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Stability of relativistic transverse cold plasma waves. Part 2. Linearly polarized waves

Published online by Cambridge University Press:  13 March 2009

F. J. Romeiras
F. J. Romeiras
Affiliation:
Centro do Electrodinâmica, Instituto Superior Técnico, Lisboa-1, Portugal
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Abstract

This is part 2 of a paper concerned with the stability against small perturbations of a certain class of nonlinear wave solutions of the equations that describe a cold unmagnetized plasma. It refers to transverse linearly polarized waves in an electron-positron plasma. A numerical method, based on Floquet's theory of linear differential equations with periodic coefficients, is used to solve the perturbation equations and obtain the instability growth rates. All the three possible types of perturbations are discussed for a typical value of the (large) amplitude of the nonlinear wave: electrically longitudinal slightly unstable modes (with maximum growth rate γ approximately equal to 0·07ω0, where ω0 is the frequency of the nonlinear wave); purely transverse moderately unstable modes (with γ ≃ 0·26ω0); and highly unstable electrically transverse modes (with γ ≃ l·5ω0).

Type
Research Article
Information
Journal of Plasma Physics , Volume 22 , Issue 2 , October 1979 , pp. 201 - 222
Copyright
Copyright © Cambridge University Press 1979

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References

REFERENCES

Clemmow, P. C. 1974 J. Plasma Phys. 12, 297.Google Scholar
Coddington, E. A. & Levinson, N. 1955 Theory of Ordinary Differential Equations. McGraw-Hill.Google Scholar
Eastham, M. S. P. 1973 The Spectral Theory of Periodic Differential Equations. Scottish Academic Press.Google Scholar
Hale, J. K. 1969 Ordinary Differential Equations. Wiley.Google Scholar
Kennel, C. F. & Pellat, R. 1976 J. Plasma Phys. 15, 335.CrossRefGoogle Scholar
Krein, M. G. 1955 Am. Math. Soc. Translations (2) 1, 163.Google Scholar
Magnus, W. & Winkler, S. 1966 Hill's Equation. Wiley.Google Scholar
McLachlan, N. W. 1964 Theory and Application of Mathieu Functions. Dover.Google Scholar
Romeiras, F. J. 1977 Ph.D Thesis, University of Cambridge.Google Scholar
Romeiras, F. J. 1978 J. Plasma Phys. 20, 479.Google Scholar
Starzinskii, V. M. 1955 Am. Math. Soc. Translations (2) 1, 189.CrossRefGoogle Scholar
Sweeney, G. S. S. & Stewart, P. 1975 Astron. & Astrophys. 41, 431.Google Scholar