Modelling the Effect of Stationary Fluctuations in Nuclear Reactors Using Probabilistic Methods

Abstract

A Monte-Carlo-based method for determining the effect on the neutron flux of stationary fluctuations in 1D and 2D is proposed in this study. The cross-sections of the two-group balance equations relying on the diffusion approximation in the frequency domain are split into their real and imaginary parts, and a modified Green’s function technique is used. In this technique, the balance equations for the real part of the balance equations are mimicked with Monte Carlo using an equivalent subcritical system. The exact same balance equations are obtained for the imaginary part. The coupling between the real and imaginary parts are resolved outside of the Monte Carlo Code, taking advantage of the properties of the Green’s function. The amplitude and phase close to the point of perturbation agree well with diffusion based-codes such as CORE SIM. This method is applicable to any frequency, and any type of cross-section perturbation. The Green’s function is furthermore found to be insensitive to frequencies around and above the plateau region. Using the Green’s function at one given frequency within this frequency range has thus a negligible impact on the estimated fluctuations in neutron flux.