Neutron noise theory in the P 1 approximation

Abstract

The validity of the use of the diffusion approximation in neutron noise theory is investigated through a comparison with P 1 theory. The motivation comes from the fact that both static and dynamic perturbations act as non-isotropic sources in the P 1 expansion of the static angular flux and the angular noise, respectively, and the neglection of these terms, which would allow the use of diffusion theory, is not obvious. In addition, the effect of noise sources that affect primarily the scattering cross section (diffusion coefficient) has not been the subject of a thorough investigation before. The P 1 theory of static and dynamic perturbations is developed in this paper and the results show the corrections introduced by P 1 theory. It is found that for cases when the fluctuation of the absorption cross section dominates, the quantitative difference between the diffusion and P 1 theory results is negligible in general. For cases when the perturbation leads to the fluctuation of the scattering cross section only, such as in cases of density fluctuations in a heavy water moderator or even a small light water reactor, P 1 theory needs to be used and the results differ markedly from the noise induced by an equivalent absorption cross section fluctuation in diffusion theory. Some concrete cases are investigated both qualitatively and quantitatively.