Correlation and transport properties for mixtures at constant pressure and temperature

Alexander J. White, Lee A. Collins, Joel D. Kress, Christopher Ticknor, Jean Clérouin, Philippe Arnault, and Nicolas Desbiens

Phys. Rev. E 95, 063202 – Published 2 June 2017

Abstract

Transport properties of mixtures of elements in the dense plasma regime play an important role in natural astrophysical and experimental systems, e.g., inertial confinement fusion. We present a series of orbital-free molecular dynamics simulations on dense plasma mixtures with comparison to a global pseudo ion in jellium model. Hydrogen is mixed with elements of increasingly high atomic number (lithium, carbon, aluminum, copper, and silver) at a fixed temperature of 100 eV and constant pressure set by pure hydrogen at $2 {g / cm}^{3}$ , namely, 370 Mbars. We compute ionic transport coefficients, such as self-diffusion, mutual diffusion, and viscosity for various concentrations. Small concentrations of the heavy atoms significantly change the density of the plasma and decrease the transport coefficients. The structure of the mixture evidences a strong Coulomb coupling between heavy ions and the appearance of a broad correlation peak at short distances between hydrogen atoms. The concept of an effective one component plasma is used to quantify the overcorrelation of the light element induced by the admixture of a heavy element.

Received 10 March 2017

DOI:https://doi.org/10.1103/PhysRevE.95.063202

Physics Subject Headings (PhySH)

Dense plasma focus Plasma transport

Core of giant planets Inertially confined plasmas Warm-dense matter

First-principles calculations in plasma physics Fokker-Planck & Vlasov model Hybrid model Molecular dynamics

Plasma Physics

Authors & Affiliations

Alexander J. White¹, Lee A. Collins¹, Joel D. Kress¹, Christopher Ticknor¹, Jean Clérouin², Philippe Arnault², and Nicolas Desbiens²

¹Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
²CEA, DAM, DIF, 91297 Arpajon, France

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Vol. 95, Iss. 6 — June 2017

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Images

Figure 1
(a) Densities of mixtures versus $χ_{Z}$ . The symbols represent densities actually used in the OFMD simulation and the resulting effective coupling parameter $Γ_{eff}$ . The lines represent the prediction of the simple isobaric model used in the PIJ model. (b) $Γ_{eff}$ versus heavy element concentration $χ_{Z}$ for H-Li [(black squares) (solid line)], H-C [(blue circles) (dotted line)], H-Al [(red triangles) (dashed line)], H-Cu [(green triangles) (dashed-dot line)], H-Ag [(violet crosses) (long dashed line)], and pure H (teal long dashed and short dashed lines). The gray area defines the weak coupling region where kinetic formulation is the main contribution $Γ_{eff} < 1$ .
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Figure 2
(a) Viscosity $η (mPa s)$ of the $H - Z$ mixture as a function of the atomic number of the high mass component (symbols: OFMD simulations; lines: the PIJ model), $χ_{Z} = 0.00$ (squares, long dashed, and short dashed lines), 0.05 (circle, long dashed-dotted line), 0.10 (triangles, long dashed line), 0.25 (diamond, dotted line), 0.50 (cross, dashed line), and 1.00 (filled circles, solid line). (b) (Alternate view) Viscosity as a function of $χ_{Z}$ for $H - Z$ mixtures (symbols: OFMD simulations; lines: the PIJ model, see Fig. 1). All simulations are at a temperature of $k T = 100 eV$ and pressure matched to 100% H at $2.00 g / {cm}^{3}$ .
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Figure 3
Self-diffusion for hydrogen $D_{H}$ [(black circles) (solid line)], high- $Z$ self-diffusion $D_{Z}$ [(red triangles) (dashed line)], and mutual-diffusion $D_{H - Z}$ [(blue circle) (dotted line)] as a function of $χ_{Z}$ . From top to bottom: H-Ag, H-Cu, H-Al, H-C, and H-Li mixtures (symbols: OFMD simulations; lines: the PIJ model).
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Figure 4
Hydrogen self-diffusion $D_{H}$ for varied concentration, normalized by pure hydrogen diffusion [OFMD: symbols, PIJ: solid line, see Fig. 2].
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Figure 5
Radial pair distribution functions for different mixtures at 75% heavy element ( $Z$ ), 25% hydrogen: Top: $Z - Z$ , middle: $H - Z$ , bottom: H-H. The bottom inset, a closer view of the H-H correlation feature [OFMD: symbols, see Fig. 2; EOCP: solid lines]. We emphasize that the lines are the EOCP model not the lines drawn between symbols. The gray area in the inset corresponds to the region of overcorrelation between hydrogens compared to their pure element values (the black solid line at $Γ = 0.2$ ).
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Figure 6
Radial pair-distribution functions for different concentrations of Cu in the H-Cu mixture: top: Cu-Cu; middle: H-Cu; bottom: H-H. The bottom inset, closer view of the H-H correlation feature. Squares: 5% Cu; circles: 10% Cu; triangles: 25% Cu; cross: 75% Cu. The full lines are the EOCP model, and the gray area in the inset is the overcorrelation region.
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