Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-23T07:47:19.681Z Has data issue: false hasContentIssue false
  • English
  • Français

Electrostatic waves in periodic inhomogeneous plasma

Published online by Cambridge University Press:  13 March 2009

P. Bertrand ,
M. R. Feix  and
G. Baumann
P. Bertrand
Affiliation:
Groupe Physique Théorique et Plasma, Universite de Nancy
M. R. Feix
Affiliation:
Groupe Physique Théorique et Plasma, Universite de Nancy
G. Baumann
Affiliation:
Groupe Physique Théorique et Plasma, Universite de Nancy
Get access Rights & Permissions [Opens in a new window]

Abstract

In periodic, inhomogeneous plasma, the dispertion relation w(k) can begeneralized to a relation w(k, K), where K is the wave-number of the periodic steady state. Two models are studied: the ‘water-bag’ model and the ‘two-stream’ model. The solution for these models is obtained easily by the introduction of a Lagrangian formulation. Results are presented. It is shown that, in the water-bag case, the appearance of narrow bands of allowed frequencies practically discretizes the lower part of the spectrum. In the two-stream case, while the long wavelengths have a smaller growth rate, an increased instability is found for k/K = ½

Type
Research Article
Information
Journal of Plasma Physics , Volume 6 , Issue 2 , October 1971 , pp. 351 - 366
Copyright
Copyright © Cambridge University Press 1971

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

Bernstein, I., Greene, J. & Kruskal, M. 1957 Phys. Rev. 108, 546.CrossRefGoogle Scholar
Bertrand, P. & Feix, M. R. 1970 Journal de Physique, 31, 451.CrossRefGoogle Scholar
Bertrand, P., Feix, M. R. & Baumann, G. 1970 Comptes Rendus Acad. Sciences, 270, 1153.Google Scholar
Berteand, P., Baumann, G. & Feix, M. R. 1970 Proc. 4th European Conf. on Controlled Fusion and Plasma Phys., Rome, p. 140.Google Scholar
Bloomberg, H., Bertrand, P., Doremus, J. P. & Feix, M. R. 1970 A.P.S. Bulletin, 15, 1430.Google Scholar
Brillouin, L. & Parodi, M. 1956 Propagation des ondes dans les milieux périodiques. Masson et Cie.Google Scholar
De Packh, D. C. 1962 J. Electronics and Control, 13, 417.CrossRefGoogle Scholar
Engelmann, F., Feix, M. R. & Minardi, E. 1963 Il Nuovo Cimento, 30, 820.CrossRefGoogle Scholar
Hohl, F. 1969 Phys. Fluids, 12, 230.CrossRefGoogle Scholar
Jackson, E. A. & Raether, M. 1966 Phys. Fluids, 9, 1257.CrossRefGoogle Scholar
Kalman, G. & Feix, M. R. 1969 Non-linear Effects in Plasma. Gordon and Broach.Google Scholar
Knorr, G. 1968 Phys. Fluids, 11, 885.CrossRefGoogle Scholar
Pierce, J. R. 1950 Travelling Waves in Tubes. Van Nostrand.Google Scholar
Roberts, K. V. & Berk, H. L. 1967 Symp. on Computer Simulation of Plasma and the Many-Body Problem. NASA SP153.Google Scholar
Rowlands, G. 1969 J. Plasma Phys. 3, 567.CrossRefGoogle Scholar
Staton, L. D. 1968 Ph.D. Thesis, Virginia Polytechnic Institute.Google Scholar
Whittaker, E. T. & Watson, G. N. 1965 Modern Analysis. Cambridge University Press.Google Scholar