Introduction

Abstract

Kinetic theory is the link between the complete dynamic and statistical descriptions of gases and plasmas as many particle systems (microscopic theory) and the macroscopic (or phenomenological) description of physical transport phenomena in continuous media. Examples of macroscopic theories are hydrodynamics and the Chew-Goldberger-Low theory in plasma physics. These theories consist always of a closed system of partial differential equations for a number of (scalar, vectorial, tensorial) fields depending on position and time as independent variables. In kinetic theory the number of independent variables is larger: at least three velocity coordinates are added. The goals of kinetic theory may be formulated as follows:

• derivation and improvement of macroscopic equations.

• calculation of transport coefficients. These occur in the macroscopic theory, but cannot be determined by it.

• description of phenomena for which the macroscopic theory is inadequate.

Examples of the last mentioned category are:

• slip. This is the relative macroscopic velocity of a gas near a wall with respect to that wall.

• thermophoresis, i.e. the force exerted on a solid particle in a gaseous medium with a temperature gradient.

• dispersion of sound waves in gases.

• Landau damping and many micro-instabilities in plasmas.

• Brownian motion and hydrodynamical fluctuations.