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Dispersion of electron Bernstein waves including weakly relativistic and electromagnetic effects. Part 1. Ordinary modes

Published online by Cambridge University Press:  13 March 2009

P. A. Robinson
P. A. Robinson
Affiliation:
School of Physics, University of Sydney, NSW 2006, Australia
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Abstract

Ordinary solutions of the weakly relativistic, electromagnetic dispersion relation are investigated for waves propagating perpendicular to a uniform magnetic field in a Maxwellian plasma. Weakly relativistic resonance broadening, frequency downshift and damping are found to alter dramatically the dispersion predicted by the corresponding strictly non-relativistic (‘classical’) theory in the neighbourhood of harmonics of the cyclotron frequency Ωe. All classical resonances and cut-offs are removed except the cut-off at the plasma frequency ωp. At frequencies above ωp the infinite family of classically predicted modes is replaced by a single weakly damped mode whose dispersion differs only slightly from that predicted by cold plasma theory. No weakly damped modes exist in the range of harmonics s satisfying (ωp/Ωe)⅔/8 ≲ S < Ωp/Ωe, however, one such mode is located immediately below each harmonic for s ≲ (ωp/Ωe)⅔/8. A companion paper investigates extraordinary solutions of the dispersion relation.

Type
Research Article
Information
Journal of Plasma Physics , Volume 37 , Issue 3 , June 1987 , pp. 435 - 447
Copyright
Copyright © Cambridge University Press 1987

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References

REFERENCES

Abramowitz, M. & Stegun, I. A. 1970 Handbook of Mathematical Functions. Dover.Google Scholar
Airoldi-Crescentini, A., Lazzaro, E. & Orefice, A. 1980 Proceedings of 2nd Joint Grenoble-Varenna Symposium on Heating in Toroidal Plasmas, p. 225.Google Scholar
Batchelor, D. B., Goldfinger, R. C. & Weitzner, H. 1984 Phys. Fluids, 27, 2835.CrossRefGoogle Scholar
Bernstein, I. B. 1958 Phys. Rev. 109, 10.CrossRefGoogle Scholar
Bornatici, M., Cano, R., De Barbieri, O. & Engelmann, F. 1983 Nucl. Fusion, 23, 1153.CrossRefGoogle Scholar
Bornatici, M., Engelmann, F., Maroli, C. & Petrillo, V. 1981 Plasma Phys. 23, 89.CrossRefGoogle Scholar
Bornatici, M., Maroli, C. & Petrillo, V. 1982 Proceedings of 3rd Joint Varenna-Grenoble Symposium on Heating in Toroidal Plasmas, p. 691.Google Scholar
De Barbieri, O. 1980 Euratom-CEA, Grenoble, Report EUR-CEA-FC-1035.Google Scholar
Dnestrovskii, Y. N. & Kostomarov, D. P. 1961 Soviet Phys. JETP, 13, 986.Google Scholar
Dnestrovskii, Y. N. & Kostomarov, D. P. 1962 Soviet Phys. JETP, 14, 1089.Google Scholar
Dnestrovskii, Y. N., Kostomarov, D. P. & Skrydlov, N. V. 1964 Soviet Phys. Tech. Phys. 8, 691.Google Scholar
Gross, E. P. 1951 Phys. Rev. 82, 232.CrossRefGoogle Scholar
Lazzaro, E. & Orefice, A. 1980 Phys. Fluids, 23, 2330.CrossRefGoogle Scholar
Lazzaro, E. & Ramponi, G. 1981 Plasma Phys. 23, 53.CrossRefGoogle Scholar
Lominadze, D. G. 1981 Cyclotron Waves in Plasma. Pergamon.Google Scholar
Maroli, C. & Petrillo, F. 1981 Physica Scripta, 34, 955.CrossRefGoogle Scholar
Melrose, D. B., Rönnmark, K. G. & Hewitt, R. G. 1982 J. Geophys. Res. 87, 5140.CrossRefGoogle Scholar
Pritchett, P. L. 1984 Geophys. Res. Lett. 11, 143.CrossRefGoogle Scholar
Puri, S., Leuterer, F. & Tutter, M. 1973 J. Plasma Phys. 9, 89.CrossRefGoogle Scholar
Puri, S., Leuterer, F. & Tutter, M. 1975 J. Plasma Phys. 14, 169.CrossRefGoogle Scholar
Robinson, P. A. 1986 a J. Math. Phys. 27, 1206.CrossRefGoogle Scholar
Robinson, P. A. 1986 b J. Plasma Phys. 35, 187.CrossRefGoogle Scholar
Robinson, P. A. 1987 J. Plasma Phys. 37, 449.CrossRefGoogle Scholar
Shkarofsky, I. P. 1966 a Phys. Fluids, 9, 561.CrossRefGoogle Scholar
Shkarofsky, I. P. 1966 b Phys. Fluids, 9, 570.CrossRefGoogle Scholar
Tataronis, J. A. & Crawford, F. W. 1970 J. Plasma Phys. 4, 231.CrossRefGoogle Scholar
Winglee, R. M. 1983 Plasma Phys. 25, 217.CrossRefGoogle Scholar
Winglee, R. M. 1985 Astrophys. J. 291, 160.CrossRefGoogle Scholar
Wu, C. S. 1985 Space Sci. Rev. 41, 215.CrossRefGoogle Scholar
Wu, C. S., Lin, C. S., Wong, H. K., Tsai, S. T. & Zhou, R. L. 1981 Phys. Fluids, 24, 2191.CrossRefGoogle Scholar