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Slowly varying nonlinear waves in a cold plasma stream

Published online by Cambridge University Press:  13 March 2009

R. J. Gribben  and
E. J. Parkes
R. J. Gribben
Affiliation:
Department of Mathematics, University of Strathelyde, Glasgow
E. J. Parkes
Affiliation:
Department of Mathematics, University of Strathelyde, Glasgow
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Abstract

This paper is concerned with the propagation of one-dimensional nonlinear waves in the relatively simple physical situation of a cold, collisionless, field-free, slightly non-uniform plasma comprising a stream of oscillating electrons and a stream of ions whose oscillatory motion is neglected. The waves are considered as a small perturbation from the corresponding uniform periodic solution. The equations which govern the slow variation of certain gross quantities associated with the waves are obtained by applying the ‘two-timing’ technique to the basic plasma equations. The properties of the resulting modulation equations are discussed and an exact solution of an initial value problem for them is given.

Type
Research Article
Information
Journal of Plasma Physics , Volume 18 , Issue 3 , December 1977 , pp. 495 - 508
Copyright
Copyright © Cambridge University Press 1977

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References

REFERENCES

Butler, D. S. & Gribben, R. J. 1968 J. Plasma Phys. 2, 257.CrossRefGoogle Scholar
Infeld, E. 1972 J. Plasma Phys. 8, 105.CrossRefGoogle Scholar
Kakutani, T. & Sugimoto, N. 1974 Phys. Fluids, 17, 1617.CrossRefGoogle Scholar
Kalman, G. 1960 Ann. Phys. (N.Y.) 10, 29.CrossRefGoogle Scholar
Luke, J. C. 1966 Proc. Roy. Soc. A292, 403.Google Scholar
Mjølhus, E. 1976 J. Plasma Phys. 16, 321.CrossRefGoogle Scholar
Montgomery, D. & Tidman, D. A. 1964 Phys. Fluids, 7, 242.CrossRefGoogle Scholar
Rowlands, G. 1969 J. Plasma Phys. 3, 567.CrossRefGoogle Scholar
Seshadri, S. R. 1976 Can. J. Phys. 54, 39.CrossRefGoogle Scholar
Tam, C. K. W. 1970 J. Plasma Phys. 4, 109.CrossRefGoogle Scholar
Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley-Interscience.Google Scholar