An electron plasma wave is a type of wave that propagates through a plasma, which is a gas made up of charged particles (ions and electrons). Specifically, an electron plasma wave is a type of longitudinal wave that occurs when the electrons in the plasma oscillate collectively in response to an external disturbance, such as an electric field.

The wave is characterized by its frequency, wavelength, and amplitude. The frequency of the wave is determined by the properties of the plasma, such as its density and temperature. The wavelength of the wave is determined by the distance between two adjacent crests or troughs in the wave. The amplitude of the wave is the height of the crest or the depth of the trough.

Electron plasma waves have many applications in plasma physics, including in plasma diagnostics and heating. They are also important in the study of space plasmas, such as the ionosphere and the solar wind. In addition, they are used in plasma-based particle accelerators and in plasma processing for material synthesis and modification.

The thermal motion is responsible for the plasma oscillation to propagate. To observe thermal effect, let us add - ∇Pe (Pressure gradient) in equation of motion. Then the equation of motion becomes

Now equation 1 becomes

The equation of continuity is

The poisson equation is

We know that, to solve above equation, the following assumptions are made

Now, the above equation becomes

are neglected because they represents quadratic term. Considering linear theory, equation 3 becomes

Using equation 9, 10 and 11, we get

from equation 12, the group velocity is finite because the frequency depends on k. So differentiate with respect to k

From the graph, the slope of the line drawn from the origin gives the phase velocity. The slope of the curve at point P gives the group velocity which is always less than the normal velocity.

Fig: Dispersion relation for electron plasma waves.

Previous topic: Theory of Plasma oscillation

Next topic: Electron cyclotron resonance

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