Hostname: page-component-8448b6f56d-sxzjt Total loading time: 0 Render date: 2024-04-18T01:07:58.747Z Has data issue: false hasContentIssue false
  • English
  • Français

On the modulational instability of hydromagnetic waves parallel to the magnetic field

Published online by Cambridge University Press:  13 March 2009

Einar Mjølhus
Einar Mjølhus
Affiliation:
The Auroral Observatory, University of Tromsø, Norway
Get access Rights & Permissions [Opens in a new window]

Abstract

The stability of circularly polarized waves of finite amplitude propagating parallel to the magnetic field is studied. A set of equations for slowly varying waves of arbitrary amplitude is obtained. A discussion of the stability of the waces is based on this set of equations. Earlier results are confirmed; in addition we find that finite amplitude always promotes stability. An amplitude dependent stability condition for long waves, previously obtained by the author, is confirmed.

Type
Research Article
Information
Journal of Plasma Physics , Volume 16 , Issue 3 , December 1976 , pp. 321 - 334
Copyright
Copyright © Cambridge University Press 1976

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

Bretherton, F. P. & Garrett, C. J. R. 1969 Proc. Roy. Soc. A 302, 529.Google Scholar
Ferraro, V. C. A. 1955 Proc. Roy. Soc. A 233, 310.Google Scholar
Furutani, Y. 1975 J. Plasma Phys. 13, 499.CrossRefGoogle Scholar
Gardner, C. S. & Morikawa, G. K. 1960 Report NYO-9082, Courant Institute of Mathematical Sciences.Google Scholar
Hasegawa, A. 1972 Phys. Fluids, 15, 870.CrossRefGoogle Scholar
Kako, M. 1972 J. Phys. Soc. Japan, 33, 1678.CrossRefGoogle Scholar
Kadomtsev, B. B. & Karpman, V. I. 1971 Soviet Physics Uspekhi, 14, 40.CrossRefGoogle Scholar
Karpman, V. I. 1967 JETP Letters, 6, 277.Google Scholar
Lighthill, M. J. 1965 J. Inst. Math. Appl. 1, 269.CrossRefGoogle Scholar
Mizohata, S. 1973 The Theory of Partial Differential Equations, chapter 4. CambridgeUniversity Press.Google Scholar
Mjølhus, E. 1974 Report no. 48, Department of Applied Mathematics, University of Bergen.Google Scholar
Tam, C. K. W. 1970 J. Plasma Phys. 4, 109.CrossRefGoogle Scholar
Taniuti, T. & Washimi, H. 1968 Phys. Rev. Letters, 21, 209.CrossRefGoogle Scholar
Taniuti, T. & Wei, C.-C. 1968 J. Phys. Soc. Japan, 24, 941.CrossRefGoogle Scholar
Whitham, G. B. 1965 J. Fluid Mech. 22, 273.CrossRefGoogle Scholar
Zakharov, V. E. & Shabat, A. B. 1972 Soviet Phys. JETP, 34, 62.Google Scholar