Adjoint P₁ equations for neutron slowing down

Abstract

To solve the large-group diffusion adjoint equation the averaged group constants have to be pre-calculated. However, at this point the forward and adjoint fluxes are unknown. Thus, an alternative method, independent of the solution of this equation, has to be provided. This method is divided into two steps. In the first, the forward and adjoint spectra should be obtained for a unit cell assuming infinite medium. The second step consists of the correction for a finite medium by approximating the spatial dependence by a single Fourier fundamental mode in terms of the geometrical buckling B2. This paper is dedicated to the solution of the second step. Therefore, forward and adjoint P1 equations were both obtained and numerically solved in lethargy space in order to provide the neutron fluxes in a finite unit fuel cell. Moreover, the direct, adjoint and bilinear weighting for calculation of macrogroup constants is discussed.