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Numerical solution of nonlinear electron kinetic equation in self-similar variables

Published online by Cambridge University Press:  09 June 2011

I. F. POTAPENKO  and
S. I. KRASHENINNIKOV
I. F. POTAPENKO
Affiliation:
Keldysh Institute of Applied Mathematics, RAS, 125047 Moscow, Russian Federation (firena@yandex.ru, irina@keldysh.ru)
S. I. KRASHENINNIKOV
Affiliation:
University of California at San Diego, La Jolla, San Diego, CA 92093, USA
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Abstract

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We present numerical solution of a fully nonlinear electron kinetic equation in self-similar variables, which on the one hand has all features of a ‘standard’ hydrodynamics (ratios of the electron mean free path to the scale length γ ≡ λC/L 1), and on the other hand has no restriction on the smallness of the parameter γ. The self-similar variable approach reduces dimensionality of the space-dependent kinetic equation, thereby providing numerical analysis of the electron heat transport in the velocity space. The electron distribution structure and its super thermal power-law tail are examined.

PACS number(s): 52.25.Dg, 52.65.Ff, 52.50.-b

Type
Papers
Information
Journal of Plasma Physics , Volume 77 , Issue 6 , December 2011 , pp. 803 - 812
Copyright
Copyright © Cambridge University Press 2011

References

[1]Chapman, S. and Cowling, T. 1970 Mathematical Theory of Non-uniform Gases. Cambridge, UK: Cambridge University Press.Google Scholar
[2]Grad, H. 1949 Commun. Pure and Appl. Math. 2, 331.Google Scholar
[3]Cercignani, C. 1975 Theory and Application of the Boltzmann Equation. Edinburgh, UK: Scottish Academic Press.Google Scholar
[4]Braginskii, S. I. 1965 Transport processes in a plasma. In: Review of Plasma Physics, Vol. 1. New York: Consultants Bureau.Google Scholar
[5]Landau, L. D. and Lifshitz, E. M. 2002 Cource of Theoretical Physics, Vol 10: “Physical Kinetics” (ed. Pitaevskii, L. P. and Lifshitz, E. M.). Oxfordshire, UK: Pergamon Press.Google Scholar
[6]Chandrasekhar, S. 1960 Radiative Transfer. New York: Dover.Google Scholar
[7]Spitzer, L. and Harm, R. 1953 Rev. Phys. 89, 977.Google Scholar
[8]Luciani, J. F., Mom, P. and Virmont, J. 1983 Phys. Rev. Lett. 51, 1664.Google Scholar
[9]Albritton, J. R., Williams, E. A., Bernstein, I. B. and Swartz, K. P. 1986 Phys. Rev. Lett. 57, 1887.CrossRefGoogle Scholar
[10]Krasheninnikov, S. I. 1993 Phys. Fluids B 5, 74.Google Scholar
[11]Belyi, V. V., Demaulin, W. and Paiva-Veretennikoff, I. 1989 Phys. Fluids B 1, 305, 317.CrossRefGoogle Scholar
[12]Krasheninnikov, S. I. 1988 Sov. Phys. JETP 67, 2483.Google Scholar
[13]Gurevich, A. V. 1961 Sov. Phys. JETP 12, 904.Google Scholar
[14]Lebedev, A. N. 1965 Zh. Exp. Teor. Fiz. 48, 1396.Google Scholar
[15]Connor, J. W. and Hastie, R. J. 1975 Nucl. Fusion 15, 415.Google Scholar
[16]Krasheninnikov, S. I. and Bakunin, O. G. 1992 Contrib. Plasma Phys. 32, 255; Bakunin, O. G. and Krasheninnikov, S. I. 1995 Plasma Phys. Reports 21, 502.CrossRefGoogle Scholar
[17]Batishchev, O. V., Bychenkov, V. Yu.Detering, F., Rozmus, W., Sydora, R., Capjack, C. E. and Novikov, V. N. 2002 Phys. Plasmas 9, 2302.Google Scholar
[18]Helander, P. and Krasheninnikov, S. I. 1996 Phys. Plasmas 3, 226.Google Scholar
[19]Krasheninnikov, S. I., Dvornikova, N. A. and Smirnov, A. P. 1990 Contrib. Plasma Phys. 30, 67.Google Scholar
[20]Potapenko, I. F., Bobylev, A. V. and Mossberg, E. 2008 Transp. Theory Stat. Phys. 37, 113.Google Scholar
[21]Killeen, J., Kerbel, G. D., McCoy, M. G. and Mirin, A. A. 1986 Computational Methods for Kinetic Models of Magnetically Confined Plasmas. New York: Springer-Verlag.Google Scholar
[22]Dnestrovskij, Yu. N. and Kostomarov, D. P. 1986 Numerical Simulations of Plasmas. Berlin, Germany: Springer-Verlag.Google Scholar
[23]Meyer-Vernet, N. 2001 Planet. Space Sci. 49, 247.CrossRefGoogle Scholar
[24]Gurevich, A. V., Millikh, G. M. and Roussel-Dupre, R. 1992 Phys. Lett. A 165, 463.Google Scholar
[25]Levinson, I. B. 1965 Sov. Phys. – Solid State 6, 1952.Google Scholar
[26]Stenflo, L. 1966 Plasma Phys. 8, 665.Google Scholar
[27]Potapenko, I. F., Bobylev, A. V., Azevedo, C. A., Assis, A. S. 1997 Phys. Rev. E 56, 7159.Google Scholar
[28]Chavanis, P-H. and Lemou, M. 2005 Phys. Rev. E 72, 061106.Google Scholar