Strengths and weaknesses of the modal expansion method for perturbations calculations in nuclear reactor physics

Reactor design and uncertainties propagation request repeated execution of neutron diffusion calculations. To address this, one can rely on the Generalized Perturbation Theory which is restricted to single integral values such as reaction rate ratios. To overpass such limitations, the perturbed flux could be calculated with the modal expansion method. The difficulty to calculate more than one eigenvector has limited its use. Hence, modal expansion lacks a clear explanation of its strengths and weaknesses. Using recent advances in eigenvalues solvers, we have successfully applied modal expansion to the 2D-BIBLIS and IAEA-3D benchmarks. Our results are promising for fission and capture cross sections perturbations. Still, modal expansion is faulty for local perturbations or when it concerns the reflector. In terms of computational cost, modal expansion is more efficient than solving the direct problem with a calculation time divided by 8 for a basis of 20 eigenvectors.