Abstract
Solution of the Boltzmann kinetic equation by Chapman–Enskog approach and method of determining the plasma transport coefficients are presented. The transport equation can be obtained from the Boltzmann kinetic equation is showed. The appropriate mass, energy, and momentum flows are determined on the Boltzmann kinetic equation. The formulas for higher order calculation of the viscosity, diffusion, thermal diffusion, electrical conductivity, and thermal conductivity of a multicomponent plasma were obtained.
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References
Chapman S., Cowling T.G. The Mathematical Theory of Non-Uniform Gases. Cambridge: Cambridge University Press, 1970.
J. O. Hirschfelder, Ch. F. Curtiss, R. B. Bird. Molecular theory of gases and liquids / John Wiley and Sons, New York. 2nd Edition: 1964.
Ferzinger J.H., Kaper H.G. Mathematical Theory of Transport Processes in Gases, North-Holland. Amsterdam, 1972.
Loyalka S.K., Tipton E.L., Tompson R.V. Chapman-Enskog solutions to arbitrary order in Sonine polynomials I: Simple, rigid-sphere gas // Phys. Rev. A. 2007. Vol. 379. PP. 417–435.
Transport properties in a two temperature plasma: theory and application / Rat V. et al. // Phys. Rev. E. 2001. Vol. 64.
Rat V., Andre P., Aubreton J. et al. // Phys. D: Applied Phys. 2001. Vol. 34. P. 2191–2204.
Transport coefficients including diffusion in a two-temperature argon plasma / V. Rat, et al. // J. Phys. D: Appl. Phys. 2002. Vol. 35. P. 981–991.
R.V. Tompson, E.L. Tipton, S.K. Loyalka. Chapman–Enskog solutions to arbitrary order in Sonine polynomials V: Summational expressions for the viscosity-related bracket integrals // European Journal of Mechanics B/Fluids 29 (2010) 153–179.
Devoto R.S. Transport coefficients of ionized argon // Phys. Fluids. 1973. Vol. 16. № 5. P. 616–623.
Devoto R.S. Transport coefficients of partially ionized argon // Phys. Fluids. 1967. Vol. 10. № 2. PP. 354–364.
Kulik P.P. Essays on physics and chemistry of Low-temperature plasma / Ed. by L.S. Polak. M.: Nauka, 1971.
Boulos M.I., Fauchais P., Pfender E. Thermal plasmas, Fundamentals and Applications. New York: Plenum Press, 1994. Vol. 1.
Shi Nguyen-Kuok. Modeling of equilibrium plasma in RF and Arc plasma torches // Proc. of the International Scientific and Technical. Conf. “Electrophysical and electrochemical technology” SPb. 1997. pp. 63-66.
Zhdanov V.M. Transport phenomena in multicomponent plasma. M.: Energoizdat 1982.
R.V. Tompson, E.L. Tipton, S.K. Loyalka. Chapman–Enskog solutions to arbitrary order in Sonine polynomials IV: Summational expressions for the diffusion- and thermal conductivity-related bracket integrals // European Journal of Mechanics B/Fluids 28 (2009), 695–721.
Devoto R.S. Simplified expressions for the transport properties of ionized monatomic gases // Phys. Fluids. 1967. Vol. 10. № 10. P. 2105–2112.
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Nguyen-Kuok, S. (2017). The Boltzmann Kinetic Equation and Calculation of the Transport Coefficients. In: Theory of Low-Temperature Plasma Physics. Springer Series on Atomic, Optical, and Plasma Physics, vol 95. Springer, Cham. https://doi.org/10.1007/978-3-319-43721-7_5
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DOI: https://doi.org/10.1007/978-3-319-43721-7_5
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