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On the stability of self-consistent large-amplitude waves in a cold plasma. Part 2. Longitudinal waves in the absence of large-scale magnetic field

Published online by Cambridge University Press:  13 March 2009

M. A. Lee
Affiliation:
McDonnell Center for the Space Sciences and Department of Physics, Washington University, St Louis, Missouri 63130
I. Lerche
Affiliation:
Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago, II. 60637

Abstract

We demonstrate that self-consistent large-amplitude longitudinal waves in a cold plasma are unstable to at least transverse perturbations, with an instability growth rate which is roughly of the order of the plasma frequency of the system. The instability statements derived here are conservative, since modes not discussed may be more unstable.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1979

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References

REFERENCES

Clemmow, P. C. 1974 J. Plasma Phys. 12, 297.CrossRefGoogle Scholar
Feenberg, E. 1948 Phys. Rev. 74, 206.CrossRefGoogle Scholar
Hochstadt, H. 1975 Differential Equations – A Modern Approach. Dover.Google Scholar
Ince, E. L. 1956 Ordinary Differential Equations. Dover.Google Scholar
Lee, M. A. & Lerche, I. 1978 J. Plasma Phys. 20, 313.CrossRefGoogle Scholar
Liapounov, M. A. 1896 Comptes Rend. 123, 1248.Google Scholar
Liapounov, M. A. 1899a Comptes Rend. 128, 910.Google Scholar
Liapounov, M. A. 1899b Comptes Rend. 128, 1085.Google Scholar
Morse, P. M. & Feshbach, H. 1953 Methods of Theoretical Physics. McGraw-Hill.Google Scholar
Titchmarsh, E. C. 1962 Eigenfunction Expansions. Oxford University Press.Google Scholar