The derivation of model kinetic equation for gases and for plasmas

TL;DR

This paper introduces a new model collision operator for gases and plasmas that accurately accounts for hydrodynamic moment relaxation, simplifies the collision integral, and satisfies Boltzmann's H-theorem.

Contribution

A novel form of the model collision operator for gases and plasmas that properly incorporates hydrodynamic moments and simplifies the collision integral.

Findings

Collision operator accounts for relaxation of 13 hydrodynamic moments

Derived expression for Langevin source intensity

Proved Boltzmann's H-theorem for the new model

Abstract

A new form of the model collision operator for a Boltzmann gas of hard spheres and Coulomb plasma is derived. One-component and many-component systems are considered. The collision operator proposed takes properly into account the relaxation of the first 13 hydrodynamic moments. An expression for the intensity of the Langevin source in the model kinetic equation is obtained in the same approximation. A technique for reconstruction of the model collision integral based on a known expression for the model linearized operator is proposed. It is shown that, within our model, the collision integral does not contain a complicated exponential, common for the ellipsoidal statistical type models. Boltzmann's H-theorem is proved for our model.