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Homogenization of the criticality spectral equation in neutron transport. (English) Zbl 0931.35010
Summary: We address the homogenization of an eigenvalue problem for the neutron transport equation in a periodic heterogeneous domain, modeling the criticality study of nuclear reactor cores. We prove that the neutron flux, corresponding to the first and unique positive eigenvector, can be factorized in the product of two terms, up to a remainder which goes strongly to zero with the period. One term is the first eigenvector of the transport equation in the periodicity cell. The other term is the first eigenvector of a diffusion equation in the homogenized domain. Furthermore, the corresponding eigenvalue gives a second order corrector for the eigenvalue of the heterogeneous transport problem. This result justifies and improves the engineering procedure used in practice for nuclear reactor cores computations.

MSC:
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
82D75 Nuclear reactor theory; neutron transport
65R20 Numerical methods for integral equations
35P05 General topics in linear spectral theory for PDEs
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