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# Wave Propagation Across Ion Cyclotron Resonance Harmonic Layers

Wave Propagation Across Ion Cyclotron Resonance Harmonic Layers
Kaya Imre
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We find the ion current to be the sum of (18) and (22). We readily observe that our boundary layer -35- expansion is consistent provided that 8 = eâ€ž, , (81) Xp/Xg = (Zp/Zg)''(nj, /ng)(mp/mg) = 2(Zg/Zp) (n^/ng) = 0(8).
We add the electron current obtained from the charge neutrality, drop terms of order m /m. , and eliminate E, to obtain e 1 - {1 + d^ + (1 + H + d^)[dA(s)d - B(s)]}E^ = 0, (82) where 2 2 \i = (e _ - nji )/ (e^, ^ ~ Â°|| ^ ' \ = (e__ - 4 )(%+ - 4 )/(eâ€ž - 4 ).
d = d/ds.
s = -2Â£8n Ixo
.../c. ^ c ^^^^ =^s"l, o/^^x-4>' B(s) =^^.
e -n XX II According to (81) the density ratio n^/nâ€ž=0(8) and this might seem to be an uninteresting parameter range. However, the numerical calculations given in Sec. VI show that a maximum in the wave energy absorption occurs with a rather small addition of minority species on the order of 1% of the electron number density. Such a small minority fraction is consistent with our ordering. We note that if the ordering (81) is not satisfied, within the layer E must get much smaller in magnitude in order to keep the first term in the right-hand side of the first equation in (22) balanced.

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