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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
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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

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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