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Title
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Nonlinear Fourier analysis for unmagnetized plasma waves
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Author
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Abstract
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| We apply the nonlinear Fourier analysis developed by Callebaut [1] to an infinite homogeneous plasma calculating many higher order terms (computer algebra) and obtaining in this way some analytic expressions. (a) For cold plasma: the maximum amplitude is 2/e (i.e., 73% of n(0)) of the initial density no. otherwise the series diverges. For exponentials (sum of two waves) the maximum amplitude is halved, i.e n(0)/e. (b) For plasma with electron pressure, the radius of convergence decreases as the ratio of k(2)v(s-)(2) (1 + Gamma(-))/omega(-)(2) increases (Gamma(-) is the polytropic exponent; omega(-) is the plasma angular frequency for electrons; k is the wave number; v(s-) is the sound velocity for the electrons). (c) Suggestions for experimental verification are made. (d) In the limit of sound waves (no plasma) the radius of convergence is zero. Nevertheless the correct dispersion relation is obtained. A direct analysis confirmed these results for sound waves. (e) The cases where the method fails are indicated. (I) Plasma where both ions and electrons may move. are briefly considered (relevant for comet tails, fullerenes and electron-positron plasmas). |
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Language
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English
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Source (journal)
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Physica scripta / Kungliga Svenska Vetenskaps Akademien. - Stockholm, 1970, currens
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Publication
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Stockholm
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Royal Swedish Academy of Sciences
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2003
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ISSN
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0031-8949
[print]
1402-4896
[online]
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DOI
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10.1238/PHYSICA.REGULAR.068A00007
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Volume/pages
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68
:1
(2003)
, p. 7-21
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ISI
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000184274900001
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Full text (Publisher's DOI)
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Full text (open access)
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