Reactivity effects and flux perturbations due to spatial random dispersal in the number densities of core materials

Abstract

An analysis was made on the reactivity and the flux profile modulation caused by spatial random perturbations in the number densities of core materials of a bare, uniform, critical, reference reactor. Using an orthonormal function set of the Helmholtz modes, a one-group diffusion equation with the multiplication factor k is transformed into an infinite dimensional vector equation with the reactivity ϱ = 1 − 1 k . The problem is then analyzed as the perturbations in the smallest eigenvalue in magnitude and the corresponding eigenvector of an infinite dimensional matrix. This approach leads to the conclusion that spatial random perturbations cause the positive reactivity effect and a flattened flux profile. The results are exact up to the second order of perturbations when zero ensemble average of perturbations is assumed, and are exact up to the third order of perturbations when the Gaussian distribution is assumed in addition.