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Third‐Order Oscillations in a Maxwellian Plasma

 

作者: S. Peter Gary,  

 

期刊: Physics of Fluids(00319171)  (AIP Available online 1967)
卷期: Volume 10, issue 3  

页码: 570-581

 

ISSN:0031-9171

 

年代: 1967

 

DOI:10.1063/1.1762150

 

出版商: AIP

 

数据来源: AIP

 

摘要:

Nonlinear plasma oscillations in a classical, nonrelativistic, collisionless, Maxwellian electron gas are considered. There is assumed a small, sinusoidal variation in the spatial part of the initial distribution function, corresponding to excitation of wavenumber modes ±k0. The nonlinear Vlasov equation is solved to third order in the long time limit via the Montgomery‐Gorman perturbation expansion, where the expansion parameter is &egr;, the amplitude of the initial perturbation. The linear, first‐orderk0mode of the electric field is dominated by the Landau solution with (negative) damping decrement &ggr;L. The third‐orderk0mode is modified, however, by singling out the spatially uniform part of the distribution function for special treatment, much in the manner of the quasi‐linear theory. A nonlinear damping decrement results such that, for many values ofk0and &egr;, &ggr;L< &ggr;N. Thus at sufficiently long times, the modified third‐order mode dominates the solution. For certain &egr; andk0this behavior resembles the results of Knorr and Armstrong, obtained by numerical integration of the nonlinear Vlasov equation.

 

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