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Let’s assume a constant uniform magnetic field along some axis in a electron-ion plasma.

Again we will neglect thermal motion as well as collisions between the particles.

Suppose we send an E/M wave propagating along the magnetic field.

In this case, it is easier to consider the wave, not as linearly polarized (that is, the electric field lying on one direction). But rather as circularly polarized (the electric field rotating on a plane, perpendicular to the direction of propagation).

The two possibilities are the so-called Left-Handed and Right-Handed waves.

But what is their difference, why to we make this distinction?

Let’s forget about everything for a moment and think about a particle moving in a magnetic field. The parallel movement is unaffected, but the perpendicular happens on a circle. What is the direction of this rotation? It depends on the CHARGE of the particle!

There you have it! The two polarizations are different, because they cooperate mostly with the particles that move in the same direction around the magnetic field!

Let us examine the Right-Handed wave more closely (the Left Handed is an easy analogy), which cooperates with the electrons.

Omitting the calculations, we plot the square of the refraction index as a function of frequency

The most interesting feature of the above graph is the divergence! Can we understand it without actually deriving the relations?

Sure we can. First of all, the frequency where the divergence appears is the cyclotron frequency for the electrons. This also gives us a hint as to what causes it.

Imagine the electrons rotating around the magnetic field lines. Then we introduce an electric field, again rotating in the same direction. When the rotation frequency of the field is equal to the rotation frequency of the electrons, they see a constant electric field for all time! That means that they are accelerated by the electromagnetic wave. This is called electron cyclotron resonance.

Of course the divergence is still unphysical. The way to heal this problem, is by introducing a mechanics for the electron to lose energy, that is collisions! By colliding with the ions, part of the electron’s energy is taken away, so they are not infinitely accelerated, as implied by the above graph. This can be used for heating plasmas to achieve fusion! If one sends a high power wave, tuned at the electron cyclotron resonance, then most of its energy will be absorbed by the electrons. They in turn will give part of this energy to the ions via collisions. The net result is the increase of the plasma’s energy => Heating!

In the case, where the direction of wave propagation is perpendicular to the magnetic field, the situation becomes more complicated and such easy explanations are not available.

I hope that I gave you a feeling of some characteristics of collective behavior of plasmas, without going into complicated mathematical derivations