Introduction

Fluid equations are conventionally obtained by taking velocity space moments of the kinetic equation (see Section 3.2),

Here, , , and

(4.2) |

Furthermore, and are the species- electrical charge and mass, respectively, whereas and are the ensemble-averaged electromagnetic fields.

In general, it is extremely difficult to solve the kinetic equation directly, because of the
complexity of the collision operator. However, there are some situations
in which collisions can be completely neglected. In such cases, the kinetic equation simplifies to give the so-called *Vlasov equation*,

(4.3) |

The Vlasov equation is tractable in sufficiently simple geometry. (See Chapter 8.) Nevertheless, the fluid approach possesses significant advantages, even in the Vlasov limit. These advantages are as follows.

First, fluid equations involve fewer dimensions than the Vlasov equation. That is, three spatial dimensions instead of six phase-space dimensions. This advantage is especially important in computer simulations.

Second, the fluid description is intuitively appealing. We immediately understand the significance of fluid quantities such as density and temperature, whereas the significance of distribution functions is far less obvious. Moreover, fluid variables are relatively easy to measure in experiments, whereas, in most cases, it is extraordinarily difficult to measure a distribution function accurately. There seems remarkably little point in centering our theoretical description of plasmas on something that we cannot generally measure.

Finally, the kinetic approach to plasma physics is spectacularly inefficient. The species distribution functions provide vastly more information than is needed to obtain the constitutive relations [i.e., Equations (3.1) and (3.2)] that close Maxwell's equations. (See Section 3.2.) After all, these relations only depend on the two lowest moments of the species distribution functions.