https://doi.org/10.1140/epjp/i2018-12245-1
Regular Article
The time eigenvalue spectrum for nuclear reactors in multi-group diffusion theory
1
Politecnico di Torino, Dipartimento Energia, Corso Duca degli Abruzzi, 24, 10129, Torino, Italy
2
INFN, Sezione di Torino, Via P. Giuria, 1, 10125, Torino, Italy
3
INFN, Sezione di Genova, Via Dodecaneso, 33, 16146, Genova, Italy
4
Centro Fermi, Piazza del Viminale, 1, 00184, Roma, Italy
* e-mail: saracco@ge.infn.it
Received:
19
February
2018
Accepted:
9
August
2018
Published online:
28
September
2018
We develop a fully analytical study of the spectrum of the neutron diffusion operator both for spatially homogeneous and reflected reactors in a multi-group energy model. We illustrate and discuss the results of the analysis of the time spectrum of the diffusion operator, to highlight some general properties of the neutronic evolution in a multiplying system. Various new results are presented, particularly regarding the possible existence of complex time eigenvalues, the appearance of a continuum part of the spectrum and the orthogonality properties of the eigenfunctions in the case of an infinite reflector.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2018
