In this chapter we go into more detail in describing how calculations of plasma properties may be done. Analytic models, the role of experiments in model building, and computational models are considered. We provide the basis for a mathematical description of the transport and of the density of the plasma in a plasma reactor. Next, we discuss experimental design and its role in model building. We then turn to a survey of the most widely applicable computational methods for describing plasmas.

Analytic Plasma Models

We begin this section with a review of solutions to simple diffusion equations in one and two dimensions. We turn, after that, to a one-dimensional description of the plasma. The plasma is divided into the main plasma and the sheath. The main plasma is quasineutral, whereas the sheath, which is the region of strong electric fields near the chamber wall, is positively charged since it has relatively very few electrons in it. The main plasma is also divided into a “presheath” and an interior region. The presheath is the part of the main plasma, next to the sheath (so at the outside of the main plasma) which is responsible for most of the acceleration of the ions before they enter the sheath.