The Multi-Group Neutron Diffusion Equation in General Geometries Using the Parseval Identity

Multi-group neutron diffusion equation is still one of the most frequently employed equations for nuclear reactor neutronics calculations, although its limitations are well known. The equation is obtained under the assumptions that scattering is isotropic in the laboratory coordinate system and the region of interest is considered piecewise homogeneous, so that the diffusion coefficients are invariant under spatial transforms like translation and others. It is well known, that such a derivation of diffusion theory rests on certain assumptions, i.e. the flux being sufficiently smooth especially by virtue of neutron absorption or production, which is reasonable since the mean free path is typically larger than the dimensions of the fuel cell and moderator space geometry. The solution of the diffusion equation system is obtained by Parseval relation for different kinds of geometry, where fluctuations (higher moments) are neglected. Further, the continuous energy distribution of neutrons is reduced by the use of two energy groups and the results was compared to literature