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The Green' function forwaves in a homogeneous anisotropic absorbing plasma

Published online by Cambridge University Press:  13 March 2009

J. A. Bennett
J. A. Bennett
Affiliation:
Institute for Theoretical Physics, The University of Düsseldorf
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Abstract

The Green's function (or matrix) for a source of sinusoidal time dependence in an infinite homogeneous absorbing magneto-ionic plasma is written as a Fourier integral over wavenumber space. It is shown that this Fourier integral solution exists, and is unique as a generalized function. By extending the Fourier integral to complex wavenumbers, it is shown that the far-field expression for the Green's function may be written as an integral over sections of the dispersion surface, which in this case is a complex sub-manifold of the space of three complex variables. Use of the saddle-point method in two dimensions allows a further simplification of the far-field result. The matrix coefficients in the resulting expression are shown to represent a decomposition into modes. Corresponding results are also obtained for sources with spatial dependence, described by either functions of compact support or rapidly decreasing functions.

Type
Research Article
Information
Journal of Plasma Physics , Volume 15 , Issue 1 , February 1976 , pp. 133 - 150
Copyright
Copyright © Cambridge University Press 1976

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References

REFERENCES

Arbel, E., & Felsen, L. B. 1963 Electromagnetic Theory and Antennas (ed. Jordan, E. C.), p. 391. Pergamon.Google Scholar
Bennett, J. A. 1974 Proc. IEEE, 62, 1577.CrossRefGoogle Scholar
Bennett, J. A. 1976 J. Plasma Phys. 15, 151.CrossRefGoogle Scholar
Brandstatter, J. J., & Schoenberg, M. 1973 Department of Environmental Sciences, Tel-Aviv University, ES–73–010.Google Scholar
Budden, K. G. 1961 Radio Waves in the Ionosphere. Cambridge University Press.Google Scholar
Budden, K. G. 1964 Lectures on Magnetoionic Theory. Blackie.Google Scholar
Budden, K. G., & Jull, G. W. 1964 Can. J. Phys. 42, 113.CrossRefGoogle Scholar
Budden, K. G., & Daniell, G. J. 1965 J. atmos. terr. Phys. 27, 395.CrossRefGoogle Scholar
Budden, K. G., & Terry, P. D. 1971 Proc. Roy. Soc. A 321, 275.Google Scholar
Bunkin, F. V. 1957 J. Exp. Theor. Phys. (USSR) 32, 338.Google Scholar
Clemmow, P. C. 1963 Electromagnetic Theory and Antennas (ed. Jordan, E. C.), p. 461. Pergamon.Google Scholar
Copson, E. T. 1965 Asymptotic Expansions. Cambridge University Press.CrossRefGoogle Scholar
Connor, K. A., & Felsen, L. B. 1974 Proc. IEEE, 62, 1586.CrossRefGoogle Scholar
Gunning, R. C., & Rossi, H. 1965 Analytic Functions of Several Complex Variables. Prentice-Hall.Google Scholar
Hörmander, L. 1964 Linear Differential Operators. Springer.CrossRefGoogle Scholar
Jones, R. M. 1970 Radio Sci. 5, 793.CrossRefGoogle Scholar
Kogelnik, H., & Motz, H. 1963 Electromagnetic Theory and Antennas (ed. Jordan, E. C.), p. 477. Pergamon.Google Scholar
Lancaster, P. 1969 Theory of Matrices. Academic.Google Scholar
Lewis, R. M. 1964 Asymptotic Solutions of Differential Equations (ed. Wilcox, C. H.), p. 53. Wiley.Google Scholar
Lewis, R. M. 1965 Arch. Rat. Mech. Anal. 20, 191.CrossRefGoogle Scholar
Lewis, R. M., & Granoff, B. 1970 Alta Frequenza, 38, 51.Google Scholar
Lighthill, M. J. 1960 Phil. Trans. A 252, 397.Google Scholar
Lighthill, M. J. 1962 Fourier Analysis and Generalized Functions. Cambridge University Press.Google Scholar
McConnell, A. J. 1957 Applications of Tensor Calculus. Dover.Google Scholar
Mittra, R., & Deschamps, G. A. 1963 Electromagnetic Theory and Antennas (ed. Jordan, E. C.), p. 495. Pergamon.Google Scholar
Sen, H. K., & Wyller, A. A. 1960 J. Geophys. Res. 65, 3931.CrossRefGoogle Scholar
Sommerfeld, A. 1909 Ann. Phys. 28, 665.CrossRefGoogle Scholar
Suchy, K. 1972a J. Plasma Phys. 8, 33.CrossRefGoogle Scholar
Suchy, K. 1972b J. Plasma Phys. 8, 53.CrossRefGoogle Scholar
Suchy, K. 1974 Proc. IEEE 62, 1571.CrossRefGoogle Scholar
Weyl, H. 1919 Ann. Phys. 60, 481.CrossRefGoogle Scholar
Wilcox, C. H. 1967 Arch. Rat. Mech. 25, 201.CrossRefGoogle Scholar
Wilcox, C. H. 1970 Arch. Rat. Mech. 37, 323.CrossRefGoogle Scholar