Plasma waves

spaceweb@oulu.fi - last update: 24 November 1998, 1440 UT (RR)

One of the most obvious features of the plasma state is the rich variety of wave motions which plasmas can support. Waves of a particular kind are said to be in a particular wave mode. The idea of a wave mode is familiar from other contexts. For example, in a compressible gas there are sound waves and, if there is a gravitational field present, there are also internal gravity waves. The study of the waves in plasmas is very useful for plasma diagnostics, since the wave modes of a plasma depend on the plasma properties.

Some important wave parameters in general are:

Phase velocity
Group velocity
Polarization

Closer analysis of the waves reveals some additional parameters. There are two main different methods of approach used in analysing the plasma waves. One uses the dielectric tensor of the plasma, the other dispersion relation. The latter one is often simpler. The way the dispersion relation is calculated depends on the adopted plasma theory, which also determines the available wave modes. Important things to consider in plasma theories from the wave point of view are:

What is the proper truncation level for the moments of Boltzmann's equation
- this is the selection between the hot, warm, and cold plasma model
- the more advanced is the initial theory, the more complicated wave modes can be studied
What plasma particles are taken into account
- only electrons, or one or more ions added, or perhaps fluid (MHD) theory
- the more complicated the medium is, the more wave modes it support (we cannot have, e.g., ion plasma waves if ion motion is neglected in the first place, no matter how hot plasma is considered!)
- as a rule, if the studied wave frequency is large when compared to the ion cyclotron frequency, ions can be neglected (ions are much heavier than the electrons, and cannot respond to the wave fields as readily)
Is the external magnetic field important or not
- the presence of B affects greatly the propagation of some plasma wave modes
- wave modes are often listed, accordingly, in four groups:
  1. B=0 (wave propagation direction [direction of k] not important)
  2. B>0, k parallel to B
  3. B>0, k perpendicular to B
  4. B>0, k in arbitrary direction to B
Are collisions between the particles important
- damping of plasma wave modes can occur when collisions between particles is considered
- note, however, that in the case of hot plasma theory, Landau damping takes place without collisions!
What is the amplitude of the waves
- by considering only small amplitude waves, linear perturbation theory can be used

The dispersion relations calculated are typically divided into two basic modes, longitudinal and transverse, according to the angle between the electric field component of the wave and the propagation vector k. However, to make things unnecessarily complicated, the nomenclature for the various plasma wave modes derived is far from systematic, being a mixture of historical names (e.g., Langmuir, Alfven, Bernstein), of names descriptive of the wave motion (e.g., ion acoustic waves, electron cyclotron waves, transverse waves), and of names characteristic of the theory used to derive the wave properties (e.g., magnetoionic waves, MHD waves, drift waves).

For more information about the wave theories, see:

Magnetohydrodynamic (MHD) waves and shocks
Waves in cold plasmas
Waves in warm plasmas
Waves in hot plasmas
Plasma instabilities

For more information about the ULF frequency wave types found in the magnetosphere, see geomagnetic pulsations.