Landau Damping an Initial-Value Problem

Abstract

As we have seen in the preceding five chapters, many wave phenomena in plasmas can be studied using only the fluid-theory model in which the plasma is considered as two or more interpenetrating fluids (one for the electrons and one for each ion species). The main disadvantage of this model, as has been pointed out several times, is that only the velocity average of each plasma specie can be taken into account, so that any velocity-dependent effects, such as the Landau damping to be discussed in this chapter, are not predicted by the theory. From a mathematical point of view, the main advantage of the model is that it is a much simpler model than the kinetic-theory model to be used in the present and remaining chapters of the book. Because of this relative simplicity, unless velocity-dependent phenomena are of specific interest, the fluid-theory model is always used. For non-velocity-dependent effects, the fluid-theory model and the kinetic-theory model give identical results. As we employ the kinetic theory in the remaining chapters of the book, we shall see that not only are velocity-dependent effects predicted, but that we will recover many of the fluid-theory wave phenomena already found.