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Computational Reactor Physics

**Computational Reactor Physics**

**Modal analysis**

Similar to describing vibrating media such as strings or musical instruments, the dynamics of neutron transport can be modeled by a modal description. Various types of modes can be formulated for the neutron transport equation, where for dynamic behavior analysis the time-eigenvalues (alpha-modes) are of interest. Although the theory has been known for a long time we have been the first to describe methods where these modes can be obtained effectively in large-scale simulation framework (see references below). The key to efficiently obtaining multiple modes is the coupling of the neutronics simulation tools to dedicated Krylov subspace methods such as Arpack. We have shown that scalable performance can be achieved through these tools. Early work targeted diffusion, but Boltzmann transport modes have also been investigated. Our research into alpha mode calculations has been applied to further the understanding of the dynamics of subcritical systems and measured detector signals and to the optimization of the location of detectors for subcriticality monitoring.

Some references

D. Lathouwers, Iterative computation of time-eigenvalues of the neutron transport equation, Annals of Nuclear Energy 30(17), pp. 1793-1806, 2003.

J. Kophazi and D. Lathouwers, Three-dimensional transport calculation of multiple alpha-modes in subcritical systems, Annals of Nuclear Energy 50, pp. 167-174, 2012.

W. Uyttenhove, Reactivity monitoring of accelerator-driven nuclear reactor systems,PhD thesis, Delft University of Technology, 2016.

**Core calculation procedures**

Industrial core calculations combine cross section processing on assemblies using reflective boundary conditions with nodal diffusion solvers for criticality calculations and corresponding 3D power distributions. These procedures are adequate for regular reactor systems where similar assemblies neighbor others, but inadequate for heterogeneous systems with varying enrichment, MOX assemblies and control assemblies. Improvement of core calculation procedures for real reactor geometries is studied in collaboration with AREVA. Current efforts are focused on the use of rehomogenization methods where nodal cross sections are corrected by reconstructing the global flux changes originating from heterogeneities in space and energy.