Resonant Layers

where and .

The time-averaged Poynting flux in the -direction is written

(6.56) |

Now, the Faraday-Maxwell equation yields

(6.57) |

Thus, we have

(6.58) |

Let us ascribe any variation of with to the wave energy emitted by the plasma. We then obtain

(6.59) |

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

Equations (6.55) and (6.60) yield

(6.61) |

Note that , because , so wave energy is absorbed by the plasma. It is clear, from the previous formula, that the absorption takes place in a narrow layer, of thickness , centered on the resonance point, .