Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-08T04:24:29.494Z Has data issue: false hasContentIssue false

Resonant four-wave mixing of finite-amplitude Alfvén waves

Published online by Cambridge University Press:  13 March 2009

S. Rauf
Affiliation:
Department of Electrical and Computer Engineering, University of Wisconsin, Madison, Wisconsin 53706, U.S.A.
J. A. Tataronis
Affiliation:
Department of Electrical and Computer Engineering, University of Wisconsin, Madison, Wisconsin 53706, U.S.A.

Abstract

Using the derivative nonlinear SchrÖdinger equation, resonant four-wave mixing of finite-amplitude Alfvén waves is explored in this paper. The evolution equations governing the amplitudes of the interacting waves and the conservation relations ale derived from the basic equation. These evolution equations are used to study parametric amplification and oscillation of two small-amplitude Alfvén waves due to two large-amplitude pump (Alfvén) waves. It is also shown that three pump waves can mix together to generate a low-frequency Alfven wave in a dissipative plasma.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Davidson, R. C. 1972 Methods in Nonlinear Plasma Theory. Academic Press, New York.Google Scholar
Domier, C. W. & Luhmann, Jr, , N. C. 1993 Phys. Fluids B5, 2398.CrossRefGoogle Scholar
Galeev, A. A. & Oraevskii, V. N. 1962 Soviet Phys. Dokl. 7, 988.Google Scholar
Goldman, M. V. & Williams, E. A. 1991 Phys. Fluids B3, 751.CrossRefGoogle Scholar
Mio, K., Ogino, T., Minami, K. & Takeda, S. 1976 J. Phys. Soc. Jpn 41, 265.CrossRefGoogle Scholar
Mjθlhus, E. 1976 J. Plasma Phys. 16, 321.Google Scholar
Mjθlhus, E. & Wyller, J. 1986 Physica Scrita 33. 442.CrossRefGoogle Scholar
Nebezahl, I., Ron, A. & Rostoker, N. 1988 Phys. Rev. Lett. 60, 1030.CrossRefGoogle Scholar
Papen, G. C. & Tataronis, J. A. 1989 J. Plasma Phys. 42, 457.Google Scholar
Rauf, S. & Tataronis, J. A. 1994 Bull. Am. Phys. Soc. 39, 1624.Google Scholar
Rauf, S. & Tataronis, J. A. 1995 Phys. Plasmas (to appear).Google Scholar
Sagdeev, R. Z. & Galeev, A. A. 1969 Nonlinear Plasma Theory. Benjamin, New York.Google Scholar
Shen, Y. R. 1984 The Principles of Nonlinear Optics. Wiley, New York.Google Scholar
Sprangler, S. R. & Sheerin, J. P. 1982 J. Plasma Phys. 27, 193.CrossRefGoogle Scholar
Weiland, J. & Wilhelmsson, H. 1977 Coherent Non-Linear Interaction of Waves in Plasmas. Pergamon Press, Oxford.Google Scholar