Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-26T01:53:06.626Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

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

Adlam, J. H. & Allen, J. E. 1958 Phil. Mag. 3, 448.CrossRefGoogle Scholar
Cordey, J. G. & Saffman, P. G. 1967 J. Plasma Phys. 1, 129.CrossRefGoogle Scholar
Davis, L., Lüst, R. & Schlüter, A. 1958 Z. Naturforsch. A13, 916.CrossRefGoogle Scholar
Friedman, H. W., Linson, L. M., Patrick, R. M. & Petschek, H. E. 1971 Annual Review of Fluid Mechanics, vol. 3 (ed. Van Dyke, M. and Vincenti, W. G.). Annual Reviews.Google Scholar
Inoue, Y. 1969 J. Phys. Soc. Japan, 26, 521.CrossRefGoogle Scholar
Inoue, Y. 1971 J. Plasma Phys. 6, 513.CrossRefGoogle Scholar
Kakutani, T. 1966 J. Phys. Soc. Japan, 21, 385.CrossRefGoogle Scholar
Kakutani, T. 1968 J. Phys. Soc. Japan, 24, 660.CrossRefGoogle Scholar
Kellogg, P. J. 1964 Phys. Fluids 7, 1555.CrossRefGoogle Scholar
Montgomery, D. 1959 Phys. Fluids, 2, 585.CrossRefGoogle Scholar
Saffman, P. G. 1961 a J. Fluid Mech. 11, 16.CrossRefGoogle Scholar
Saffman, P. G. 1961 b J. Fluid Mech. 11, 552.CrossRefGoogle Scholar
Saito, T. 1951 Math. Soc. Japan, 3, 279.CrossRefGoogle Scholar
Siegel, C. F. 1945 Ann. Math. 46, 423.CrossRefGoogle Scholar
Tidman, D. A. & Krall, N. A. 1971 Shock Waves in Collisionless Plasmas. Interscience.Google Scholar