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Second-order oscillations of a Vlasov–Poisson plasma in Fourier-transformed velocity space

Published online by Cambridge University Press:  13 March 2009

Zdeněk Sedláček  and
Luigi Nocera
Zdeněk Sedláček
Affiliation:
Institute of Plasma Physics, Czechoslovak Academy of Sciences, Pod vodárenskou věží 4, CS-182 11 Prague 8, Czech Republic
Luigi Nocera
Affiliation:
Institute of Plasma Physics, Czechoslovak Academy of Sciences, Pod vodárenskou věží 4, CS-182 11 Prague 8, Czech Republic
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Abstract

We study the Vlasov–Poisson system of equations in Fourier-transformed velocity space. First we reformulate some results of the linear theory: in the new representation the van Kampen–Case eigenmodes are found to be ordinary functions with convenient continuity properties. We give a transparent derivation of the free-streaming temporal echo in terms of the kinematics of wave packets in Fourier-transformed velocity space. We further extend this analysis to include Coulomb interactions, which allows us to establish a connection between the echo theory, the second-order oscillations of Best and the phenomenon of linear side bands. The calculation of the time evolution of the global second-order electric field is performed in detail in the case of a Maxwellian equilibrium distribution function. We conclude that the phenomenon of linear side bands may be properly explained in terms of the intrinsic features of the equilibrium distribution function.

Type
Research Article
Information
Journal of Plasma Physics , Volume 48 , Issue 3 , December 1992 , pp. 367 - 389
Copyright
Copyright © Cambridge University Press 1992

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