Approximated Space-Energy Resolution of Fast-Neutron Fluxes

This Note expands on a previously communicated synthetic slowing down model to determine the neutron spectra in fast reactors. Based on a polynomial approximation, the model accuracy increases with the order of the expansion. It is, in fact, a generalization to N terms of the one-term classical slowing down models such as those of Fermi, Wigner, and Greuling-Goertzel. Equivalent to the classical and synthetic expression of our Q_N model, this Note proposes a determination of a “differential” expression of the model, allowing the calculation of a set of functions approximating the kernel Σ_s(u′ → u). To be used in reactor codes, the spectrum determination has to he associated to a spatial resolution; the second part of this Note is devoted to the adaptation of the Q_N method to the collision probability approximation or the calculation of a spatial Green's function, to obtain a flux (r,E). The applications in the isotropic collision approximation can be extended to the linearly anisotropic approximation, and various results that demonstrate the validity of the method are given.