The 13-moment system of transport equations was introduced in Chapter 3 and several associated sets of collision terms were derived in Chapter 4. However, a rigorous application of the 13-moment system of equations for a multi-species plasma is rather difficult and it has been a common practice to use significantly simplified equation sets to study ionospheric behavior. The focus of this chapter is to describe, in some detail, the transport equations that are appropriate under different ionospheric conditions. The description includes a clear presentation of the major assumptions and approximations needed to derive the various simplified sets of equations so that potential users know the limited range of their applicability.

The equation sets discussed in this chapter are based on the assumption of collision dominance, for which the species velocity distribution functions are close to drifting Maxwellians. This assumption implies that the stress and heat flow terms in the 13-moment expression of the velocity distribution (3.49) are small. Simplified equations are derived for different levels of ionization, including weakly, partially, and fully ionized plasmas. A weakly ionized plasma is one in which Coulomb collisions can be neglected and only ion-neutral and electron-neutral collisions need to be considered. In a partially ionized plasma, collisions between ions, electrons, and neutrals have to be accounted for. Finally, in a fully ionized plasma, ion and electron collisions with neutrals are negligible.