Innovative techniques in evaluating neutron fluxes of the multi-energy groups diffusion for homogeneous cubic and spherical reactors

The study of neutron diffusion in nuclear reactors is pivotal for ensuring safe and efficient reactor operation. This paper presents a comprehensive analysis of multi-energy group neutron diffusion, focusing on the derivation of spatial functions for cubic and spherical reactor geometries and the development of volume-integrated multigroup point kinetics equations. Analytical solutions for the time-integrated multigroup point kinetics equations are derived using Hermite piecewise polynomial methods for one-energy group, two-energy groups, and four-energy groups, incorporating temperature feedback effects. Numerical results are provided for step and ramp reactivity insertions in cubic and spherical reactors, analyzing delayed supercritical, supercritical, and subcritical cases for the spherical reactor. The study further evaluates the impact of temperature feedback on reactor dynamics. Results demonstrate high accuracy in the proposed analytical solutions, with significant implications for reactor design and safety analysis. This work provides a robust framework for modeling neutron behavior in multi-energy group systems, offering valuable insights for both theoretical and applied nuclear engineering.