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A dielectric tensor for a uniform magnetoplasma with a generalized Lorentzian distribution

Published online by Cambridge University Press:  13 March 2009

R. L. Mace
R. L. Mace
Affiliation:
Plasma Physics Research Institute, Department of Physics, University of Natal, Durban, South Africa
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Abstract

It is demonstrated that the dielectric tensor for a non-relativistic magnetized plasma whose particle velocity distributions can be modelled by isotropic kappa, or generalized Lorentzian, distributions admits an expression similar to that obtained by Trubnikov for a relativistic plasma. The kappa distribution is a useful distribution for modelling space plasmas containing significant numbers of superthermal particles, i.e. those that have energies in excess of the thermal energy. The dielectric tensor is valid for arbitrary wavevectors, and is shown to reproduce the known limiting case of wave propagation parallel to the magnetic field. Even in this limiting case, the results obtained represent a generalization of previous results to arbitrary real values of the index K, the parameter that shapes the superthermal tail on the distribution. The expression for the dielectric tensor might be useful as a starting point for numerical studies of waves and instabilities in plasmas containing superthermal particles.

Type
Research Article
Information
Journal of Plasma Physics , Volume 55 , Issue 3 , June 1996 , pp. 415 - 429
Copyright
Copyright © Cambridge University Press 1996

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References

REFERENCES

Abraham-Shrauner, B. & Feldman, W. C. 1977 Electromagnetic ion-cyclotron wave growth rates and their variation with velocity distribution function shape. J. Plasma Phys. 17, 123–131.Google Scholar
Abraham-Shrauner, B., Asbridge, J. R., Bame, S. J. & Feldman, W. C. 1979 Proton-driven electromagnetic instabilities in high-speed solar wind streams. J. Geophys. Res. 84, 553–559.Google Scholar
Abramowitz, N. & Stegun, I. A. 1965 Handbook of Mathematical Functions, pp. 557–559. Dover, New York.Google Scholar
Bornatici, M., Cano, R., De Barbieri, O. & Engelmann, F. 1983 Electron cyclotron emission and absorption in fusion plasmas. Nucl. Fusion 23, 1153–1257.Google Scholar
Butkov, E. 1968 Mathematical Physics, p. 397, Addison-Wesley, Reading, MA.Google Scholar
De Barbieri, O. 1980 Synchrotron emission from high-temperature plasmas.Association Euratom — CEA, Grenoble, Report EUR-GEA -FC-1035.Google Scholar
Drury, L. O'C. 1983 An introduction to the theory of diffusive shock acceleration of energetic particles in tenuous plasmas. Rep. Prog. Phys. 46, 973–1026.CrossRefGoogle Scholar
Fried, B. D. & Conte, S. D. 1961 The Plasma Dispersion Function. Academic Press, New York.Google Scholar
Mace, R. L. & Hellberg, M. A. 1995 A dispersion function for plasmas containing superthermal particles. Phys. Plasmas 2, 2098–2109.CrossRefGoogle Scholar
Mace, R. L., Amery, G. & Hellberg, M. A. 1995 Proceedings of 22nd European Physical Society Conference on Controlled Fusion and Plasma Physics, Bournemouth, UK.Google Scholar
Melrose, D. B. 1986 Instabilities in Space and Laboratory Plasmas, pp. 11, 181. Cambridge University Press.CrossRefGoogle Scholar
Meng, Z., Thorne, R. M. & Summers, D. 1992 Ion-acoustic wave instability driven by drifting electrons in a generalized Lorentzian distribution. J. Plasma Phys., 47, 445–464.CrossRefGoogle Scholar
Prudnikov, A. P., Brychkov, Yu. A. & Marichev, O. I. 1986 a Integrals and Series, Vol. 1, p 323 (equation 7), p. 395 (equation 11). Gordon & Breach, New York.Google Scholar
Prudnikov, A. P., Brychkov, Yu. A. & Marichev, O. I. 1986 b Integrals and Series, Vol. 2, p. 349 (equation3). Gordon & Breach, New YorkGoogle Scholar
Robinson, P. A. & Newman, D. L. 1988 Approximation of the dielectric properties of Maxwellian plasmas: dispersion functions and physical constraints. J. Plasma Phys. 40, 553–566.CrossRefGoogle Scholar
Shkarofsky, I. P. 1966 Dielectric tensor in Vlasov plasmas near cyclotron harmonics. Phys. Fluids 9, 561–570.CrossRefGoogle Scholar
Summers, D. & Thorne, R. M. 1991 The modified plasma dispersion function. Phys. Fluids B3, 1835–1847.CrossRefGoogle Scholar
Thorne, R. M. & Summers, D. 1991 Landau damping in space plasmas. Phys. Fluids B3, 2117–2123.Google Scholar
Trubnikov, B. A. 1959 Plasma Physics and the Problem of Thermonuclear Reactions (ed. Leontovich, M. A.), Vol. 3, p. 122. Pergainon Press, New York.Google Scholar
Xue, S., Thorne, R. M. & Summers, D. 1993 Electromagnetic ion-cyclotron instability in space plasmas. J. Geophys. Res. 98, 17475–17484..CrossRefGoogle Scholar