Macroscopic Transport Equations

Abstract

In the previous chapters we have seen that the macroscopic variables of physical interest for a plasma, such as number density n _α , mean velocity u _α , temperature T _α , and so on, can be calculated if we know the distribution function for the system under consideration. For the case of a system in thermal equilibrium we have calculated, in Chapter 7, several of these macroscopic parameters using the Maxwell-Boltzmann distribution function. In principle, the distribution function for a system not in equilibrium can be obtained by solving the Boltzmann equation. However, the solution of the Boltzmann equation is generally a matter of great difficulty. We will see, in this chapter, that it is not necessary to solve the Boltzmann equation for the distribution function in order to determine the macroscopic variables of physical interest. The differential equations governing the temporal and spatial variations of these macroscopic variables can be derived directly from the Boltzmann equation without solving it. These differential equations are known as the macroscopic transport equations, and their solutions, under certain assumptions, give us directly the macroscopic variables.