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Conductivity tensors of all orders in a collisionless plasma

Published online by Cambridge University Press:  13 March 2009

J. Larsson
J. Larsson
Affiliation:
Department of Plasma Physics, Umeå University, S-901 87 Umså, Sweden
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Abstract

Expressions for the conductivity tensors of all orders are obtained, for both relativistic and unrelativistic magnetized Vlasov–Maxwell plasmas, closely related to the well-known formula for the linear conductivity tensor. Thus the unperturbed orbit integrations and the ø-integration in velocity space have been performed and each conductivity tensor is expressed as an infinite series with terms involving ordinary Bessel functions. Jα(K⊥V⊥/ωc) and denominators of type ω–KzVz–αωc for integers.α a. The symmetries related to the Manley-Rowe relations are explicitly seen in the formulae presented. These conductivity tensor formulae provide a much better starting point than the basic equations for many nonlinear investigations.

Type
Research Article
Information
Journal of Plasma Physics , Volume 21 , Issue 3 , June 1979 , pp. 519 - 536
Copyright
Copyright © Cambridge University Press 1979

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References

REFERENCES

Akhiezer, A. I., Akhiezer, I. A., Polovin, R. V., Sitenko, A. G.& Stepanov, K. N. 1975 Plasma Electrodynamics, vol. 2: Non-Linear Theory and Fluctuations (transl. terHaar, D.). Pergamon.Google Scholar
Bulgakov, A. A., Khankina, S. I.& Yakovenko, V. M. 1971 Soviet Phys. Solid State, 12, 1503.Google Scholar
Dougherty, J. P. 1970 J. Plasma Phys. 4, 761.CrossRefGoogle Scholar
Galloway, J. J.& Kim, H. 1971 J. Plasma Phys. 6, 53.CrossRefGoogle Scholar
Giles, M. J. 1974 Plasma Phys. 16, 99.CrossRefGoogle Scholar
Ichimaru, S. 1973 Basic Principles of Plasma Physics. Benjamin.Google Scholar
Johnston, S.& Kaufman, A. N. 1977 Plasma Physics (ed. Wilhelmsson, H.). Plenum.Google Scholar
Johnston, S.& Kaufman, A. N. 1978 Phys. Rev. Lett. 40, 1266.CrossRefGoogle Scholar
Larsson, J. 1975 J. Plasma Phys. 14, 467.CrossRefGoogle Scholar
Larsson, J. 1979 a J. Math. Phys. (To be published.)Google Scholar
Larsson, J. 1979 b J. Math. Phys. (To be published.)Google Scholar
Larsson, J.& Stenflo, L. 1973 Beitr. Plasmaphysik, 13, 169.CrossRefGoogle Scholar
Larsson, J.& Stenflo, L. 1974 Beitr. Plasmaphysik, 14, 7.CrossRefGoogle Scholar
Larsson, J.& Stenflo, L. 1976 Beitr. Plasmaphysik, 16, 79.CrossRefGoogle Scholar
Pustovalov, V. V.& Silin, V. P. 1975 Theory of Plasmas (transl. Barbour, J. B., ed. Skobel'tsyn, D. V.). Consultants Bureau.Google Scholar
Stenflo, L. 1973 Planet. Space Sci. 21, 391.CrossRefGoogle Scholar
Sturrock, P. A. 1958 Ann. Phys. 4, 306.CrossRefGoogle Scholar
Tsytovich, V. N. 1977 Theory of Turbulent Plasma (transl. Burdiek, D. L.). Consultants Bureau.CrossRefGoogle Scholar
Tsytovich, V. N.& Stenflo, L. 1974 Physica Scripta, 10, 194.CrossRefGoogle Scholar
Watson, D. C.& Bers, A. 1975 Quarterly Progress Report No. 115, M.I.T., p. 172.Google Scholar
Weibel, E. S. 1974 Plasma Phys. 16, 921.CrossRefGoogle Scholar