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The second-harmonic resonance for nonlinear hydromagnetic waves

Published online by Cambridge University Press:  13 March 2009

Yasuji Matsumoto ,
Nobumasa Sugimoto  and
Yoshinori Inoue
Yasuji Matsumoto
Affiliation:
Faculty of Engineering Science, Osaka University, Toyonaka, Osaka, Japan
Nobumasa Sugimoto
Affiliation:
Faculty of Engineering Science, Osaka University, Toyonaka, Osaka, Japan
Yoshinori Inoue
Affiliation:
Faculty of Engineering Science, Osaka University, Toyonaka, Osaka, Japan
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Abstract

We investigate second-harmonic resonance for weakly nonlinear hydromagnetic waves travelling in a cold collisionless plasma by the method of multiple scales. We find that the second-harmonic resonance can occur between the magneto-acoustic modes; but it can occur neither between the magneto-acoustic and the Alfvé n modes, nor between the Alfvé n modes. The resonant frequency of the magneto-acoustic modes is characterized by the geometric mean of the ion and electron Larmor frequencies. We obtain steady-state solutions to the dynamical equations governing the second-harmonic resonance. The result of analysis shows that the envelopes of the two resonant waves are composed of two periodic wave- trains, two solitary pulses or a solitary pulse and a phase jump. We also extend the problem to more general dispersive wave systems.

Type
Research Article
Information
Journal of Plasma Physics , Volume 14 , Issue 1 , August 1975 , pp. 53 - 64
Copyright
Copyright © Cambridge University Press 1975

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References

REFERENCES

Armstrong, J. A., Bloembergen, N., Ducuing, J. & Pershan, P. S. 1962 Phys. Rev. 127, 1918.CrossRefGoogle Scholar
Davidson, R. C. 1972 Methods in Nonlinear Plasma Theory. Academic.Google Scholar
Franken, P. A., Hill, A. E., Peters, C. W. & Weinreich, G. 1961 Phys. Rev. Letters, 7, 118.CrossRefGoogle Scholar
Inoue, Y. & Matsumoto, Y. 1974 J. Phys. Soc. Japan, 36, 1446.CrossRefGoogle Scholar
Larsson, J. & Stenflo, L. 1973 Beiträ ge aus der Plasma Physik, 13, 169.CrossRefGoogle Scholar
McGoldrick, L. F. 1970 a J. Fluid Mech. 40, 251.CrossRefGoogle Scholar
McGoldrick, L. F. 1970 b J. Fluid Mech. 42, 193.CrossRefGoogle Scholar
Nayfeh, A. H. 1965 Phys. Fluids, 8, 1896.CrossRefGoogle Scholar
Sagdeev, R. Z. & Galeev, A. A. 1969 Nonlinear Plasma Theory. Benjamin.Google Scholar
Simmons, W. F. 1969 Proc. Roy. Soc. A 309, 551.Google Scholar
Stenflo, L. 1973 Planet. Space Sci. 21, 391.CrossRefGoogle Scholar
Tsytovich, V. N. 1970 Nonlinear Effects in Plasma. Plenum.CrossRefGoogle Scholar
Wilton, J. R. 1915 Phil. Mag. 29, 688.CrossRefGoogle Scholar