Neutron Noise Calculations in Hexagonal Geometry and Comparison with Analytical Solutions

This paper presents the development of a neutronic and kinetic solver for neutron noise calculations in hexagonal geometries. The tool is developed based on diffusion theory with multienergy groups and several groups of delayed neutron precursors allowing the solutions of forward and adjoint problems of static and dynamic states. The tool is applicable to both thermal and fast systems with hexagonal geometries. In the dynamic problems, the small stationary fluctuations of macroscopic cross sections are considered as noise sources, then the induced first-order noise is solved fully in the frequency domain. Numerical algorithms for solving the static and noise equations are implemented using finite differences for spatial discretization and a power iterative solution. A coarse-mesh finite difference technique for accelerating the convergence has been adopted. Verification calculations have been performed and compared to analytical solutions based on a two-dimensional homogeneous system with two energy groups and one group of delayed neutron precursors, in which pointlike perturbations of thermal absorption cross section at central and noncentral positions are considered as noise sources.