ABSTRACT
Recently we proposed a method to solve the perturbed Boltzmann equation modeled by the Bhatnagar-Gross-Krook operator [Phys. Rev. E 74, 041204 (2006)]. In this work we use this method to derive linear transport equations in the whole collisionality range. A comparison of the closure relations derived up to the third order in the Knudsen number (super-Burnett) yields the same results as the Chapman-Enskog expansion. The contribution of the projection operators to the transport is investigated. It is pointed out that their contributions are not negligible in the super-Burnett equations and very significant in the collisionless range. The test of stability of the super-Burnett equations is also performed. It is shown that the stability problem can be related to the positivity of the generalized transport coefficients. Using the Padé approximants, nonlocal transport coefficients are proposed which present the desirable stability properties.
ABSTRACT
In a one-component plasma constituted by electrons with a uniform positive background, the correlations are studied in the framework of the Singwi, Tosi, Land, and Sjölander (STLS) model. The local-field corrections (LFCs) are calculated with electron density ranging from 10;{19}to10;{26}cm;{-3} and with a temperature of 10;{4}K . Then, a dielectric formalism is used to deduce the potential energy of a positive test charge (a proton) imbedded in the electron medium. A significant departure of this potential from the random phase approximation (RPA) one has been found. In particular, as the density increases, the discrepancy between the two potentials grows up to reach a maximum correlated to the maximum of the electron coupling parameter. In addition, it is found that in both high and low density limits, the STLS and RPA approaches yield similar results. On the other hand, the effect of the LFC on the electrical conductivity is also estimated in hydrogen plasmas.
ABSTRACT
The transport processes in dilute neutral gases are studied by using the kinetic equation with a collision relaxation model that meets all conservation requirements. The kinetic equation is solved keeping the whole anisotropic part of the distribution function with the use of the continued fractions. The conservative laws of the collision operator are taken into account with the projection operator techniques. The generalized heat flux and stress tensor are calculated in the linear approximation, as functions of the lower moments, i.e., the density, the flow velocity and the temperature. The results obtained are valid for arbitrary collision frequency nu with the respect to kv(t) and the characteristic frequency omega, where k(-1) is the characteristic length scale of the system and v(t) is the thermal velocity. The transport coefficients constitute accurate closure relations for the generalized hydrodynamic equations. An application to the dispersion and the attenuation of sound waves in the whole collisionality regime is presented. The results obtained are in very good agreement with the experimental data.
