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Computational Mathematics and Modeling

, Volume 21, Issue 1, pp 1–17 | Cite as

Mathematical model of fuel layer degradation when the laser target is heated by thermal radiation in the reactor working chamber

  • A. A. Belolipetskii
  • E. A. Malinina
  • K. O. Semenov
Mathematical Modeling

We propose a mathematical model of the changes occurring in the geometrical properties of the deuterium–tritium layer on the laser target in the process of its insertion into the reactor working chamber. The model is a parabolic equation of general form in spherical coordinates with nonlinear boundary conditions on a moving boundary. We show that under physically justified assumptions this problem may be regarded as a Stefan problem for a singularly perturbed parabolic equation. The first terms of the solution series are written out. Numerical calculations of the fuel layer degradation time are presented for a real target.

Keywords

Thermal Radiation Combustion Zone Stefan Problem Asymptotic Series Nonlinear Boundary Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    A. A. Belolipetskii, “A singularly perturbed Stefan problem describing fuel layer degradation in a laser target,” Vestnik MGU, ser. 15, Vychisl. Matem. Kibern., No. 1, 10 –18 (2008).Google Scholar
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    A. A. Belolipetskii, “Modeling complex physical systems,” in: Proc. 2nd Russian Sci. Conf. on Mathematical Modeling of Developing Economics ECOMOD-2007, Kirov, 9 –15 July 2007 [in Russian], (2007), pp. 37– 48.Google Scholar
  3. 3.
    I. V. Aleksandrova, A. A. Belolipetskii, E. R. Koresheva, and others, “Preserving the parameters of a cryogenic target in the process of insertion into the thermonuclear combustion zone,” Voprosy Atomnoi Nauki i Tekhniki, No. 3, 27– 47 (2007).Google Scholar
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    R. Siegel and J. Howell, Thermal Radiation Heat Transfer [Russian translation], Mir, Moscow (1975).Google Scholar
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    L. G. Loitsyanskii, Fluid and Gas Dynamics [in Russian], Nauka, Moscow (1970).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  • A. A. Belolipetskii
    • 1
  • E. A. Malinina
    • 1
  • K. O. Semenov
    • 1
  1. 1.Faculty of Computational Mathematics and CyberneticsMoscow State UniversityMoscowRussia

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