Theoretical study of transport coefficients of dense plasmas mixtures: the shear viscosity and the interdiffusion

The originality of this thesis work is based on the quantitative results we obtained for two types of models: the hydrogen plasma and the binary ionic mixture. Thus we have analyzed two transport coefficients using kinetic theory. The first part deals with electron and proton viscosity in the hydrogen plasma model. We examine the pseudopotential diffraction of Barker and Deutsch. We also know that the use of this potential in the study of static properties leads to satisfactory results because this pseudopotential takes into account the quantum effects when two particles approach each other at a distance smaller than the de Broglie distance. At this stage the question is: can dynamic properties be described using this potential? To answer this question, we have developed three classical approaches: the free flow approximation which takes into account the static correlations, the mean field approximation which introduces the Debye dynamic correlations in addition to the static correlations, and the Braginkii approximation which takes into account only the actual correlations related to the potential. The answer is partially positive for the thermodynamic conditions considered in this thesis, i.e. for a large degeneracy parameter in front of 1 (θ=T/T_F ≥≥ 1). In a second part, we evaluated the shear viscosity of a mixture with two species of ions for a binary ionic plasma. This model is better suited to study ion transport coefficients. The objective is to determine the effects related to the presence of impurities generally composed of heavy ions on the viscosity of light ions in a laser inertial melting experiment. We find that a small proportion of heavy ions leads to a systematic decrease in the viscosity of light ions, and that the higher the charge of heavy ions, the greater the decrease in viscosity. An attenuation factor appears which depends on the inverse square of the charge of the heavy ion, with mass effects playing little role. These quantitative results are obtained in a range of weak and intermediate couplings and we did not evaluate the direct viscosity in the approximation of the mean field for strong couplings. A possible solution is the extension for plasmas of a semi-empirical approach derived from the Lovesey method for liquids. It consists in constructing correlation functions from hydrodynamic modes previously evaluated by kinetic theory. This method opens a new research path for the evaluation of transport coefficients in the field of strong couplings. In a third part, we study the interdiffusion coefficient in the approximation of the 13 moments based on a Kubo type description. We obtain numerical values of the interdiffusion coefficient for a wide range of parameters (n, T) from weak to strong couplings. Inspecting these numerical results, we found the following unexpected effect: the results do not compare well with the values obtained by molecular dynamics, especially in the weak and intermediate coupling domains. At this stage, we cannot say whether this difference is related to the approximation of the 13 moments. So we evaluated only the matrix elements corresponding to the direct interdiffusion coefficient. The direct interdiffusion coefficient gives satisfactory results with respect to molecular dynamics at weak and intermediate couplings. We also studied the mean value of the self-scattering by kinetic theory. This compares well with the experimental points in molecular dynamics. On the basis of these results, we believe that it would be highly desirable to reconsider the model of correlation functions in order to obtain numerical values of the interdiffusion coefficient in the approximation of the 13 moments that compare with the results of molecular dynamics. In addition, there is no analytical relationship between the interdiffusion coefficient and viscosity in a binary ionic mixture. Finally, a more realistic model for the binary ionic mixture that approximates the plasmas generated in the laboratory is to take into account the electron polarization. A simple model consists in taking into account a Thomas-Fermi type shielding. This shielding becomes important when the Thomas-Fermi length is of the order of the mean distance between the particles. Unfortunately this study was not carried out for a two-component plasma where the diffusion coefficients could be strongly modified. This approach may give rise to future developments. (author)