Hostname: page-component-848d4c4894-p2v8j Total loading time: 0.001 Render date: 2024-05-21T00:52:04.823Z Has data issue: false hasContentIssue false
  • English
  • Français

On the nonlinear development of the Langmuir modulational instability

Published online by Cambridge University Press:  13 March 2009

R. O. Dendy  and
D. Ter Haar
R. O. Dendy
Affiliation:
Department of Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP, U.K.
D. Ter Haar
Affiliation:
Department of Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP, U.K.
Get access Rights & Permissions [Opens in a new window]

Abstract

Using the Zakharov equations in their Fourier-transformed form, we consider the development of the modulational instability (MI) both for the monochromatic and the finite-width cases. In the static approximation and considering a monochromatic Langmuir wave which is coupled only to a single pair of Stokes and anti-Stokes Langmuir perturbations, we show that the resultant set of equations is integrable and we discuss the analytical solution of these equations. We show how a finite-width driver will lead to a threshold for the MI. We compare our results with those obtained by other authors.

Type
Research Article
Information
Journal of Plasma Physics , Volume 31 , Issue 1 , February 1984 , pp. 67 - 79
Copyright
Copyright © Cambridge University Press 1984

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

REFERENCES

Abramowitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions. Dover.Google Scholar
Berry, M. V. 1978 AIP Conference Proceedings, No. 46, La Jolla, p. 16.Google Scholar
Bingham, R. & Lashmore-Davies, C. N. 1979 J. Plasma Phys. 21, 51.CrossRefGoogle Scholar
Dendy, R. O. & Ter Haar, D. 1983 Phys. Lett. 97A, 129.CrossRefGoogle Scholar
Gibbons, J., Thornhill, S. G., Wardrop, M. J. & Ter Haar, D. 1977 J. Plasma Phys. 17, 153.CrossRefGoogle Scholar
Giles, M. J. 1983 J. Plasma Phys. 29, 513.CrossRefGoogle Scholar
Goldman, M. V., Reiter, G. F. & Nicholson, D. R. 1980 Phys. Fluids, 23, 388.CrossRefGoogle Scholar
Kono, M., ŠKorić, M. M. & Ter Haar, D. 1981 J. Plasma Phys. 26, 123.CrossRefGoogle Scholar
Lanczos, C. 1970 Variational Principles of Mechanics. University of Toronto Press.Google Scholar
Lashmore-Davies, C. N. 1975 Nucl. Fusion, 15, 213.CrossRefGoogle Scholar
Nicholson, D. R. 1981 Phys. Fluids, 24, 908.CrossRefGoogle Scholar
Papadopoulos, K., Goldstein, M. L. & Smith, R. A. 1974 Ap. J. 190, 175.Google Scholar
Thomson, J. J. & Karush, J. I. 1974 Phys. Fluids, 17, 1608.CrossRefGoogle Scholar
Thornhill, S. G. & Ter Haar, D. 1978 Phys. Reports, 43, 43.CrossRefGoogle Scholar
Tsytovich, V. N. 1977 Theory of the Turbulent Plasma. Consultants Bureau.CrossRefGoogle Scholar
Weatherall, J. C. 1982 Phys. Fluids, 25, 212.Google Scholar
Weiland, J. & Wilhelmsson, H. 1977 Coherent Nonlinear Interaction of Waves in Plasmas. Pergamon.Google Scholar
Whittaker, E. T. & Watson, G. N. 1946 A Course of Modern Analysis. Cambridge University Press.Google Scholar
Zakharov, V. E. 1972 Soviet Phys. JETP, 35, 908.Google Scholar