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Analysis of Alpha Modes in Multigroup Diffusion

Abstract : The alpha eigenvalue problem in multigroup neutron diffusion is studied with particular attention to the theoretical analysis of the model. Contrary to previous literature results, the existence of eigenvalue and eigenflux clustering is here investigated without the simplification of a unique fissile isotope or a single emission spectrum. A discussion about the negative decay constants of the neutron precursor concentrations as potential eigenvalues is provided. An in-hour equation is derived by a perturbation approach recurring to the steady state adjoint and direct eigenvalue problems of the effective multiplication factor and is used to suggest proper detection criteria of flux clustering. In spite of prior work, the in-hour equation results for a necessary and sufficient condition for the existence of the eigenvalue-eigenvector pair. A simplified asymptotic analysis is used to predict bands of accumulation of eigenvalues close to the negative decay constants of the precursor concentrations. The resolution of the problem in one-dimensional heterogeneous problems shows numerical evidence of the predicted clustering occurrences and also confirms previous theoretical analysis and numerical results.
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R. Sanchez, D. Tomatis, I. Zmijarevic, K. Dugan. Analysis of Alpha Modes in Multigroup Diffusion. Nuclear Engineering and Technology, Elsevier, 2017, Special Issue on International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering 2017 (M&C 2017), 49 (6), pp.1259-1268. ⟨cea-02434003⟩

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