Then the pinkish region is the outer Van Allen radiation belt. In the context, we saw all plasma waves are distinguished by their phase velocities, viz. w / k where w is the plasma frequency and k the wave number vector. In the case of the standard magnetosonic wave we have:
w2 / k 2 = c 2 (v A 2 + v s 2 ) / (v A 2 + c 2 )
Where v A is the Alfven velocity, v s is the ion sound speed and c the velocity of light. In the limit of low magnetic fields, for which v A -> 0 the wave becomes an ordinary ion acoustic wave. Basically the waves under review get their energy by interacting with protons trapped in Earth's magnetic field spiraling around magnetic field lines.
Of particular interest in plasma physics research is what occurs - or what do we get - when we convert some of the plasma waves surrounding the Earth into sound waves. Well, it's been found that when these waves are converted to sound - somewhat analogous to a radio playing FM broadcasts- the space around Earth sounds like a "jungle" with different species of particles all emitting distinct "calls".
One of the mysterious sounds isolated resembles what can best be called a plasmaspheric hiss: an ever present sibilance in the inner regions of Earth's magnetic field. To be more specific, it sounds like pure static spanning 100 Hz to several kilohertz. This is a frequency range roughly equivalent to that produced by the middle third of a piano. We already know, for reference, that this hiss plays a crucial role in shaping the structure of the Earth's radiation belts, in particular disrupting them by knocking their energetic particles out into the atmosphere.
Despite knowing what the waves do, the source of the hiss is still unknown. One theory is that it arises from spiraling electrons high over the Earth's equator. Another proposes that it consists of the remnants of distant whistlers or chorus waves that devolve into incoherence. The graph below is useful to separate out the whistlers from other waves, e..g electron cyclotron:
The R-waves of which the whistler forms the lower edge are called right circularly polarized. The electron cyclotron waves are an example at higher plasma frequencies (given by the ordinate). From the graph we can see that V_g = d w/ dk (group velocity) decreases as the plasma frequency w increases.
This is called the whistler wave because the high frequency components of the wave packet travel faster than its low frequency components. As a prosaic example, an observer some distance away from a lightning strike will then hear a whistle (for the associated sound wave) starting at high frequencies and descending to lower ones. Note the critical slope in particular, defined by: c = w/ k.
The most interesting aspect is that plasma physicists previously assumed this hiss was just random white noise with no coherent features. Now, however, Summers et al (Journal of Geophysical Research: Space Physics, 2014) have analyzed NASA satellite measurements of the hiss from 2013 and fond something quite different.
That is, after breaking the signal down into its spectrum of frequencies they discovered barely detectable rising and falling tones similar to those generated by whistlers, but at frequencies rising to roughly middle C and falling for about two octaves. The authors conjecture this is made possible by the high resolution of the instruments on the satellites: NASA's Van Allen probes and their particularly useful orbit - which keeps them mostly within Earth's radiation belts.
A cautionary note: Though the waves with the plasmaspheric hiss resemble whistler tones (and I lead toward that association) and share similarities in mathematical wave theory, the physical mechanism that generates the hiss is still wide open for debate.
Summers et al hope that their recent findings will generate renewed interest in the subject of plasma waves and the plasmaspheric hiss and perhaps drive vigorous inquiry to pin down the source.
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