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Pseudoatom Molecular Dynamics Method for Calculating the Coefficients of Viscosity and Ion Self-Diffusion in a Dense Plasma

  • STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS
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Abstract

A semiclassical version of the pseudoatom molecular dynamics method is used to calculate the coefficients of dynamic viscosity and ion self-diffusion of a warm and moderately heated dense plasma of a number of chemical elements, which are of interest for the high-energy-density physics, the solution of a number of applied geophysical and planetology problems, and a comparison with the calculated data of other authors. The effects caused by the Coulomb interaction in a medium and the quantum properties of the electronic subsystem of plasma are taken into account. Analytical approximations are proposed for the coefficients of viscosity and ion self-diffusion, and they can be used to simulate the dynamics of dense ionized matter for describing experiments in the high-energy-density physics.

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Notes

  1. In Section 2, the Hartree atomic units (e = \(\hbar \) = me = 1) are used.

  2. In the spherically symmetric case under study, the three-dimensional integral Fourier transform is reduced to Fourier sine transform, but, of the function multiplied by 4πr/k during the forward transform and of the function multiplied by k/(πr) during the inverse transform; here, r is the radial coordinate and k is the wavenumber.

  3. Starrett and Saumon [23, 24] showed that the substitution of a steplike Heaviside function for RDF in Eqs. (7) and (9) does not cause a substantial change in the screening electron density. The search for the next approximations for RDF, gII(r) ≠ \(g_{{II}}^{0}\)(r) can be based on both the results of PAMD simulation of the ionic microstructure of matter and the solution to a system of Ornstein–Zernike equations [43] for determining realistic gII(r) RDFs [14, 15, 44]. A simultaneous iteration refinement of RDF and the screening electron density allows us to obtain a self-consistent solution for the Starrett–Saumon model, which has an insignificant meaning in terms of PAMD because it takes a huge amount of calculations.

  4. The logarithmic dependence on arguments allows Eqs. (17) and (18) to be applied in problems with a strong space and/or time inhomogeneity of the ρ and T fields.

  5. In our PAMD calculations, the maximum statistical error of the ion self-diffusion coefficients with respect to their averages does not exceed 10% and that of the coefficient of viscosity, 15%, which is comparable with the accuracy of results calculated by QMD with a semiclassical (OFMD) description of the electron subsystem [36, 37].

  6. gII(r) in [9] was calculated by the same authors using the same model as in [35].

  7. The time step of calculation was 0.15 fs, whereas in [36] it was 2.5–5 fs.

  8. Note that the application of Eqs. (17) and (18) does not imply an additional calculation of the degree of plasma ionization, as in the case of approximations in [55, 56].

  9. A similar statistical error is also characteristic of the transport coefficients calculated by other methods (see, e.g., [33, 36, 37]).

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Authors and Affiliations

  1. Russian Federal Nuclear Center, Zababakhin All-Russia Research Institute of Technical Physics, 456770, Snezhinsk, Chelyabinsk oblast, Russia

    A. L. Falkov, P. A. Loboda & A. A. Ovechkin

  2. National Research Nuclear University MEPhI, 115409, Moscow, Russia

    P. A. Loboda & S. V. Ivliev

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  1. A. L. Falkov
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  2. P. A. Loboda
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  3. A. A. Ovechkin
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  4. S. V. Ivliev
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Correspondence to A. L. Falkov, P. A. Loboda or A. A. Ovechkin.

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Translated by K. Shakhlevich

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Falkov, A.L., Loboda, P.A., Ovechkin, A.A. et al. Pseudoatom Molecular Dynamics Method for Calculating the Coefficients of Viscosity and Ion Self-Diffusion in a Dense Plasma. J. Exp. Theor. Phys. 134, 371–383 (2022). https://doi.org/10.1134/S1063776122030049

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