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Phase diagram of helium in the temperature-pressure plane: the melting line from ab inito simulations of Preising et al. 74 (bold blue line) and experimental data (dashed orange line and symbols) of Refs. 81-88. Shown are the P -T condictions where the BG closes in fluid helium according to the broadened method (dotted lines, results of Ref. 34 in orange and of this work in red), the histogram technique of this work for the fluid (bold red line) and that of Ref. 32 for the solid (bold orange line), and the HOMO-LUMO definition of Ref. 35 (orange dash-dotted line). The black lines display exemplarily P -T conditions for astrophysical objects which contain substantial fractions of helium: an old white dwarf, 89 the brown dwarf KOI-889b, 90 and the gas giant planet Jupiter. 91
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We examine the metallization of fluid helium with molecular dynamics simulations based on density functional theory. The insulator-to-metal transition is studied at densities between 1 and 22g/cm3 and temperatures between 10 000 and 50 000 K. We calculate the equation of state, the band gap dependent on density and temperature by using different de...
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... results of neither the EOS, the DC conductivity, the reflectivity or the ionization degree demonstrate hints where the nonmetal-to-metal phase transition takes place. We instead use the histogram BG closure as a marker for the IMT. We summarize our findings for the IMT in dense fluid helium and propose a new highpressure phase diagram in Fig. 6, with special emphasis on the region where the BG closes. ) and that of Ref. 32 for the solid (bold orange line), and the HOMO-LUMO definition of Ref. 35 (orange dash-dotted line). The black lines display exemplarily P -T conditions for astrophysical objects which contain substantial fractions of helium: an old white dwarf, 89 the ...
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... for astrophysical objects which contain substantial fractions of helium: an old white dwarf, 89 the brown dwarf KOI-889b, 90 and the gas giant planet Jupiter. 91 We consider the histogram method as most reliable in order to locate the BG closure and the corresponding IMT in dense fluid helium in P -T space. Therefore, the bold red line in Fig. 6 separates the non-metallic (left) from the metallic fluid (right) according to our extensive DFT-MD simulations and evaluations outlined in detail in Sections III A to III ...
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... astrophysical objects like gas giant planets, brown dwarfs, or the atmosphere of old and cool white dwarfs which contain large fractions of helium. For instance, the P -T conditions inside Jupiter, 91 the largest gas giant planet in our Solar System, do not intersect our results for BG closure according to the histogram method (bold red line in Fig. 6) which we consider as most reliable. Therefore, Jupiter probably does not contain metallic helium in its deep interior. Since hydrogen is metallic under these conditions, 5,71 the consequences for H-He demixing, the solubility of heavier elements in H-He (core erosion), and its actual structure near the core have to be studied, see ...
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... and hotter than Jupiter (hot Jupiters) 93 reach more extreme P -T conditions in their interior and could, therefore, contain metallic helium. This has consequences for the calculation of their interior profiles, evolution scenarios, and magnetic field structure. 3 The brown dwarf KOI-889b intersects the metallization lines of all methods shown in Fig. 6 and therefore probably contains metallic helium in its deep interior. The representative white dwarf model 89 has a higher temperature than the scope of this study. However, unless the slope of the band gap closure lines changes drastically, this particular white dwarf should contain metallic ...
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... for jumps or discontinuities in any of our results. In particular, the ionization calculated from the TRK sum rule method clearly shows a continuous transition to full ionization of 2.0, see Fig. 5. Therefore, we conclude that the metallization transition in dense fluid helium is driven by BG closure and continuous or of higher order, see Fig. ...
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... Yet, the validity of this chemical picture is particularly questionable in the WDM regime, where electrons can be weakly localized around the ions. 55 The present state-of-the-art appeals to the Kubo-Greenwood (KG) formalism, based on eigenvalues and occupations of the Kohn-Sham density functional theory [56][57][58] for obtaining the dielectric function in the optical limit. It can subsequently be extended to all wave numbers in terms of the Mermin dielectric function, with the required collision frequencies calculated from the KG dielectric function. ...
The accurate interpretation of experiments with matter at extreme densities and pressures is a notoriously difficult challenge. In a recent work [Dornheim et al., Nat. Commun. 13, 7911 (2022)], we have introduced a formally exact methodology that allows extracting the temperature of arbitrary complex materials without any model assumptions or simulations. Here, we provide a more detailed introduction to this approach and analyze the impact of experimental noise on the extracted temperatures. In particular, we extensively apply our method both to synthetic scattering data and to previous experimental measurements over a broad range of temperatures and wave numbers. We expect that our approach will be of high interest to a gamut of applications, including inertial confinement fusion, laboratory astrophysics, and the compilation of highly accurate equation-of-state databases.
... The method of molecular dynamics seems to be rather promising in studying the helium metallization [13,14]. Here, the interval of examined densities equals 1-22 g/cm 3 , and the temperature interval is 10000-50000 K. ...
Дослiдженi термодинамiчнi властивостi рiдкого металiчного гелiю в другому порядку теорiї збурень за псевдопотенцiалом електрон-iонної взаємодiї. При цьому використано псевдопотенцiал, знайдений з перших принципiв. Цей псевдопотенцiал є нелокальним i нелiнiйним. Нелокальнiсть псевдопотенцiалу приводить до того, що у розвиненнi внутрiшньої енергiї, вiльної енергiї i тиску рiдкого металiчного гелiю в ряд за псевдопотенцiалом присутнiй член першого порядку. Його дiагональний матричний елемент виявляється того ж порядку величини, що i член нульового порядку. В результатi цей член дає важливий внесок у внутрiшню i вiльну енергiю, а залежнiсть їх вiд густини i температури стає суттєвiшою. Вiдповiдно зростає i тиск, при якому може реалiзовуватись рiдка металiчна фаза гелiю. Цей тиск на порядок перевищує вiдповiдний тиск у металiчному воднi i на сьогоднi є недосяжним на експериментi. Аналiз ентропiї дозволив з’ясувати область iснування рiдкої металiчної фази i з’ясувати умови її кристалiзацiї. Порiвняння з густинами, тисками i температурами всерединi газових гiгантiв Юпiтера i Сатурна дозволило зробити висновок про те, що в центральних частинах цих планет не лише водень, а i гелiй перебувають у металiчному станi. Проте тиск в надрах планет є недостатнiм для кристалiзацiї гелiю.
... The state of the art is using the Kubo-Greenwood (KG) formalism based on eigenvalues and occupations of Kohn-Sham density functional theory [54][55][56] for obtaining the dielectric function in the optical limit. It can subsequently be extended to all wavenumbers in terms of the Mermin dielectric function, with the required collision frequencies calculated from the KG dielectric function [57]. ...
The accurate interpretation of experiments with matter at extreme densities and pressures is a notoriously difficult challenge. In a recent work [T.~Dornheim et al., Nature Comm. (in print), arXiv:2206.12805], we have introduced a formally exact methodology that allows extracting the temperature of arbitrarily complex materials without any model assumptions or simulations. Here, we provide a more detailed introduction to this approach and analyze the impact of experimental noise on the extracted temperatures. In particular, we extensively apply our method both to synthetic scattering data and to previous experimental measurements over a broad range of temperatures and wave numbers. We expect that our approach will be of high interest to a gamut of applications, including inertial confinement fusion, laboratory astrophysics, and the compilation of highly accurate equation-of-state databases.
... A third set of simulations focused on the transition of He from an insulating atomic fluid to a conducting, fully ionized plasma [242]. This recent work found that the EOS, the conductivity and the ionization fraction all vary smoothly as density is increased at fixed temperature. ...
... The high pressure melting curve of He [241] (heavy blue curve) and the insulatormetal transition in the solid phase [240] (heavy purple curve) are first order transitions. The insulator-metal transition in the fluid phase (also known as pressure ionization) is indicated by the closure of the band gap (blue dotted curve) and occurs continuously [242]. These transitions in dense He are compared to pure He white dwarf atmosphere models of T eff = 4000 K to 8000 K (left panel, orange lines) and He-rich white dwarf interior models with T eff = 4000 K and 5000 K (right panel, red curves). ...
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... Helium is the second most abundant element in the universe (after Hydrogen) and therefore understanding its behaviour under a wide range of conditions is important for our understanding of many astrophysical processes. Of particular interest are the conditions under which Helium is expected to undergo a transition from insulating to metallic behaviour in the outer layers of white dwarfs, which are characterized by densities of around 1 − 20 g cm −3 and temperatures of 10 − 50 kK [PR20]. These conditions are a typical example of the WDM regime. ...
Average-atom models are an important tool in studying matter under extreme conditions, such as those conditions experienced in planetary cores, brown and white dwarfs, and during inertial confinement fusion. In the right context, average-atom models can yield results with similar accuracy to simulations which require orders of magnitude more computing time, and thus they can greatly reduce financial and environmental costs. Unfortunately, due to the wide range of possible models and approximations, and the lack of open-source codes, average-atom models can at times appear inaccessible. In this paper, we present our open-source average-atom code, atoMEC. We explain the aims and structure of atoMEC to illuminate the different stages and options in an average-atom calculation, and facilitate community contributions. We also discuss the use of various open-source Python packages in atoMEC, which have expedited its development.
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High energy density physics (HEDP) and inertial confinement fusion (ICF) research typically relies on computational modeling using radiation-hydrodynamics codes in order to design experiments and understand their results. These tools, in turn, rely on numerous charged particle transport and relaxation coefficients to account for laser energy absorption, viscous dissipation, mass transport, thermal conduction, electrical conduction, non-local ion (including charged fusion product) transport, non-local electron transport, magnetohydrodynamics, multi-ion-species thermalization, and electron-ion equilibration. In many situations, these coefficients couple to other physics, such as imposed or self-generated magnetic fields. Furthermore, how these coefficients combine are sensitive to plasma conditions as well as how materials are distributed within a computational cell. Uncertainties in these coefficients and how they couple to other physics could explain many of the discrepancies between simulation predictions and experimental results that persist in even the most detailed calculations. This paper reviews the challenges faced by radiation-hydrodynamics in predicting the results of HEDP and ICF experiments with regard to these and other physics models typically included in simulation codes.
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