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Ergodic behaviour of nonlinear hydromagnetic waves in a cold collisionless plasma

Published online by Cambridge University Press:  13 March 2009

Youshinori Inoue  and
Noriaki Kimura
Youshinori Inoue
Affiliation:
Faculty of Engineering Science, Osaka University, Toyonaka, Osaka
Noriaki Kimura
Affiliation:
Faculty of Engineering Science, Osaka University, Toyonaka, Osaka
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Abstract

Nonlinear hydromagnetic waves propagating along a magnetic field in a cold collisionless plasma are investigated. A criterion for ergodicity of the waves is obtained using the usual method of analytical dynamics. According to this criterion, it is found that, if a parameter b00 is a rational number, the wave is periodic, and that, if b00 is an irrational number, the wave is ergodic. Therefore, the waves are almost always ergodic, i.e. the trajectory of the wave fills up a region in the phase plane of the magnetic field. On the other hand, periodic solutions can exist only with measure zero.

Type
Research Article
Information
Journal of Plasma Physics , Volume 8 , Issue 1 , August 1972 , pp. 97 - 104
Copyright
Copyright © Cambridge University Press 1972

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