in the theoretical study of WDM with state-of-the-art simulations, i.e. quantum Langevin molecular dynamics and first principles path integral molecular dynamics. The related applications for WDM are also included.

Mixing with applications to inertial-confinement-fusion implosions

Approximate one-dimensional (1D) as well as 2D and 3D simulations are playing an important supporting role in the design and analysis of future experiments at National Ignition Facility. This paper is mainly concerned with 1D simulations, used extensively in design and optimization. We couple a 1D buoyancy-drag mix model for the mixing zone edges with a 1D inertial confinement fusion simulation code. This analysis predicts that National Ignition Campaign (NIC) designs are located close to a performance cliff, so modeling errors, design features (fill tube and tent) and additional, unmodeled instabilities could lead to significant levels of mix. The performance cliff we identify is associated with multimode plastic ablator (CH) mix into the hot-spot deuterium and tritium (DT). The buoyancy-drag mix model is mode number independent and selects implicitly a range of maximum growth modes. Our main conclusion is that single effect instabilities are predicted not to lead to hot-spot mix, while combined mode mixing effects are predicted to affect hot-spot thermodynamics and possibly hot-spot mix. Combined with the stagnation Rayleigh-Taylor instability, we find the potential for mix effects in combination with the ice-to-gas DT boundary, numerical effects of Eulerian species CH concentration diffusion, and ablation-driven instabilities. With the help of a convenient package of plasma transport parameters developed here, we give an approximate determination of these quantities in the regime relevant to the NIC experiments, while ruling out a variety of mix possibilities. Plasma transport parameters affect the 1D buoyancy-drag mix model primarily through its phenomenological drag coefficient as well as the 1D hydro model to which the buoyancy-drag equation is coupled.

Effective potential theory for diffusion in binary ionic mixtures

Self-diffusion and interdiffusion coefficients of binary ionic mixtures are evaluated using the effective potential theory (EPT), and the predictions are compared with the results of molecular dynamics simulations. We find that EPT agrees with molecular dynamics from weak coupling well into the strong-coupling regime, which is a similar range of coupling strengths as previously observed in comparisons with the one-component plasma. Within this range, typical relative errors of approximately 20% and worst-case relative errors of approximately 40% are observed. We also examine the Darken model, which approximates the interdiffusion coefficients based on the self-diffusion coefficients.

Transport properties of hydrogen-helium mixtures at extreme density and temperature conditions

We perform a systematic study of hydrogen-helium mixtures using quantum molecular dynamics (QMD) with a focus on the equations of state and structural and transport properties such as electrical conductivity, diffusion, and viscosity at conditions of giant planet interiors of 0.2∼2.3 g/cm(3) and 1000∼80,000 K for a typical helium mass fraction of 0.245. The H-He separation is found at low temperatures by analyzing the trajectories and pair distribution functions. We show that the diffusion coefficients exhibit transitions from kinetics- to potential-, and then to demixing-dominated regimes. In addition, we identify the discontinuity feature of optical absorption of a H-He mixture at low density and temperature conditions, which results from the change from an intraband to an interband transition. The Stokes-Einstein relation between the diffusion and viscosity coefficients is also discussed.

Transport properties and equation of state for HCNO mixtures in and beyond the warm dense matter regime

We present simulations of a four-component mixture of HCNO with orbital free molecular dynamics (OFMD). These simulations were conducted for 5-200 eV with densities ranging between 0.184 and 36.8 g/cm3. We extract the equation of state from the simulations and compare to average atom models. We found that we only need to add a cold curve model to find excellent agreement. Additionally, we studied mass transport properties. We present fits to the self-diffusion and shear viscosity that are able to reproduce the transport properties over the parameter range studied. We compare these OFMD results to models based on the Coulomb coupling parameter and one-component plasmas.

Modified Enskog kinetic theory for strongly coupled plasmas

Concepts underlying the Enskog kinetic theory of hard-spheres are applied to include short-range correlation effects in a model for transport coefficients of strongly coupled plasmas. The approach is based on an extension of the effective potential transport theory [S. D. Baalrud and J. Daligault, Phys. Rev. Lett. 110, 235001 (2013)] to include an exclusion radius surrounding individual charged particles that is associated with Coulomb repulsion. This is obtained by analogy with the finite size of hard spheres in Enskog's theory. Predictions for the self-diffusion and shear viscosity coefficients of the one-component plasma are tested against molecular dynamics simulations. The theory is found to accurately capture the kinetic contributions to the transport coefficients, but not the potential contributions that arise at very strong coupling (Γ≳30). Considerations related to a first-principles generalization of Enskog's kinetic equation to continuous potentials are also discussed.

Effective potential and interdiffusion in binary ionic mixtures

We calculate interdiffusion coefficients in a two-component, weakly or strongly coupled ion plasma (gas or liquid, composed of two ion species immersed into a neutralizing electron background). We use an effective potential method proposed recently by Baalrud and Daligaut [Phys. Rev. Lett. 110, 235001 (2013)]. It allows us to extend the standard Chapman-Enskog procedure of calculating the interdiffusion coefficients to the case of strong Coulomb coupling. We compute binary diffusion coefficients for several ionic mixtures and fit them by convenient expressions in terms of the generalized Coulomb logarithm. These fits cover a wide range of plasma parameters spanning from weak to strong Coulomb couplings. They can be used to simulate diffusion of ions in ordinary stars as well as in white dwarfs and neutron stars.

Determination of the shear viscosity of the one-component plasma

The shear viscosity coefficient of the one-component plasma is calculated with unprecedented accuracy using equilibrium molecular dynamics simulations and the Green-Kubo relation. Numerical and statistical uncertainties and their mitigation for improving accuracy are analyzed. In the weakly coupled regime, our results agree with the Landau-Spitzer prediction. In the moderately and strongly coupled regimes, our results are found in good agreement with recent results obtained for the Yukawa one-component plasma using nonequilibrium molecular dynamics. A practical formula is provided for evaluating the viscosity coefficient across coupling regimes, from the weakly coupled regime to solidification threshold. The results are used to test theoretical predictions of the viscosity coefficients found in the literature.

Diffusivity in asymmetric Yukawa ionic mixtures in dense plasmas

In this paper we present molecular dynamics (MD) calculations of the interdiffusion coefficient for asymmetric mixed plasma for thermodynamic conditions relevant to astrophysical and inertial confinement fusion plasmas. Specifically, we consider mixtures of deuterium and argon at temperatures of 100-500 eV and a number density ∼10(25) ions/cm(3). The motion of 30,000-120,000 ions is simulated in which the ions interact via the Yukawa (screened Coulomb) potential. The electric field of the electrons is included in this effective interaction; the electrons are not simulated explicitly. The species diffusivity is then calculated using the Green-Kubo approach using an integral of the interdiffusion current autocorrelation function, a quantity calculated in the equilibrium MD simulations. Our MD simulation results show that a widely used expression relating the interdiffusion coefficient with the concentration-weighted sum of self-diffusion coefficients overestimates the interdiffusion coefficient. We argue that this effect due to cross-correlation terms in velocities is characteristic of asymmetric mixed plasmas. Comparison of the MD results with predictions of kinetic theories also shows a discrepancy with MD giving effectively a larger Coulomb logarithm.

Nuclear quantum dynamics in dense hydrogen

Nuclear dynamics in dense hydrogen, which is determined by the key physics of large-angle scattering or many-body collisions between particles, is crucial for the dynamics of planet's evolution and hydrodynamical processes in inertial confinement confusion. Here, using improved ab initio path-integral molecular dynamics simulations, we investigated the nuclear quantum dynamics regarding transport behaviors of dense hydrogen up to the temperatures of 1 eV. With the inclusion of nuclear quantum effects (NQEs), the ionic diffusions are largely higher than the classical treatment by the magnitude from 20% to 146% as the temperature is decreased from 1 eV to 0.3 eV at 10 g/cm(3), meanwhile, electrical and thermal conductivities are significantly lowered. In particular, the ionic diffusion is found much larger than that without NQEs even when both the ionic distributions are the same at 1 eV. The significant quantum delocalization of ions introduces remarkably different scattering cross section between protons compared with classical particle treatments, which explains the large difference of transport properties induced by NQEs. The Stokes-Einstein relation, Wiedemann-Franz law, and isotope effects are re-examined, showing different behaviors in nuclear quantum dynamics.

Dynamics of two-dimensional one-component and binary Yukawa systems in a magnetic field

We consider two-dimensional Yukawa systems in a perpendicular magnetic field. Computer simulations of both one-component and binary systems are used to explore the equilibrium particle dynamics in the fluid state. The mobility is found to scale with the inverse of the magnetic field strength (Bohm diffusion), for strong fields (ωc/ωp≳1). For bidisperse mixtures, the magnetic field dependence of the long-time mobility depends on the particle species, providing an external control of their mobility ratio. At large magnetic fields, the highly charged particles are almost immobilized by the magnetic field and form a porous matrix of obstacles for the mobile low-charge particles.

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.

From transport to disorder: thermodynamic properties of finite dust clouds

The quantities entropy and diffusion are measured for two- and three-dimensional (3D) dust clusters in the fluid state. Entropy and diffusion are predicted to be closely linked via unstable modes. The method of instantaneous normal modes is applied for various laser-heated clusters to determine these unstable modes and the corresponding diffusive properties. The configurational entropy is measured for 2D and 3D clusters from structural rearrangements. The entropy shows a threshold behavior at a critical temperature for the 2D clusters, allowing us to estimate a configurational melting temperature. Further, the entropic disorder increases for larger clusters. Finally, the predicted relation between entropy and unstable modes has been confirmed from our experiments for 2D systems, whereas 3D systems do not show such a clear correlation.

Collective modes in two-dimensional binary Yukawa systems

We analyze via theoretical approaches and molecular dynamics simulations the collective mode structure of strongly coupled two-dimensional binary Yukawa systems, for selected density, mass, and charge ratios, both in the liquid and crystalline solid phases. Theoretically, the liquid phase is described through the quasilocalized charge approximation (QLCA) approach, while in the crystalline phase we study the centered honeycomb and the staggered rectangular crystal structures through the standard harmonic phonon approximation. We identify "longitudinal" and "transverse" acoustic and optic modes and find that the longitudinal acoustic mode evolves from its weakly coupled counterpart in a discontinuous nonperturbative fashion. The low-frequency acoustic excitations are governed by the oscillation frequency of the average atom, while the high-frequency optic excitation frequencies are related to the Einstein frequencies of the systems.

Velocity relaxation in a strongly coupled plasma

Collisional relaxation of Coulomb systems is studied in the strongly coupled regime. We use an optical pump-probe approach to manipulate and monitor the dynamics of ions in an ultracold neutral plasma, which allows direct measurement of relaxation rates in a regime where common Landau-Spitzer theory breaks down. Numerical simulations confirm the experimental results and display non-Markovian dynamics at early times.

Practical model for the self-diffusion coefficient in Yukawa one-component plasmas

A practical physically motivated interpolation formula is presented for the self-diffusion coefficient in Yukawa one-component plasmas that is valid for a wide range of inverse screening lengths and over the entire fluid region.