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Nonlocal electron transport in laser created plasmas

Published online by Cambridge University Press:  09 March 2009

P. Mora  and
J.F. Luciani
P. Mora
Affiliation:
Centre de Physique Théorique (UPR 14 du CNRS), Ecole Polytechnique, 91128 Palaiseau, France
J.F. Luciani
Affiliation:
Centre de Physique Théorique (UPR 14 du CNRS), Ecole Polytechnique, 91128 Palaiseau, France
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Abstract

The classical linear Spitzer-Härm formula has been shown to lead to an overestimation of the electron heat flux in laser-plasma interaction experiments. We briefly review the classical theory of heat transport in a plasma, and give a simplified demonstration of the Spitzer-Härm formula. The electron heat conductivity is calculated for a large value of the ion charge Z. Correction due to a finite value of Z is evaluated with a simplified electron-electron collision operator. We then show that in a steep temperature gradient, the collisional mean free path of the electrons that transport the energy may be larger than the scale length of the temperature gradient. In this case the Spitzer-Härm formula overestimates the actual heat flux in the main part of the temperature gradient, and predicts a too small heat flux slightly away from the location of the large temperature gradient.A nonlocal macroscopic formula, which is a sort of convolution of the Spitzer-Härm heat flux by a delocalization function, is shown to accurately describe the electron heat flow in both smooth and steep temperature gradients. This nonlocal formula for the heat flow is analytically justified. A selection of slightly different delocalization functions proposed in the literature is compared to the original one and to the results of Fokker-Planck calculations of the heat flow.

Type
Research Article
Information
Laser and Particle Beams , Volume 12 , Issue 3 , September 1994 , pp. 387 - 400
Copyright
Copyright © Cambridge University Press 1994

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References

REFERENCES

Alaterre, P. et al. 1985 Phys. Rev. A 32, 324.CrossRefGoogle Scholar
Albritton, J.R. et al. 1986 Phys. Rev. Lett. 57, 1887.CrossRefGoogle Scholar
Bell, A.R. 1983 Phys. Fluids 26, 279.CrossRefGoogle Scholar
Bell, A.R. et al. 1981 Phys. Rev. Lett. 46, 243.CrossRefGoogle Scholar
Bendib, A. & Luciani, J.F. 1987 Phys. Fluids 30, 1353.CrossRefGoogle Scholar
Bendib, A. et al. 1988 Phys. Fluids 31, 711.CrossRefGoogle Scholar
Epperlein, E.M. 1990 Phys. Rev. Lett. 65, 2145.CrossRefGoogle Scholar
Epperlein, E.M. 1991 Phys. Fluids B3, 3082.CrossRefGoogle Scholar
Epperlein, E.M. & Short, R.W. 1991 Phys. Fluids B3, 3092.CrossRefGoogle Scholar
Epperlein, E.M. & Short, R.W. 1992 Phys. Fluids B3, 2211.CrossRefGoogle Scholar
Epperlein, E.M. et al. 1992 Phys. Rev. Lett. 69, 1765.CrossRefGoogle Scholar
Fabbro, R. & Mora, P. 1982 Phys. Lett. A90, 48.CrossRefGoogle Scholar
Fabbro, R. et al. 1982 Phys. Rev. A26, 2289.CrossRefGoogle Scholar
Fabre, E. et al. 1985 Plasma Phys. and Contr. Fus. Res. 1984, Vol. 3, IAEA-CN-44/B-III-4, Vienne.Google Scholar
Forslund, D.W. & Brackbill, J.U. 1982 Phys. Rev. Lett. 48, 1614.CrossRefGoogle Scholar
Goldsack, T.J. et al. 1982 Phys. Fluids 25, 1634.CrossRefGoogle Scholar
Gray, D.R. & Kilkenny, D.J. 1980 Plasma Phys. 22, 81.CrossRefGoogle Scholar
Holstein, P.A. & Decoster, A. 1987 J. Appl. Phys. 62, 3592.CrossRefGoogle Scholar
Holstein, P.A. et al. 1986 J. Appl. Phys. 60, 2296.CrossRefGoogle Scholar
Kho, T.H. & Haines, M.G. 1985 Phys. Rev. Lett. 55, 825.CrossRefGoogle Scholar
Krasheninnikov, S.I. 1993 Phys. Fluids B5, 74.CrossRefGoogle Scholar
Ljepojevic, N.N. & MacNeice, P. 1989 Phys. Rev. A40, 981.CrossRefGoogle Scholar
Luciani, J.F. 1985 Thèse d'Etat, Université Paris VI (unpublished).Google Scholar
Luciani, J.F. & Mora, P. 1986 J. Stat. Phys. 43, 281.CrossRefGoogle Scholar
Luciani, J.F. et al. 1983 Phys. Rev. Lett. 51, 1664.CrossRefGoogle Scholar
Luciani, J.F. et al. 1985a Phys. Fluids 28, 835.CrossRefGoogle Scholar
Luciani, J.F. et al. 1985b Phys. Rev. Lett. 55, 2421.CrossRefGoogle Scholar
Matte, J.P. & Virmont, J. 1982 Phys. Rev. Lett. 49, 1936.CrossRefGoogle Scholar
Matte, J.P. et al. 1984 Phys. Rev. Lett. 53, 1461.CrossRefGoogle Scholar
Matte, J.P. et al. 1987 Phys. Rev. Lett. 58, 2067.CrossRefGoogle Scholar
Mead, W.C. et al. 1981 Phys. Rev. Lett. 47, 1289.CrossRefGoogle Scholar
Minotti, F. & Ferro Fontan, C. 1990 Phys. Fluids B2, 1725.CrossRefGoogle Scholar
Mora, P. & Yahi, H. 1982 Phys. Rev. A26, 2259.CrossRefGoogle Scholar
Prasad, M.K. & Kershaw, D.S. 1989 Phys. Fluids B1, 2430.CrossRefGoogle Scholar
Prasad, M.K. & Kershaw, D.S. 1991 Phys. Fluids B3, 3087.CrossRefGoogle Scholar
Rose, H.A. & DuBois, D.F. 1992 Phys. Fluids B4, 1394.CrossRefGoogle Scholar
Sanmartin, J.R. et al. 1990 Phys. Fluids B2, 2519.CrossRefGoogle Scholar
Schmitt, A.J. 1993 Phys. Fluids B5, 932.CrossRefGoogle Scholar
Short, R.W. & Epperlein, E.M. 1992 Phys. Rev. Lett. 68, 3307.CrossRefGoogle Scholar
Spitzer, L. & Härm, R. 1953 Phys. Rev. 89, 977.CrossRefGoogle Scholar
Wyndham, E.S. et al. 1982 J. Phys. D15, 1683.Google Scholar