## Abstract

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 ƒ(**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 ƒ_{1}(*v*_{ x }) and ƒ_{2}(*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.

## Keywords

Phase Velocity Kinetic Theory Plasma Wave Maxwellian Distribution Vlasov Equation## Preview

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