Neutron multiplication and fissile material distribution in a nuclear reactor

The paper studies the effect of the distribution of the fissile material in a nuclear system on its multiplication properties. Some general results and specific examples on the dependence of the value of the effective multiplication constant on the fuel distribution are presented. The approach to the problem is established on a rather general mathematical ground, referring to a variational approach which leaves room to add constraints, when needed. Examples in one-and two-group diffusion are illustrated. It is well known that the effective multiplication factor of a homogeneous system can be increased by the addition of a reflector but it is not obvious that it is possible to obtain an effective multiplication factor larger than the value of the infinite medium multiplication factor of the material constituting the core region. This can never happen in a one group model, as can be easily demonstrated, for instance, in diffusion theory. However, when taking into account spectral effects related to slowing down phenomena, it is shown in this work that such a situation can be realized by a proper choice of the reflector material. Some analyses are carried out in the frame of two-group diffusion theory and comparisons are performed with Monte Carlo evaluations.