Plasma Waves

Abstract

In this chapter we will catch a glimpse on the vast zoo of plasma waves. The formalism to derive these waves, perturbation theory, briefly will be introduced. We will not derive all types of waves formally; instead, we will limit ourselves to the magnetohydrodynamic waves, which are Alfvén waves and ion acoustic waves. The derivation of the dispersion relations for other types of waves follows the same scheme, it only differs in the terms considered in the equation of motion, in the assumptions made in the equation of state, and in whether a one-fluid description of the plasma is sufficient or if a two-fluid description is required. The detailed derivations can be found e.g. in [4.1, 4.3, 4.4, 4.5, 4.7, 4.8, 4.9, 4.6]. For the purpose of this book, however, it is more important to grasp the nature of the waves than to fiddle around with the mathematical tricks involved in solving the equation of motion.

Roll on, thou deep and dark blue Ocean — roll! Ten thousand fleets sweep over thee in vain; Man marks the earth with ruin — his control Stops with the shore.

Lord Byron, Childe Harold’s Pilgrimage