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Nonlinear interaction between two electrostatic harmonics in a plasma

Published online by Cambridge University Press:  13 March 2009

Frank Verheest  and
G. J. Lewak
Frank Verheest
Affiliation:
Theoretische Mechanika, Rijksuniversiteit Gent, B-9000 Gent, Belgium
G. J. Lewak
Affiliation:
Department of Applied Physics and Information Science, University of California, San Diego, La Jolla, California 92037
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Abstract

The problem of harmonic and subharmonic generation of electrostatic waves in a general collisionless plasma, or in some other electromagnetic medium, is treated anew, using coupled-mode theory based on two time scales. A novel feature is that one of the two interacting waves may be a negative energy wave. Furthermore, the model describing the medium need not be specified, only a general linear and nonlinear conductivity or an equivalent description is required. Just by invoking wave energy conservation, the coupled-mode equations are obtained in such a way that unequivocal conclusions can be drawn.

When both waves have positive energy, they exchange part of it in a periodic fashion, provided they both have some energy initially. If initially all the energy is in the fundamental, then all of it will eventually end up (irreversibly) in thesecond harmonic. If, on the other hand, all the energy is in the harmonic initially, then no generation of the fundamental (or subharmonic) will take place. If one of the two waves is a negative-energy wave, however, an explosive instability develops, and this regardless of initial values. For comparable conditions, the instability time depends on whether the negative energy wave is in the fundamental or in the upper harmonic.

Type
Research Article
Information
Journal of Plasma Physics , Volume 15 , Issue 1 , February 1976 , pp. 91 - 103
Copyright
Copyright © Cambridge University Press 1976

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References

REFERENCES

Aamodt, R. E., & Sloan, M. L. 1968 Phys. Fluids, 11, 2218.CrossRefGoogle Scholar
Bedeaux, D., & Bloembergen, N. 1973 Physica, 69, 57.CrossRefGoogle Scholar
Bekefi, G. 1966 Radiation Processes in Plasmas. Wiley.Google Scholar
Bloembergen, N. 1965 Nonlinear Optics. Benjamin.Google Scholar
Coppi, B., Rosenbluth, M. N., & Sudan, R. N. 1969 Ann. Phys. 55, 207.CrossRefGoogle Scholar
Davidson, R. C. 1969 Phys. Fluids, 12, 149.CrossRefGoogle Scholar
Dikasov, V. M., Rudakov, L. I., & Ryutov, D. D. 1965 Soviet Phys. JETP, 21, 608.Google Scholar
Erdélyi, A., Magnus, W., Oberhettinger, F., & Tricomi, F. O. ed. 1953 Higher Transcendental Functions, vol. 2. McGraw-Hill.Google Scholar
Giles, M. J. 1974 Plasma Phys. 16, 99.CrossRefGoogle Scholar
Golden, K. I. 1973 Letters Nuovo Cim. 7, 676.CrossRefGoogle Scholar
Hamasaki, S., & Krall, N. A. 1971 Phys. Fluids, 14, 1441.CrossRefGoogle Scholar
Lewak, G. J. 1971 J. Plasma Phys. 5, 51.CrossRefGoogle Scholar
Melrose, D. B. 1972 Plasma Physics, 14, 1035.CrossRefGoogle Scholar
Pars, L. A. 1965 A Treatise on Analytical Dynamics. Heinemann.Google Scholar
Stix, T. H. 1962 The Theory of Plasma Waves. McGraw-Hill.Google Scholar
Whittaker, G. T., & Watson, G. N. 1962 A Course of Modern Analysis. Cambridge University Press.Google Scholar