Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-29T14:15:08.186Z Has data issue: false hasContentIssue false

Criteria for three-wave instabilities in a cold collisionless plasma

Published online by Cambridge University Press:  13 March 2009

A. Hruška
Affiliation:
Division of PhysicsNational Research Council of CanadaOttawa, Canada

Abstract

A new systematic method of analysis of three-wave interactions is proposed, and applied to a description of interactions of waves (0, 1 and 2) in a homogeneous electron plasma, in which Landau damping is insignificant. Transverse, linearly polarized wave 0, which may represent an external (‘ pump’ ) wave, is assumed to be in resonance with longitudinal and transverse waves 1 and 2 already existing in a weakly-turbulent plasma. The rate (d W/ dt)j, at which energy is transferred from wave j to the others, is calculated, assuming that directions of propagation of resonating waves are restricted by conditions of three-wave resonance only. Conditions of the form (dW/dt)j = 0 constitute threshold criteria for amplification of wave j to occur. There is a brief discussion of processes during which the energy of one of the resonating waves remains constant, although energy is transferred between the other two waves. The relation between energy absorbed by the plasma and energy transferred between waves is evaluated.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1975

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

Dobeš, K. 1968 Czech. J. Phys. B 18, 113.CrossRefGoogle Scholar
Drummond, J. E. 1961 Plasma Physics (ed. Drummond, J. E.), p. 21. McGraw-Hill.Google Scholar
Dubois, D. F. & Goldman, M. V. 1967 Phys. Rev. 164, 207.CrossRefGoogle Scholar
Hruška, A. 1966 J. Geophys. Res. 71, 1377.CrossRefGoogle Scholar
Jackson, E. A. 1967 Phys. Rev. 153, 235.CrossRefGoogle Scholar
Nishikawa, K. 1968 J. Phys. Soc. Japan, 24, 1152.CrossRefGoogle Scholar
Stix, T. H. 1962 The Theory of Plasma Waves. McGraw-Hill.Google Scholar