The fluid theory we have been using so far is the simplest description of a plasma; it is indeed fortunate that this approximation is sufficiently accurate to describe the majority of observed phenomena. There are some phenomena, however, for which a fluid treatment is inadequate. For these, we need to consider the velocity distribution function f(v) for each species; this treatment is called kinetic theory. In fluid theory, the dependent variables are functions of only four independent variables: x, y, z, and t. This is possible because the velocity distribution of each species is assumed to be Maxwellian everywhere and can therefore be uniquely specified by only one number, the temperature T. Since collisions can be rare in high-temperature plasmas, deviations from thermal equilibrium can be maintained for relatively long times. As an example, consider two velocity distributions f1(v x ) and f2(v x ) in a one-dimensional system (Fig. 7.1). These two distributions will have entirely different behaviors, but as long as the areas under the curves are the same, fluid theory does not distinguish between them.