The Integral Transform Method for the Average Neutron Transport Properties of a Lattice

A new approach to the determination of average neutron transport properties of regular lattices is presented in a form amenable to any desired order of approximation. It is based on the time dependent one group integro-differential transport equation in which the cross sections are expanded in Fourier series corresponding to the periodicity of the lattice. The integral transform method yields in this case the Fourier series also for the neutron density, the zero’th term of which is separated out as the average over the lattice. The remaining Fourier coefficients are solved by a method analogous to the collision probability method and expressed in terms of the angular moments of the average neutron density. An approximate integral transform of the transport equation for the average neutron angular density is obtained that contains through its effective scattering integral the effects of the anisotropy and of the heterogeneity of the lattice. The method is applied to the problem of anisotropic diffusion constants in lattices containing voids, in particular, the diffusion constant parallel to empty channels at large channel radia is resolved. As an example, the simultaneous determination of the disadvantage factor and the anisotropic diffusion constant is also presented.