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Consider the situation under investigation in the
preceding section, in which a plane wave, polarized in the direction,
is launched along the axis, from an antenna located at large positive ,
and absorbed at a resonance located at . In the vicinity
of the resonant point, the electric component of the wave satisfies

(607) 
where and .
The timeaveraged Poynting flux in the direction is written

(608) 
Now, the FaradayMaxwell equation yields

(609) 
Thus, we have

(610) 
Let us ascribe any variation of with to the wave energy emitted by the
plasma. We then have

(611) 
where is the power emitted by the plasma per unit volume.
It follows that

(612) 
Equations (607) and (612) yield

(613) 
Note that , since , so wave energy is absorbed by the
plasma. It is clear from the above formula that the absorption takes
place in a narrow layer, of thickness , centred on the
resonance point, .
Next: Collisional Damping
Up: Waves in Cold Plasmas
Previous: Resonances
Richard Fitzpatrick
20110331