Hostname: page-component-76fb5796d-skm99 Total loading time: 0 Render date: 2024-04-26T20:30:00.705Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Birkmayer, W., Hagfors, T. & Kofman, W. 1986 Small scale plasma-density depletions in Arecibo high-frequency modification experiments. Phys. Rev. Lett. 57, 1008–1011.CrossRefGoogle ScholarPubMed
Dubois, D. F., Hanssen, A., Rose, H. A. & Russell, D. 1993 Space and time distribution of HF excited Langmuir turbulence in the ionosphere: comparison of theory and experiment. J. Geophys. Res. 98, 17543–17567.CrossRefGoogle Scholar
Fejer, J. A. 1979 Ionospheric modification and parametric instabilities. Rev. Geophys. Space Phys. 17, 135–153.CrossRefGoogle Scholar
Gurevich, A. V. 1978 Nonlinear Phenomena in the lonosphere. Physics and Chemistry in Space, Vol. 1. Springer-Verlag, New York.CrossRefGoogle Scholar
Hagfors, T. & Gieraltowski, G. F. 1972 Stable electron density fluctuations in the presence of a high-frequency electric field. J. Geophys. Res. 77, 6791–6803.CrossRefGoogle Scholar
Hanssen, A. 1992 Electromagnetically driven Langmuir turbulence in the ionosphere. University of Tromso, Physics Report.Google Scholar
Kohl, H., Kopka, H., Stubbe, P. & Rietfeld, M. T. 1993 Introduction to ionospheric heating experiments at Tromsø — II. Scientific problems. J. Atmos. Terrest. Phys. 55, 601–613.CrossRefGoogle Scholar
Melrose, D. B. 1986 Instabilities in Space and Laboratory Plasmas. Cambridge University Press.CrossRefGoogle Scholar
Mima, K. & Nishikawa, K. 1984 Parametric instabilities and wave dissipation in plasmas. Handbook of Plasma Physics (ed. Rosenbluth, M. N. & Sagdeev, R. Z.), Vol. 2, pp. 451–517. North-Holland, Amsterdam.Google Scholar
Muldrew, D. B. & Showen, R. L. 1977 Height of the HF-enhanced plasma line at Arecibo. J. Geophys. Res. 82, 4793–4804.Google Scholar
Nicholson, D. R. & Goldman, M. V. 1978 Cascade and collapse of Langmuir waves in two dimensions. Phys. Fluids 25, 1766–1776.Google Scholar
Sanmartin, J. R. 1970 Electrostatic plasma instabilities excited by a high-frequency electric field. Phys. Fluids 13, 1533–1542.CrossRefGoogle Scholar
Silin, V. P. 1965 Parametric resonance in a plasma. Soviet Phys. JETP 21, 1127–1134.Google Scholar
Thornhill, S.G. & Ter Haar, D. 1978 Langmuir turbulence and modulational instability. Phys. Rep. 43, 43–99.Google Scholar
Zakharov, V. E. 1984 Collapse and self-focussing of Langmuir waves. Handbook of Plasma Physics (ed. Rosenbluth, M. N. & Sagdeev, R. Z.). North-Holland, Amsterdam.Google Scholar