Parametrization of pair correlation function and static structure factor of the one component plasma across coupling regimes

Abstract

We present a parametrization of the pair correlation function and the static structure factor of the Coulomb one component plasma (OCP) from the weakly coupled regime to the strongly coupled regime. Recent experiments strongly suggest that the OCP model can play the role of a reference system for warm dense matter. It can provide the ionic static structure factor that is necessary to interpret the x-ray Thomson scattering measurements, for instance. We illustrate this with the interpretation of a x-ray diffraction spectrum recently measured, using a Bayesian method that requires many evaluations of the static structure factor to automatically calibrate the parameters. For strongly coupled dusty plasmas, the proposed parametrization of the Coulomb OCP pair correlation function can be related to the Yukawa one, including screening. Further prospects to parametrize the static structure of Yukawa systems are also discussed.A realistic description of hot dense plasmas requires a model that includes all many-body interactions explicitly in contrast to weakly coupled plasmas that are well represented by only binary collisions and mean-field effects. This regime is characterized by strong interactions between ions, outweighing their thermal kinetic energy and leading to a liquid-like structure. Such strongly correlated plasmas are found in a variety of environments including planetary interiors, 1 dwarf stars, 2 and neutron star crusts 3 in astrophysics, and in many experimental set-ups of dusty plasmas, colloidal suspensions, 4 and warm dense matter (WDM) 5 in inertial confinement fusion studies. 6 Liquid metals 7 are also another manifestation of high Coulomb coupling in nature.In strongly coupled plasmas, the many-body interactions are not amenable to a theoretical approach in perturbation since there is no small parameters available. Besides very demanding state-of-the-art molecular dynamics simulations, a possible modeling comes through the definition of simpler idealized systems. These reference systems can be studied extensively by molecular dynamics once and for all, with results easily available through parametrizations and/or tabulations. The Coulomb 8,9 and Yukawa 10 one-component-plasma (OCP) systems are good candidates of such reference models.The Coulomb OCP represents a system of interacting ions, with the pair potential V C (r) = Qe/r, in a neutralizing uniform background of electrons. All its static and dynamic properties depend on only one parameter, the Coulomb coupling parameter Γ = Q 2 e 2 /ak B T , where Q is the ionic charge, T is the temperature, and a = (4πn/3) −1/3 is the Wigner-Seitz radius (n is the ionic density). The Coulomb coupling parameter Γ is a measure of the importance of correlation in plasmas as the ratio of the mean nearest neighbor interaction to the mean kinetic energy. The ideal gas-like behavior corresponds to Γ ≪ 1, liquid-like short-range order appears when Γ ≥ 1, and crystalline long-range order when Γ ≥ 180. Analytic parametrizations in Γ are available for the equation of ...

Sum rules and exact inequalities for strongly coupled one‐component plasmas

“…In the context of satisfaction of the Cauchy‐Bunyakovsky‐Schwarz inequality , we have checked up to seven different static schemes of determination of the one‐component, strongly coupled classical plasma SSF: the classical hyper‐netted chain (HNC) approximation [37], the bridge function‐corrected HNC by Ng [38], two different versions of the variational modified HNC Scheme, , and three different fitting procedures; see Figure . It can be seen that two schemes of SSF calculation violate the Cauchy–Bunyakovsky–Schwarz inequality, which leads to the non‐physical results for the DSF under these conditions.…”

Enhancement factor of nuclear reactions in partially ionized plasmas and asymmetric mixtures

“…The Ag‐Ag PDF exhibits a well‐defined structure, characterized by a strong peak reminiscent of the OCP. An effective ionization of Ag can be obtained by matching the peak with an analytical formulation for the PDF of the OCP . This matching procedure involves two parameters: the mean ion radius a = (3/4 πn ) 1/3 , with n the ion density, and the coupling parameter Γ = Q 2 e 2 / akT , with Q the ionization.…”

“…An effective ionization of Ag can be obtained by matching the peak with an analytical formulation for the PDF of the OCP. [12] This matching procedure involves two parameters: the mean ion radius a = (3/4 n) 1/3 , with n the ion density, and the coupling parameter Γ = Q 2 e 2 /akT, with Q the ionization. From 100 to 400 eV, the Ag-Ag peak does not evolve, and the Ag effective ionization must be doubled to compensate for the fourfold increase in temperature.…”

Enhancement of nuclear reaction rates in asymmetric binary ionic mixtures

“…Knowing the ionic density and the standard one‐component plasma (OCP) pdfs for any Γ, one can get the value of Γ e that matches best the OFMD simulation results. This procedure is automated thanks to an analytical formulation of OCP pdfs and a parameterization of the OCP structural characteristics . Finally, knowing the temperature and using the best value of Γ e , one can deduce the effective charge Q α as a by‐product of the simulation, not as an input parameter as in a classical MD simulation.…”