Hydrogen-helium Mixtures Research Articles

THE PROPERTIES OF HEAVY ELEMENTS IN GIANT PLANET ENVELOPES

ABSTRACT The core-accretion model for giant planet formation suggests a two-layer picture for the initial structure of Jovian planets, with heavy elements in a dense core and a thick H–He envelope. Late planetesimal accretion and core erosion could potentially enrich the H–He envelope in heavy elements, which is supported by the threefold solar metallicity that was measured in Jupiter’s atmosphere by the Galileo entry probe. In order to reproduce the observed gravitational moments of Jupiter and Saturn, models for their interiors include heavy elements, Z, in various proportions. However, their effect on the equation of state of the hydrogen–helium mixtures has not been investigated beyond the ideal mixing approximation. In this article, we report results from ab initio simulations of fully interacting H–He–Z mixtures in order to characterize their equation of state and to analyze possible consequences for the interior structure and evolution of giant planets. Considering C, N, O, Si, Fe, MgO, and SiO2, we show that the behavior of heavy elements in H–He mixtures may still be represented by an ideal mixture if the effective volumes and internal energies are chosen appropriately. In the case of oxygen, we also compute the effect on the entropy. We find the resulting changes in the temperature–pressure profile to be small. A homogeneous distribution of 2% oxygen by mass changes the temperature in Jupiter’s interior by only 80 K.

Novye resheniya v mass-spektrometricheskom izotopnom analize vodorodno- gelievych smesey. Uslovie polucheniya dostovernych dannych

Novye resheniya v mass-spektrometricheskom izotopnom analize vodorodno- gelievych smesey. Uslovie polucheniya dostovernych dannych

Solid deposition in the ITER cryogenic viscous compressor

A transient model for the ITER cryogenic viscous compressor (CVC) is presented. The CVC is designed to separate hydrogen isotopes from helium in the gas-mixture exhaust from the ITER torus. During their residence in the CVC, hydrogen isotopes are captured along the pump wall while helium flows through. The CVC thereby provides the first stage of helium compression. The transient model characterizes the transport phenomena (species, momentum, and energy) that occur in the CVC. The numerical results are compared with experimental data from a scaled down test of the ITER CVC using pure hydrogen. Although the model has been developed for a hydrogen–helium mixture, it is simplified here in order to compare with the experimental data. The transient model, along with other numerical models we have developed, provide guidance for the design and optimization of the ITER CVC. The model can also be a useful tool or a reference for similar analyses, such as those for cryogenic carbon capture and air ingress in vacuum isolated cryogenic vessels.

Ab Initio Values of the Gas Transport Properties of Hydrogen Isotopologues and Helium–Hydrogen Mixtures at Low Density

We employed the classical kinetic theory to calculate transport properties as a function of temperature for hydrogen isotopologues and helium–hydrogen mixtures. The viscosity, thermal conductivity, diffusion coefficient, and thermal diffusion factor were computed at low density and over a wide temperature range from 298 to 2000 K. The calculation utilized the spherically symmetric versions of the latest ab initio potentials for the interactions of the like and unlike gas molecules. The computed values are generally consistent with the limited experimental data for HD, 4He–H2, 4He–D2, 4He–HD, 3He–H2, 3He–D2, H2–HD, and D2–HD. Our results provide reliable transport property data for the considered species at temperatures where experimental information is absent.

Survey of segregation alteration of hydrogen-helium mixtures via structure factor

In this study, thermodynamic instabilities in hydrogen-helium fluid mixture have been analyzed. These kinds of investigations are inevitable for indicating hydrodynamic transitions in Hydrogen-Helium fluid mixture. Therefore, first we have derived equation of state of mixture via Barker-Henderson statistical perturbation theory. Moreover, we have used Yiping radial distribution function in calculating perturbed terms. Via equation of state, we have calculated excess Gibbs free energy and the Gibbs free energy in the long wavelength limit. By means of this energy in hand we could estimate degree of hetero-coordination and segregations of this mixture which is a measure for defining thermodynamic instabilities. At last, these measurements have made us capable of anticipating thermodynamic instabilities and coordination of mixture in different concentrations.

A PRELIMINARY JUPITER MODEL

ABSTRACT In anticipation of new observational results for Jupiter's axial moment of inertia and gravitational zonal harmonic coefficients from the forthcoming Juno orbiter, we present a number of preliminary Jupiter interior models. We combine results from ab initio computer simulations of hydrogen–helium mixtures, including immiscibility calculations, with a new nonperturbative calculation of Jupiter's zonal harmonic coefficients, to derive a self-consistent model for the planet's external gravity and moment of inertia. We assume helium rain modified the interior temperature and composition profiles. Our calculation predicts zonal harmonic values to which measurements can be compared. Although some models fit the observed (pre-Juno) second- and fourth-order zonal harmonics to within their error bars, our preferred reference model predicts a fourth-order zonal harmonic whose absolute value lies above the pre-Juno error bars. This model has a dense core of about 12 Earth masses and a hydrogen–helium-rich envelope with approximately three times solar metallicity.

Benchmarking density functionals for hydrogen-helium mixtures with quantum Monte Carlo: Energetics, pressures, and forces

An accurate understanding of the phase diagram of dense hydrogen and helium mixtures is a crucial component in the construction of accurate models of Jupiter, Saturn, and Jovian extrasolar planets. Though DFT based first principles methods have the potential to provide the accuracy and computational efficiency required for this task, recent benchmarking in hydrogen has shown that achieving this accuracy requires a judicious choice of functional, and a quantification of the errors introduced. In this work, we present a quantum Monte Carlo based benchmarking study of a wide range of density functionals for use in hydrogen-helium mixtures at thermodynamic conditions relevant for Jovian planets. Not only do we continue our program of benchmarking energetics and pressures, but we deploy QMC based force estimators and use them to gain insights into how well the local liquid structure is captured by different density functionals. We find that TPSS, BLYP and vdW-DF are the most accurate functionals by most metrics, and that the enthalpy, energy, and pressure errors are very well behaved as a function of helium concentration. Beyond this, we highlight and analyze the major error trends and relative differences exhibited by the major classes of functionals, and estimate the magnitudes of these effects when possible.

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.

Two-phase coexistence for hydrogen-helium mixtures.

We use our quantum Gibbs ensemble Monte Carlo algorithm to perform computer experiments for the two-phase coexistence of a hydrogen-helium mixture. Our results are in quantitative agreement with the experimental results of Sneed, Streett, Sonntag, and Van Wylen. The difference between our results and the experimental ones is in all cases less than 15% relative to the experiment, reducing to less than 5% in the low helium concentration phase. At the gravitational inversion between the vapor and the liquid phase, at low temperatures and high pressures, the quantum effects become relevant. At extremely low temperature and pressure, the first component to show superfluidity is the helium in the vapor phase.

Assessment of the plasma start-up in Wendelstein 7-X with neutral beam injection

Plasma start-up by neutral beam injection was investigated for stellarators. A zero-dimensional collisional model was extended to evaluate the temporal evolution of the plasma start-up in a confining toroidal magnetic field. Inclusion of different beam energy components indicated a substantial effect due to the energy dependence of beam–gas collisions. Additional collision processes and particle equations were considered to simulate the plasma start-up in helium–hydrogen mixtures. The isotope effect between operation with hydrogen and deuterium beams was also investigated.As a major objective the conditions necessary for a plasma start-up with neutral beams in W7-X have been examined. The assessed beam configuration in W7-X was found not to allow plasma start-up by neutral beam injection alone. The model has been validated for experimental data from W7-AS and Large Helical Device. Quantitative predictions of this study show that the ratio of the beam–plasma interaction length and the plasma volume is an essential quantity for the successful plasma start-up with neutral beams.

Diffusivity of heavy elements in Jupiter and Saturn

Recent work has suggested that gas giant planets such as Jupiter and Saturn may not consist of a small number of fully convective and chemically homogenous layers as has been conventionally assumed, but instead may be chemically inhomogeneous with convective redistribution of elements limited by semiconvection. Constructing accurate planetary models which include semiconvective processes requires accurate estimates of the diffusion constants of minority chemical species in planetary fluids, which have not previously been available. In this work we use ab initio density functional molecular dynamics simulations to simulate the diffusion of heavy elements (specifically carbon, silicon, iron) in hydrogen–helium mixtures at conditions corresponding to giant planet deep interiors. We find diffusivities at the high end of the previously proposed range, and estimate that semiconvective processes may be able to redistribute a substantial fraction of Jupiter’s core mass within the planet’s age.

Quantum partition functions of composite particles in a hydrogen-helium plasma via path integral Monte Carlo.

We compute two- and three-body cluster functions that describe contributions of composite entities, like hydrogen atoms, ions H(-), H2(+), and helium atoms, and also charge-charge and atom-charge interactions, to the equation of state of a hydrogen-helium mixture at low density. A cluster function has the structure of a truncated virial coefficient and behaves, at low temperatures, like a usual partition function for the composite entity. Our path integral Monte Carlo calculations use importance sampling to sample efficiently the cluster partition functions even at low temperatures where bound state contributions dominate. We also employ a new and efficient adaptive discretization scheme that allows one not only to eliminate Coulomb divergencies in discretized path integrals, but also to direct the computational effort where particles are close and thus strongly interacting. The numerical results for the two-body function agree with the analytically known quantum second virial coefficient. The three-body cluster functions are compared at low temperatures with familiar partition functions for composite entities.

Highly accurate potential energy surface for the He–H2 dimer

A new highly accurate interaction potential is constructed for the He-H2 van der Waals complex. This potential is fitted to 1900 ab initio energies computed at the very large-basis coupled-cluster level and augmented by corrections for higher-order excitations (up to full configuration interaction level) and the diagonal Born-Oppenheimer correction. At the vibrationally averaged H-H bond length of 1.448736 bohrs, the well depth of our potential, 15.870 ± 0.065 K, is nearly 1 K larger than the most accurate previous studies have indicated. In addition to constructing our own three-dimensional potential in the van der Waals region, we present a reparameterization of the Boothroyd-Martin-Peterson potential surface [A. I. Boothroyd, P. G. Martin, and M. R. Peterson, J. Chem. Phys. 119, 3187 (2003)] that is suitable for all configurations of the triatomic system. Finally, we use the newly developed potentials to compute the properties of the lone bound states of (4)He-H2 and (3)He-H2 and the interaction second virial coefficient of the hydrogen-helium mixture.

Thermophysical properties of hydrogen-helium mixtures: Re-examination of the mixing rules via quantum molecular dynamics simulations

Thermophysical properties of hydrogen, helium, and hydrogen-helium mixtures have been investigated in the warm dense matter regime at electron number densities ranging from 6.02 × 10^{29} ∼ 2.41 × 10^{30} m^{-3} and temperatures from 4000 to 20000 K via quantum molecular dynamics simulations. We focus on the dynamical properties such as the equation of states, diffusion coefficients, and viscosity. Mixing rules (density matching, pressure matching, and binary ionic mixing rules) have been validated by checking composite properties of pure species against that of the fully interacting mixture derived from quantum molecular dynamics simulations. These mixing rules reproduce pressures within 10% accuracy, while it is 75% and 50% for the diffusion and viscosity, respectively. The binary ionic mixing rule moves the results into better agreement. Predictions from one component plasma model are also provided and discussed.

AB INITIO EQUATION OF STATE FOR HYDROGEN-HELIUM MIXTURES WITH RECALIBRATION OF THE GIANT-PLANET MASS-RADIUS RELATION

Using density functional molecular dynamics simulations, we determine the equation of state for hydrogen-helium mixtures spanning density-temperature conditions typical of giant planet interiors, ~0.2-9 g/cc and 1000-80000 K for a typical helium mass fraction of 0.245. In addition to computing internal energy and pressure, we determine the entropy using an ab initio thermodynamic integration technique. A comprehensive equation of state (EOS) table with 391 density-temperature points is constructed and the results are presented in form of two-dimensional free energy fit for interpolation. Deviations between our ab initio EOS and the semi-analytical EOS model by Saumon and Chabrier are analyzed in detail, and we use the results for initial revision of the inferred thermal state of giant planets with known values for mass and radius. Changes are most pronounced for planets in the Jupiter mass range and below. We present a revision to the mass-radius relationship which makes the hottest exoplanets increase in radius by ~0.2 Jupiter radii at fixed entropy and for masses greater than ~0.5 Jupiter mass. This change is large enough to have possible implications for some discrepant "inflated giant exoplanets".

SOLUBILITY OF IRON IN METALLIC HYDROGEN AND STABILITY OF DENSE CORES IN GIANT PLANETS

The formation of the giant planets in our solar system, and likely a majority of giant exoplanets, is commonly explained by the accretion of nebular hydrogen and helium onto a large core of terrestrial-like composition. The fate of this core has important consequences for the evolution of the interior structure of the planet. It has recently been shown that H2O, MgO and SiO2 dissolve in liquid metallic hydrogen at high temperature and pressure. In this study, we perform ab initio calculations to study the solubility of an innermost metallic core. We find dissolution of iron to be strongly favored above 2000 K over the entire pressure range (0.4-4 TPa) considered. We compare with and summarize the results for solubilities on other probable core constituents. The calculations imply that giant planet cores are in thermodynamic disequilibrium with surrounding layers, promoting erosion and redistribution of heavy elements. Differences in solubility behavior between iron and rock may influence evolution of interiors, particularly for Saturn-mass planets. Understanding the distribution of iron and other heavy elements in gas giants may be relevant in understanding mass-radius relationships, as well as deviations in transport properties from pure hydrogen-helium mixtures.

Hydrogen-helium demixing from first principles: From diamond anvil cells to planetary interiors

An accurate determination of the immiscibility of helium in hydrogen has a direct impact on the understanding of the interior structure and of the evolution of Jovian planets. We extend our previous work on hydrogen-helium mixtures [Morales, Schwegler, Ceperley, Pierleoni, Hamel, and Caspersen, Proc. Natl. Acad. Sci. (USA) 106, 1324 (2009)] to lower pressures and lower temperatures, across the molecular dissociation regime in hydrogen to the low-pressure molecular liquid. Using density-functional-theory-based molecular dynamics together with thermodynamic integration techniques, we calculate the Gibbs free energy of the dense liquid as a function of pressure, temperature, and composition. We address the importance of the nonideal entropy of mixing in the solubility of helium in hydrogen and find that it is critically important in the molecular regime. The resulting demixing temperatures smoothly connect measurements done in diamond anvil cells to the high-temperature and -pressure conditions found in giant planet interiors.

Hydrogen-Terminated Graphene by Laser Vaporization-Controlled Condensation of Graphite Oxide. Observation of Hydrogen-Capped Carbon Chains CnH–, CnH+, and CnH2+ (n = 2–30) in the Gas Phase

We report the development of a facile process for the synthesis of hydrogen-terminated graphene using the laser vaporization-controlled condensation (LVCC) method. The method allows rapid deoxygenation of bulk graphite oxide (GO) in an atmosphere of helium or a helium–hydrogen mixture to produce hydrogen-terminated graphene (HTG) nanosheets without the need for any chemical reducing agents or solvents. Direct laser vaporization/ionization (LVI) of bulk GO in a vacuum coupled with a beam expansion of a carrier gas produces the carbon cluster series Cn with n in the range 4–30, in addition to hydrogenated carbon ions with a significant enhancement in the ion intensity of the n-even ions suggesting the formation of hydrogen-capped polyyne chains corresponding to the H–(C≡C)n–H+ and H–(C≡C)n– formulas. In contrast, LVI of bulk graphite under identical experimental conditions generates mainly the carbon cluster series Cn without any significant hydrogenation in both the positive and negative ion modes. The res...

Equation of state calculations of hydrogen-helium mixtures in solar and extrasolar giant planets

Using density-functional molecular dynamics simulations, we study the equation of state for hydrogen-helium mixtures at conditions of giant planet interiors of 0.2--2.3$\phantom{\rule{0.16em}{0ex}}$g$\phantom{\rule{0.16em}{0ex}}$cm${}^{\ensuremath{-}3}$ and 1000$\ensuremath{-}$80$\phantom{\rule{0.16em}{0ex}}$000$\phantom{\rule{0.16em}{0ex}}$K for a typical helium mass fraction of 0.245. In addition to computing internal energy and pressure, we determine the entropy by applying a thermodynamic integration technique in the presence of electronic excitations. We extend this technique to include the dissociations and recombination of hydrogen molecules. Results are compared to the widely used analytic model by Saumon and Chabrier. We also report evidence of spontaneous hydrogen-helium phase separation in simulations at low temperature and high density.

Antenna coupling study for ICWC plasma characterization in TEXTOR

Ion cyclotron wall conditioning (ICWC) discharges, in pulsed-mode operation, were carried out in the limiter tokamak TEXTOR to explore safe operational regimes for the experimental parameters for possible ICWC-discharge cleaning in International Thermonuclear Experimental Reactor (ITER) at half field. Antenna coupling properties obtained during the ion cyclotron range of frequencies (ICRF) wall conditioning experiments performed in helium–hydrogen mixture in TEXTOR were analysed in relation to the obtained ICWC-plasma characterization results. Satisfactory antenna coupling in the mode conversion scenario along with reproducible generation of ICRF plasmas for wall conditioning, were achieved by coupling radio frequency (RF) power from one or two ICRF antennas. The plasma breakdown results obtained in the TEXTOR tokamak have been compared with the predictions of a zero-dimensional RF plasma production model. The present study of ICWC emphasizes the beneficial effect of application of an additional (along with toroidal magnetic field) stationary vertical (B V ≪ B T) or oscillating poloidal magnetic field (B P ≪ B T) on antenna coupling and relevant plasma parameters.