Approximation theory and homogenization for neutron transport processes

In practical calculation of reactor systems homogenization is performed by some techniques mostly based on intuition and there is no uniquely accepted approach to this problem. In the first part of the paper an attempt is made to formulate mathematical basis of homogenization for the neutron diffusion and transport equations using recent developments in this field. The boundary value problems for both equations for non smooth H - periodic coefficients are related to appropriate variational problems stated in terms of bilinear forms. The behaviour of the solutions for H → 0 is investigated under various assumptions concerning a limit process to get the coefficients of homogenized equations. In the second part of the paper the assymptotic equivalence of the neutron diffusion to the transport equation is studied. The relation between homogenization procedures for both equations is also examined. As an example, the deriviation of the equations of homogenization in the case of hexagonal geometry typical for V.V.E.R. reactor is given. The obtained formulae for so called effective diffusion coefficient are analyzed for various types of lattices. (author)