The solar system and the bulk of the universe comprises matter which is mostly in the form of a plasma. Plasma is a very hot gas in which the electrons have been stripped from atoms to form a gas of negatively charged electrons and positively charged ions. In a fully thermalized, equilibrium state, these electrons and ions would oscillate about their equilibrium positions. However, any perturbation to this equilibrium would displace the charged particles in such a way as to set up electric and magnetic fields which act as restoring forces to the displaced particles. In the simplest example of such a perturbation, the electrons might be offset from the less mobile (because of their mass) ions. The electrons, then, would execute simple harmonic motion about their equilibrium positions. A measure of electric fields in this perturbed plasma would show a strong line or resonance at a particular frequency, called the electron plasma frequency, which is proportional to the square root of the electron number density of the plasma. By measuring this frequency, the electron density of the plasma can be determined. The electron plasma frequency is one of a number of characteristic frequencies of a plasma.
Another common characteristic frequency of a plasma is called the electron cyclotron frequency. If the plasma is embedded in a quasi-static magnetic field, the charged particles will be accelerated in a direction perpendicular to the magnetic field causing them to move in helixes around the field lines. The basic frequency of rotation of an electron about a magnetic field is proportional to the strength of the magnetic field. This frequency is the electron cyclotron frequency.
The study of plasma waves in space plasmas involves the measurement of the characteristic frequencies of the plasma in order to understand basic properties of the plasma such as its density and the effect of the magnetic field which may be threading the plasma. Since the charged particles in a plasma respond to static and oscillatory electromagnetic fields, strong interactions can occur between these plasma waves and the underlying charged particles in the plasma. These strong interactions are often called instabilities. Electron plasma oscillations at the plasma frequency (sometimes called Langmuir waves) are one example of an instability in a plasma. In many cases, plasma waves and instabilities are important in understanding the state of the plasma, the evolution of energy and the flux of plasma in a magnetized plasma, and a number of other interesting phenomena. One example is the case of strong whistler mode waves in the magnetosphere of a planet. These waves have phase velocities which nearly match the motion of electrons around the magnetic field and can, therefore, have a profound effect on the motion of the electrons. In this case, the result can be a scattering process which would dump electrons otherwise trapped in the Earth's Van Allen radiation belts into the atmosphere causing the aurora or northern lights. Many other examples can be discussed.
Plasma waves are generally waves that are at or below the various characteristics of a plasma. Generally speaking, such waves do not propagate very far in a plasma and are strongly influenced by the magnetized plasma when they do propagate. In many cases the plasma or plasma waves can generate waves at frequencies that are very high in frequency compared to the highest characteristic frequency of a plasma. In this case the waves are electromagnetic and can propagate away from their source with little interaction with the surrounding medium. These high frequency waves are often referred to as radio waves. Unlike plasma waves, radio waves can propagate more or less freely through a plasma from the source to an observer and the radio waves become part of the remotely sensed electromagnetic spectrum of the body just like visual, infrared, or ultraviolet emissions. Jupiter was the first planet discovered to have a radio spectrum and it was from this spectrum that many conclusions were drawn about the existence of a strong magnetic field, hence substantial magnetosphere, at Jupiter long before Pioneer 10 flew past the planet to make in situ observations. In addition to a simple detection of the magnetic field, radio waves allowed an accurate estimate of the intensity of the planetary magnetic field, the orientation of the field with respect to the rotational axis of the planet, and even a measurement of the internal rotation rate of Jupiter.