Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-26T04:51:13.781Z Has data issue: false hasContentIssue false
  • English
  • Français

Dispersion of electron Bernstein waves including weakly relativistic and electromagnetic effects. Part 2. Extraordinary 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
Get access Rights & Permissions [Opens in a new window]

Abstract

Extraordinary solutions of the weakly relativistic, electromagnetic dispersion relation are investigated for waves propagating perpendicular to a uniform magnetic field in a Maxwellian plasma. As in a companion paper, which treated ordinary modes, weakly relativistic effects are found to modify dramatically the dispersion predicted by strictly non-relativistic ‘classical’ theory in the neighbourhood of harmonics of the cyclotron frequency Ωe. The infinite families of classical Gross–Bernstein and Dnestrovskii–Kostomarov modes are truncated to include only harmonics s satisfying s ≲ (ω2p mc2/4kB TΩ2e)⅓ and s ≲(ωp/Ωe)⅔/8 respectively where ωp is the plasma frequency and T the temperature. All classical cut-offs and resonances are removed apart from the x– and z– mode cut-offs. The only coupling between large- and small-wave-vector modes is between the z mode and a Gross–Bernstein mode near the upper-hybrid frequency and between the x mode and the second Gross–Bernstein mode near 2Ωe. Dispersion of the weakly relativistic counterpart of the x mode departs only slightly from that predicted by cold plasma theory except near Ωe and 2Ωe.

Type
Research Article
Information
Journal of Plasma Physics , Volume 37 , Issue 3 , June 1987 , pp. 449 - 465
Copyright
Copyright © Cambridge University Press 1987

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

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., 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
Bornatici, M., Ruffina, U. & Westerhof, E. 1985 Fifth International Workshop on ECE and ECH, San Diego, p. 88.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
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. 00, 000.Google Scholar
Shkarofsky, I. P. 1966 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
Wu, C. S., Lin, C. S., Wong, H. K., Tsai, S. T. & Zhou, R. L. 1981 Phys. Fluids, 24, 2191.CrossRefGoogle Scholar