Introduction

Historically studies of wave propagation in plasmas have provided one of the keystones in the development of plasma physics and they remain a focus in contemporary research. Much was already known about plasma waves long before the subject itself had any standing, early studies being prompted by practical concerns. The need to allow for the effect of the geomagnetic field in determining propagation characteristics of radio waves led to the development, by Hartree in 1931, of what has become known as Appleton–Hartree theory. About the same time another basic plasma mode, electron plasma oscillations, had been identified. In 1926 Penning suggested that oscillations of electrons in a gas discharge could account for the anomalously rapid scattering of electron beams, observed over distances much shorter than a collisional mean free path. These oscillations were studied in detail by Langmuir and were identified theoretically by Tonks and Langmuir in 1928.

Alfvén's pioneering work in the development of magnetohydrodynamics led him to the realization in 1942 that magnetic field lines, pictured as elastic strings under tension, should support a class of magnetohydrodynamic waves. The shear Alfvén wave, identified in Section 4.8, first appeared in Alfvén's work on cosmical electrodynamics. Following the development of space physics we now know that Alfvén (and other) waves pervade the whole range of plasmas in space from the Earth's ionosphere and magnetosphere to the solar wind and the Earth's bow shock and beyond.

There is a bewildering collection of plasma waves and schemes for classifying the various modes are called for. Plasma waves whether in laboratory plasmas or in space are in general non-linear features.