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Plasma Oscillations and Landau Damping

We know all about plasma oscillations: A longitudinal wave comes in, the electric field is parallel to the direction of propagation, the electrons move back and forth and thus the wave moves through the plasma forever.
Right? Wrong!

What we didn’t talk about is the so-called thermal motion of the electrons.

So far we acted as if the electrons are at rest before the appearance of the wave. But this is not true! The electrons have a random motion, just like atoms and molecules in an ordinary gas. They move around, and statistically the number of electrons gets smaller, as the velocity gets higher (keep that in mind)

In the following picture, we show the potential created by a longitudinal wave (because of charge density distribution, as explained before)

The particles that move with the same velocity as the wave, will always see a constant potential (resonance).

Those particles that move slightly faster than the wave, will be decelerated, so part of their kinetic energy (since it cannot be lost) will be given to the wave (case A of the above figure).

Those particles that move slightly slower than the wave, will be accelerated, so they will take energy from the wave and turn it into kinetic energy (case B of the above figure).

We said that the particles with smaller velocities are more than the particles with larger velocities!

So overall the wave will give away MORE energy than it will gain! This means that the wave will be attenuated, as it travels through the plasma!

This phenomenon is known as “Landau Damping”

We are now experts in longitudinal waves. What else is there?

But transverse waves of course! Do you remember the term? Transverse waves have their electric and magnetic fields perpendicular to the direction of wave propagation. Now the real wave zoo appears! There is a whole bunch of different cases of waves, but we will just mention some of them, which can be explained without cumbersome math, and can give you a feeling about plasmas.