The concept of a kinetic transport theory

Abstract

In fluid theory, the kinetic equation is converted into a system of moment equations. Any wanted moment is thereby coupled with other moments in an infinite set of equations. In plasma kinetic theory, the linearized Fourier-transformed kinetic equation is solved for the distribution function, and the wanted moments are obtained afterward as functions of the electric field strength. A complete knowledge of the frequency and wavenumber electric field spectrum is needed for these moments to be determined as functions of t and r. This standard kinetic approach is not suitable beyond the weak turbulence limit, in which the interaction of waves is treated in the random phase approximation. In situations where regular structures in (t, r) space arise due to phase correlations, recourse is commonly taken to fluid theory. In the present paper the plasma kinetic theory is treated differently by taking the electric field not as the cause of the process to be studied, but as a mediator between different moments. An arbitrary number of moment equations can be obtained in this way. Only those that, in the fluid limit, pass over to the fluid equations will be used. Outside the fluid limit, these so-called kinetic transport equations represent a continuation of the fluid equations into the kinetic regime. One purpose of kinetic transport theory is to extend the plasma kinetic theory beyond the weak turbulence limit. In contrast to standard plasma kinetic theory, the formulation of kinetic transport theory allows an application to neutral gases by setting the particle charge to zero. Therefore a second purpose of kinetic transport theory is to extend the transport equations for neutral gases beyond the fluid limit and to define the transport coefficients for highly rarefied gases.