Waves in a Cold Plasma
This chapter begins by considering the propagation of small-amplitude plane waves in a homogeneous plasma. The principal result of the analysis is a dispersion relation that relates the frequency to the wave-vector. The chapter examines this dispersion relation and the waves. It explores the theory to inhomogeneous plasma, and shows that how to determine the amplitude and phase of a wave from the dispersion relation. The chapter provides an overview of the most important instabilities described by the cold plasma closure. The two-stream instability arises in a plasma consisting of various interpenetrating components in relative motion. It is the archetypal kinetic instability, driven by energy contained in the velocity distribution rather than in the spatial gradients. The dispersion relations for propagation at arbitrary angle are deduced by making use of the property that the index of refraction is a monotone function of the propagation angle.