As we learned in Chapter 4, the equations describing the motion of plasma are three equations that are derived from the laws of conservation of mass, momentum, and energy. These three equations express the four variables that describe the moving plasma – mass density, pressure, temperature (or energy), and velocity – as functions of spatial position and time. Since it is not possible to solve a system of three equations for four variables, we need a fourth equation relating some or all of these four variables that does not introduce another variable. The fourth equation is the equation of state. In the discussion that follows we will refer to the equation of state as the EOS.

With the EOS specified, we can then solve the equations of motion for the plasma. We will learn how this solution is done numerically in Chapter 11. In this chapter we learn the basics of how to specify the EOS for matter at extreme conditions.

Basic thermodynamic relations

We learned in Section 2.2.2 about the relaxation rates in dense plasma, that is, the rates at which thermodynamic equilibrium is established. In general, the variables characterizing the state of the plasma – mass density (or alternatively, particle number density), pressure, temperature – change slowly compared to these relaxation rates. Thus, we can consider that the plasma is, at each point in space and at each instant of time, in local thermodynamic equilibrium (LTE). In LTE the particle distribution functions for each particle species comprising the plasma can be characterized by a single parameter, the temperature.