Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-26T00:58:41.708Z Has data issue: false hasContentIssue false
  • English
  • Français

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 ([email protected], [email protected])
S. I. KRASHENINNIKOV
Affiliation:
University of California at San Diego, La Jolla, San Diego, CA 92093, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

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

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

[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