Spectrum features of the eigenvalue formulations in neutron transport

The steady state neutron transport equation can be studied resorting to different eigenvalue formulations, useful to investigate the criticality state of a nuclear system. In this respect, the knowledge of the eigenvalue spectra featuring the main eigenproblems is fundamental, from a practical standpoint, to guide the eigenvalue solvers searching for the dominant eigenpairs. The study of the eigenvalue spectrum shape on the complex plane is also relevant to better understand the physico-mathematical aspects of the neutron transport numerical approximations. This paper investigates the features of the eigenvalue spectra with respect to various parameters like modelling approximations, departure from criticality and spatial heterogeneity in a one-dimensional slab geometry framework. The sensitivity of the energy spectrum characterising the fundamental eigenfunction is then evaluated with respect to the model adopted and to perturbations in the input parameters.