Comparative study of 2-group P(1) and diffusion theories for the calculation of the neutron noise in 1D 2-region systems

In this paper, the neutron noise, i.e. the stationary fluctuations of the neutron flux around its mean value, is calculated in 2-group P(1) and diffusion theories for a 2-region slab reactor using Green's function technique. The applicability of diffusion theory for different types and locations of the perturbation, as well as different frequencies, is assessed. Material data, i.e. nuclear cross-sections and kinetic parameters, representative of a Light Water Reactor (LWR) and of a Heavy Water Reactor (HWR), respectively, are used in this work. It is demonstrated that for practical situations in LWRs and HWRs, there is no significant advantage to use P(1) theory since diffusion theory gives acceptable results. The largest deviations between the two formalisms are observed in regions of large gradients of the static neutron flux, such as close to the reflector interface and close to the perturbation. Such observations are in agreement with theoretical expectations. This study also indicates that neglecting the effect of cross-section perturbation on the diffusion coefficient gives a rather small impact on the solution. This allows drastically simplifying the determination of the neutron noise. When using numerical techniques for such a determination the memory requirements and computational effort can be significantly reduced.