landau waves: an experimental factsilas.psfc.mit.edu/introplasma/expts.pdf · landau waves: an...
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Landau Waves: An Experimental FactH.Derfler and T.C. Simonen
Phys.Rev.Lett 17 (1966) 172
First experimental verification of Landau damping and Bohm-Gross dispersion in ∼uniform 1-D plasma.
Wave launched at a
steady (real) frequency
ω, controlled by an RF
generator.
Detected at a variable
distance.
Grids used so that the problem is approximately 1-dimensional.
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Observed signalShows an oscillation strongly damped in space.
This is interpreted as giving the real and imaginary parts k = kr + iki.
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Dispersion RelationShows agreement with full kinetic theory calculation for ωp < ω <∼ 4ωp
[Bohm-Gross relation a poor approx for higher ω.]
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Dispersion of Electron Plasma WavesJ.H.Malmberg and C.B.Wharton
Phys.Rev.Lett. 17(1966)175
Performed in a longer plasma column.
The transverse gradients are large.
Not quite as ideal a situation, but rather quieter signals. Basically similar technique.
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Data Obtained
Longer wave train allows more accurate k-determination.
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Dispersion RelationHas to account for transverse variation.
Consequently is not simply
ω2 ≈ ω2p[1 + 3(kλD)2]
Theory and experiment agree well using exptl Te
(ne adjusted within exptl uncertainty to fit).
Agreement becomes exact if Te is increased 10%.
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Damping Agrees with Landau TheoryPlotting (log)ki/kr versus (ω/krvte)
2 = (vp/vte)2
gives a straight line.
Theory is verified over a factor of about 10 in damping decrement.
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Ion Acoustic WavesA.Y.Wong, N.D’Angelo, and R.W.Motley
Phys.Rev.Lett. 9 (1962) 415
In the plasma column of a Q-machine
Have constant phase-velocity, independent of frequency.
Plasma temperature not well measured.
Density varied nearly a factor of 10.
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Damping Decrement
Damping goes like exp(−x/δ)
• 1/δ ∝ ω. δ ≈ 0.6λ
• δ independent of n (not collisions).
• δ ∝ m−1/2i
Consistent with Landau damping.