https://doi.org/10.1140/epjp/i2018-12215-7
Regular Article
Mathematical foundation of the neutron diffusion problem for a reflected nuclear reactor
1
INFN, Via Dodecaneso 33, 16146, Genova, Italy
2
Politecnico di Torino, Dipartimento di Energetica, Corso Duca degli Abruzzi 24, 10129, Torino, Italy
3
INFN, Via Pietro Giuria 1, 10125, Torino, Italy
* e-mail: Nicholas.Chentre@ge.infn.it
Received:
4
June
2018
Accepted:
25
August
2018
Published online:
23
October
2018
The analytical approach to the neutron kinetics of a reflected multiplying system constitutes a challenging problem in mathematical physics and provides useful results for a full physical understanding of the multiplication process in non-homogeneous media, opening the possibility to establish reliable benchmarks. In this work, the basic mathematical features of the neutron diffusion operator in a reflected configuration are investigated. The completeness of the eigenstates is discussed and proven. The case of the infinite reflector is taken into consideration, highlighting its peculiarities that lead to the appearance of a continuum spectrum. The limitation of the critical eigenfunctions is also discussed. The analysis is carried out at first disregarding the presence of delayed emissions. The work is then extended to include also in the model the presence of delayed neutron precursors.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2018
