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On the stability of nonlinear cold plasma waves. Part 2

Published online by Cambridge University Press:  13 March 2009

E. Infeld  and
G. Rowlands
E. Infeld
Affiliation:
Institute of Nuclear Research, Hoza 69, Warsaw
G. Rowlands
Affiliation:
Department of Physics, University of Warwick
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Abstract

In part 1 (Infeld 1972), it was shown that a nonlinear stationary wave in a cold plasma is marginally stable to all perturbations that are functions of the spatial direction parallel to the direction of propagation only. The stability analysis is extended here in part 2 to include general spatial variations. Within the limitations of the treatment, it is found that, for wave amplitudes up to maximal value (onset of trapping), the wave is marginally stable. Hence one would expect these large-amplitude cold plasma waves to exist in practice.

The one-dimensional analysis of part 1 is also extended to include waves with relativistic velocities, and such waves are again found to be marginally stable.

Type
Research Article
Information
Journal of Plasma Physics , Volume 10 , Issue 2 , October 1973 , pp. 293 - 300
Copyright
Copyright © Cambridge University Press 1973

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References

REFERENCES

Infeld, E. 1972 J. Plasma Phys. 8, 105.CrossRefGoogle Scholar
Mclachlan, N. W. 1947 Theory and application of Mathieu Functions. Oxford University Press.Google Scholar
Rowlands, G. 1969 J. Plasma Phys. 3, 567.Google Scholar