On the spectrum of the multigroup diffusion equations

The present work addresses the problem of the determination of the eigenvalue spectrum of the multigroup diffusion equation for nuclear reactor physics applications. The analytical determination of the multiplication eigenvalues is presented for the material homogeneous configuration case. The characteristics of the time eigenvalue spectrum is further considered and illustrated, highlighting the possibility of the appearance of complex eigenvalues and discussing their physical significance. Various results are presented for different material compositions and energy group structure. Some comparisons to reference results, obtained with highly detailed Monte Carlo evaluations, are also carried out. Such comparisons evidence the limits of the diffusive approach and of the energy group discretization.