What are 'ordinary' and 'extraordinary' modes?

Plasmas that contain magnetic fields are a complex system, made more so by the ways in which the charged particles can interact with electromagnetic radiation that is incident upon such a system. Electromagnetic waves interact very strongly with all charged particles, and this allows energy to be exchanged between the plasma and the incident electromagnetic radiation. Plasmas are capable of oscillating, and have a natural, lowest harmonic 'plasma frequency' defined by the density of the charged particles. The speed of sound in a plasma is also modified by the presence of a magnetic field and becomes the 'magnetosonic sound speed'. below the plasma frequency, electromagnetic radiation cannot propagate.

Electrons and other charged particles tend to spiral around magnetic field lines in a plasma at a frequency called the 'gyro frequency'. The interaction between the incident electromagnetic radiation and the populations of electrons which are oscillating under the influence of the electromagnetic properties of the plasma, leads to a complex interaction between incident radiation and plasma. Some oscillation frequencies of the incident radiation diminish rapidly in strength, or may cease to penetrate the plasma, others may grow, or be transmitted.

The plasma can be characterized by comparing the phase velocity of an incident wave, with the speed of light, at different frequencies above and below the plasma frequency for a 'cold' plasma which has no magnetic field. This leads to two 'ordinary modes' of propagation. At frequencies well below the plasma frequency, the wave is not transmitted. At frequencies well above the plasma frequency, the wave is transmitted.

When a magnetic field is added, you have hybrid 'extraordinary' waves which form not just two, but three possible modes of interaction. The critical frequency splits into two ( Fp and Fh ) and becomes a combination of the plasma freqency (Fp) and the gyro frequency (Fg) so that Fh = (Fp^2 + 1/4 Fg^2)^1/2 + 1/2 Fg. The frequency Fh is sometimes called the 'hybrid' plasma frequency because it depends on the gyro frequency and the plasma frequency.

For incident waves with frequencies below Fp, you get reflected waves, for frequencies above Fh you get transmitted waves, and for frequencies between Fp and Fh you get 'trapped' oscillation modes. In these trapped modes, it is possible to pump energy from the incident electromagnetic wave into the plasma to heat it!

For more information on this subject at a technical level, visit the review article by Dr. Patricia Reiff, co-Investigator for the IMAGE RPI instrument.

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