On the model kinetic description of plasma and a boltzmann gas of hard spheres

A new form of the collision operator for a Boltzmann gas of hard spheres and Coulomb plasma is proposed. One-component and many-component systems are considered. The proposed collision operator properly takes into account the relaxation of the first 13 hydrodynamic moments. Besides this, it accounts for the non-diagonal component contribution in the quadratic approximation in the expansion of the linearized collision operator with respect to the complete system of Hermite polynomials. It is shown that for a system of charged particles with the Coulomb interaction potential, these contributions are essential and lead to Spitzer corrections to the transport coefficients. An expression for the intensity of the Langevin source in the kinetic equation is obtained in the same approximation. A new form of the model collision operator for a Boltzmann gas of hard spheres is proposed. For a many-component system we have reconstructed a non-linear model collision integral by using the linearized collision integral found. Unlike previous ones, it does not contain complicated exponential dependence and avoids coefficient ambiguity in the many-component collision integral. © 2009 IOP Publishing Ltd.SCOPUS: ar.j