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**Mathematical model of fuel layer degradation when the laser target is heated by thermal radiation in the reactor working chamber.**
*(English.
Russian original)*
Zbl 1200.80007

Comput. Math. Model. 21, No. 1, 1-17 (2010); translation from Prikl. Mat. Inf. 32, 5-19 (2009).

The authors consider a multilayer polystyrene spherical shell which is filled in with solid hydrogen isotopes (deuterium and tritium). This is called a laser target. The paper intends to model the deformations of the laser target under the action of a laser beam. The authors write the heat equations in the sphere and in the fuel layer which include a corrector coefficient linked to the deformations of the sphere. They finally write the Navier-Stokes equation for the momentum transport in a viscous gas (the heart of the sphere) and the energy transport in this gas. Transmission conditions and boundary conditions are added to this set of parabolic equations. The authors then introduce some simplifications and dimensionless variables which contain a small parameter \(\delta \) in the space variables. These simplifications lead to a singularly perturbed Stefan problem for a parabolic equation which describes the evolutions of temperature \(T_{s}\) of the fuel layer. They introduce an asymptotic expansion of \(T_{s}\) in powers of \(\delta \). They compute the first-order terms of this asymptotic expansion. The paper ends with the computation of the fuel layer degradation time taking realistic data.

Reviewer: Alain Brillard (Riedisheim)

### Keywords:

multilayer polystyrene spherical shell; laser target; laser beam; hydrogen isotopes; Stefan problem; asymptotic expansion; fuel layer degradation time### Software:

ECOMOD
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\textit{A. A. Belolipetskii} et al., Comput. Math. Model. 21, No. 1, 1--17 (2010; Zbl 1200.80007); translation from Prikl. Mat. Inf. 32, 5--19 (2009)

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### References:

[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). · Zbl 1154.80005 |

[2] | 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. |

[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). |

[4] | R. Siegel and J. Howell, Thermal Radiation Heat Transfer [Russian translation], Mir, Moscow (1975). |

[5] | L. G. Loitsyanskii, Fluid and Gas Dynamics [in Russian], Nauka, Moscow (1970). · Zbl 0247.76001 |

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