Hostname: page-component-7bb8b95d7b-lvwk9 Total loading time: 0 Render date: 2024-09-21T15:52:35.622Z Has data issue: false hasContentIssue false
  • English
  • Français

Analytical solutions for oblique wave growth from a ring-beam distribution

Published online by Cambridge University Press:  13 March 2009

Richard M. Thorne  and
Danny Summers
Richard M. Thorne
Affiliation:
Department of Atmospheric Sciences, University of California, Los Angeles, California 90024, U.S.A.
Danny Summers
Affiliation:
Department of Atmospheric Sciences, University of California, Los Angeles, California 90024, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Extract

Analytical solutions are presented for the linear growth rate of oblique plasma waves in a magnetized plasma due to resonant interactions with a model ringbeam distribution. Explicit closed-form solutions for the angular dependence are obtained in terms of modified Bessel functions of the first kind. In the limits of either quasi-longitudinal or quasi-transverse propagation the analytical solutions take the form of simple algebraic expansions, which allow an immediate comparison of the relative contributions from different harmonic resonances, and which also determine the conditions for marginal stability for any specific resonance. The results can be applied, for instance, to the growth of waves following ionization of neutrals originating from cometary, planetary, or interstellar material in the solar wind. In a weakly unstable plasma the analytical results also provide an important check on the complex numerical codes that hitherto constituted the only method available for evaluating the growth of oblique plasma waves.

Type
Research Article
Information
Journal of Plasma Physics , Volume 39 , Issue 3 , June 1988 , pp. 485 - 502
Copyright
Copyright © Cambridge University Press 1988

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

Brinca, A. L. & Tsurutani, B. T. 1987 Geophys. Res. Lett. 14, 495.CrossRefGoogle Scholar
Dory, R. A., Guest, G. E. & Harris, E. G. 1965 Phys. Rev. Lett. 14, 131.CrossRefGoogle Scholar
Fried, B. D. & Conte, S. D. 1961 The Plasma Dispersion function. Academic.Google Scholar
Gary, S. P., Smith, C. W., Lee, M. A., Goldstein, M. L. & Forslund, D. W. 1984 Phys. Fluids, 27, 1852.Google Scholar
Goldstein, M. L. & Wong, H. K. 1987 J. Geophys. Res. 92, 4695.Google Scholar
Kennel, C. F. & Petschek, H. E. 1966 J. Geophys. Res. 71, 1.CrossRefGoogle Scholar
Kennel, C. F. & Wong, H. V. 1967 J. Plasma Phys. 1, 75.Google Scholar
Rand, R. H. 1984 Computer Algebra in Applied Mathematics: An Introduction to MACSYMA. Research Notes in Mathematics No. 94. Pitman.Google Scholar
Rönmark, K. 1982 Kiruna Geophysical Institute Report No. 179.Google Scholar
Sazhin, D. S. 1986 Annales Geophysicae, 4, 155.Google Scholar
Sharma, O. P. & Patel, V. L. 1986 J. Geophys. Res. 91, 1529.CrossRefGoogle Scholar
Summers, D. & Thorne, R. M. 1987 Phys. Fluids. 30, 3761Google Scholar
Thorne, R. M. & Summers, D. 1986 Phys. Fluids, 29, 4091.CrossRefGoogle Scholar
Thorne, R. M. & Summers, D. 1987 Annales Geophysicae. (In press.)Google Scholar
Thorne, R. M. & Tsurutani, B. T. 1987 Planet. Space Sci. 35, 1501.Google Scholar
Tsurutani, B. T., Thorne, R. M., Smith, E. J., Gosling, J. T. & Matsumoto, H. 1987 J. Geophys. Res. (In press.)Google Scholar
Watson, G. N. 1966 Theory of Bessel Functions, p. 395, equation (1). Cambridge University Press.Google Scholar
Winske, D., Wu, C. S., Li, Y. Y., Mou, Z. Z. & Guo, S. Y. 1985 J. Geophys. Res. 90, 2713.Google Scholar
Wu, C. S. & Davidson, R. C. 1972 J. Geophys. Res. 77, 5399.Google Scholar
Wu, C. S. & Hartle, R. E. 1974 J. Geophys. Res. 79, 283.CrossRefGoogle Scholar