Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-18T04:42:37.619Z Has data issue: false hasContentIssue false
  • English
  • Français

Theory of weakly nonlinear VLF interactions

Published online by Cambridge University Press:  13 March 2009

N. Murdoch
N. Murdoch*
Affiliation:
Department of Mathematics, University of Exeter, Exeter
Get access Rights & Permissions [Opens in a new window]

Abstract

A mathematical description of the weakly nonlinear regime of the coherent cyclotron resonance instability in the magnetosphere which has hitherto been neglected in the literature has been developed. Using the concept that the fundamental role played by the inhomogeneity of the Earth's magnetic field is to limit the interaction time between the resonance electrons and whistler mode wave, perturbation expansions of the current equations to third order have been obtained. It is then found that the real component of resonance current can qualitatively account for excess growth found in some magnetospheric transmissions while the imaginary component gives a good quantitative estimate of frequency shifts observed in transmissions of the mains harmonics.

Type
Research Article
Information
Journal of Plasma Physics , Volume 30 , Issue 3 , December 1983 , pp. 495 - 510
Copyright
Copyright © Cambridge University Press 1983

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

Al'tshul, L. M. & Karpman, V. I. 1965 Soviet Phys. JETP, 22, 361.Google Scholar
Bell, T. F., Inan, U. S. & Helliwell, R. A. 1981 J. Geophys. Res. 86, 4649.CrossRefGoogle Scholar
Bullough, K., Tatnall, A. R. L. & Denby, M. 1976 Nature, 260, 401.CrossRefGoogle Scholar
Derfler, H. 1967 Phys. Lett. 24A, 763.CrossRefGoogle Scholar
Derfler, H. 1970 Phys. Rev. A 1, 1467.CrossRefGoogle Scholar
Dowden, R. L., Mckay, A. D., Amon, L. E. S., Koons, H. C. & Dazey, M. H. 1978 J. Geophys. Res. 83, 169.CrossRefGoogle Scholar
Gary, S. P. & Feldman, W. C. 1978 Phys. Fluids, 21, 72.CrossRefGoogle Scholar
Gendrin, R. 1975 Space Sci. Rev. 18, 145.CrossRefGoogle Scholar
Helliwell, R. A. 1965 Whistlers and Related Ionospheric Phenomena. Stanford University Press.Google Scholar
Helliwell, R. A. 1974 Space Sci. Rev. 15, 781.CrossRefGoogle Scholar
Helliwell, R. A., Katsutrakis, J. P., Bell, T. F. & Raghuram, R. 1975 J. Geophys. Res. 80, 4249.CrossRefGoogle Scholar
Helliwell, R. A., Carpenter, D. L. & Miller, T. R. 1980 J. Geophys. Res. 85, 3360.CrossRefGoogle Scholar
Ho, H. S. & Liemohn, H. B. 1972 Plasma Phys. 14, 11.CrossRefGoogle Scholar
Houghton, M. J. 1970 Plasma Waves in Space and in the Laboratory, vol. 2, p. 443. Edinburgh University Press.Google Scholar
Inan, U. S., Bell, T. F. & Carpenter, D. L. 1977 J. Geophys. Res. 82, 1177.CrossRefGoogle Scholar
Inan, U. S., Bell, T. F. & Helliwell, R. A. 1978 J. Geophys. Res. 83, 3235.CrossRefGoogle Scholar
Jåuch, J. M. & Rohlich, F. 1955 The Theory of Photons and Electrons. Addison-Wesley.Google Scholar
Liemohn, H. B. 1967 J. Geophys. Res. 72, 39.CrossRefGoogle Scholar
Liemohn, H. B. 1974 Space Sci. Rev. 15, 861.CrossRefGoogle Scholar
Luette, J. P., Park, C. G. & Helliwell, R. A. 1977 Geophys. Res. Lett. 4, 272.CrossRefGoogle Scholar
Luette, J. P., Park, C. G. & Helliwell, R. A. 1979 J. Geophys. Res. 84, 2657.CrossRefGoogle Scholar
Matsumoto, H. 1979 A Review of Wave Instabilities in Space Plasmas (ed. Palmedesso, P. J.), p. 163. Reidel.CrossRefGoogle Scholar
Nunn, D. 1974 Planet. Space Sci. 22, 349.CrossRefGoogle Scholar
Palmedesso, P. & Schmidt, G. 1971 Phys. Fluids, 14, 1411.CrossRefGoogle Scholar
Park, C. G. & Helliwell, R. A. 1980 Science, 207, 715.CrossRefGoogle Scholar
Park, C. G. & Miller, T. R. 1979 J. Geophys. Res. 84, 943.CrossRefGoogle Scholar
Stiles, G. S. & Helliwell, R. A. 1977 J. Geophys. Res. 82, 523.CrossRefGoogle Scholar
Stiles, G. S. & Helliwell, R. A. 1975 J. Geophys. Res. 80, 608.CrossRefGoogle Scholar
Stix, T. H. 1962 The Theory of Plasma Waves. McGraw-Hill.Google Scholar
Sturrock, P. A. 1959 Phys. Rev. 112, 1488.CrossRefGoogle Scholar
Vomvordis, J. L., Crystal, T. L. & Penavit, J. 1982 J. Geophys. Res. 87, 1473.CrossRefGoogle Scholar