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Electrostatic parametric resonances in a plasma revisited

Published online by Cambridge University Press:  13 March 2009

J. F. McKenzie  and
T. Hagfors
J. F. McKenzie
Affiliation:
Max-Planck-Institut Für Aeronomie, 37191 Katlenburg-Lindau, Germany Department of Physics, University of Natal, Durban, Natal 4001, South Africa
T. Hagfors
Affiliation:
Max-Planck-Institut Für Aeronomie, 37191 Katlenburg-Lindau, Germany
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Abstract

We generalize Silin's dispersion equation for electrostatic parametric resonances in an unmagnetized plasma to include interactions hitherto overlooked. Of particular interest to ionospheric physicists in this generalization is the interaction between an ion acoustic wave (shifted up in frequency by that of the pump) and an unshifted Langmuir wave. This yields growth rates equal to that of its counterpart in the Silin version, namely the ‘classical’ interaction between a Langmuir wave (shifted down by the pump frequency) and an unshifted ion acoustic wave. The more general (truncated) dispersion equation also displays resonances between ion acoustic sidebands, but this requires pump frequencies of the order of, or less than, the ion plasma frequency and therefore may be of little practical interest in the ionosphere. The system is analysed using Fourier techniques, which lead to two dispersion equations governing the Fourier transforms of the ion and electron perturbation densities. It is shown that, as far as the structure of the coupled recursion relations for the ion and electron Fourier components is concerned, there is an equivalence between the fluid and kinetic treatments. In the case of weak pump fields we calculate the growth rates associated with the various instabilities from a truncated three-wave interaction dispersion relation. Where it is appropriate, these growth rates are compared both with those from the Sum dispersion equation and the counterparts from the Zakharov model. We also discuss the case of very strong pump fields where the ‘natural’ interacting mode frequencies are not those associated with the usual Langmuir—ion acoustic modes of the unpumped plasma, but rather the oscillator frequencies corresponding to the coupled oscillator paradigm that is applicable to the system. Here again we find instabilities of a nature analogous to those arising in the weak pump case.

Type
Research Article
Information
Journal of Plasma Physics , Volume 55 , Issue 3 , June 1996 , pp. 359 - 385
Copyright
Copyright © Cambridge University Press 1996

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