2005 II 4
From QED
The wave equation is:
The two transverse waves have:
We can take the first two equations:
And combine them:
Expanding:
Which can be factored to:
Giving dispersion relations:
The last equation is longitudinal, so:
Or:
The term that goes to infinity at ω = ΩH is . This term appears in the dispersion relation:
Using the dispersion relation:
For ω real and very close to ΩH, [note: this assumption comes from Stix, we assume it is based on <i>k</i><i>v</i><i>T</i><i>i</i>˜Ω<i>H</i>. This makes sense if it is reasonable to keep the ion term as <i>Z</i>(ζ), but is not necessarily true], so we take the first term in the electron expansion:
Since :
And by quasineutrality, , so we will find:
Because will not go to infinity at the resonance.
This page was recovered in October 2009 from the Plasmagicians page on Generals_2005_II_4 dated 20:35, 15 May 2007.