By plasma model we denote a set of equations governing the temporal evolution of a plasma under a given set of boundary and initial conditions. Ideally, plasma models should be based on first principles. Unfortunately, these are not yet available, at least not from a strict point of view. In any event, simplifications are necessary to keep applications feasible.

For describing space plasma dynamics, it is largely appropriate to ignore quantum effects. The condition for this assumption to be satisfied is that typical values of the action, such as momentum × length or energy × time are much larger than Planck's constant h = 6.63 ċ 10–34 Js. This condition is well satisfied for typical space dynamical processes. Therefore, we will discuss models based on classical elementary or statistical mechanics and electromagnetism. Radiation reaction is ignored.

After the foundations were laid by Isaac Newton, James Clerk Maxwell, Ludwig Boltzmann, Albert Einstein and others, these theories have been extremely successful within their ranges of applicability and form the classical basis of modern technology. Thus, the difficulties that we will be facing, to a large extent, do not lie in uncertainties about the foundations but rather in the complexity of the interactions, which require further simplifying assumptions. Therefore, a number of different plasma models exist, each of which has its characteristic range of applicability. It is the aim of this chapter to summarize the plasma models that are relevant for our purposes.