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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

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