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Definition: |
Clemmow-Mullaly-Allis diagram. When we obtain the dispersion relation for waves in COLD UNIFORM plasma and calculate all the solutions to the resulting quartic equation, we realize that there are many categories of waves we could look at. For instance, waves parallel to the magnetic field, waves perpendicular to the magnetic field field, or waves at arbitrary field angles; high or slow frequency waves; high or low density plasma; high or low magnetic field; etc. The CMA diagram helps us to categorize the different solutions. The CMA shows the shapes (wave normal surfaces) of the dependence of phase velocity of the wave on the angle between the magnetic field (B) and the wave vector (k). There are three different types of surfaces: spheroid, dumbell lemniscoid, and wheel lemniscoid. In cold uniform plasma four major types of waves propagate. Left circularly polarized wave (L), right circularly polarized wave (R), ordinary (O) and extraordinary (X) waves. The CMA digram tells us wheather the particular wave will propagate in a certain region, and if it will, it shows its wave normal surface. To briefly visualize the CMA diagram,
imagine the first quadrant of the x-y plane. The lower left corner (closest to the origin) is designed in the CMA diagram as the high frequency region and the upper right hand corner as the low frequency region. Furthermore, the CMA diagram is divided into regions by resonance (index of refraction goes to infinity) and cutoffs (index of refraction goes to zero). Example of low frequency waves are shear and compressional Alfven wave. Example of an intermediate frequency wave is the whistler wave discovered during WWI.
More information can be found e.g. in _Waves in Plasmas_ by Stix. |
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