Deterministic and stochastic methods for sensitivity analysis of neutron noise

Abstract

Neutron noise calculated from the neutron noise equation in the frequency domain is governed by the cross section and kinetic parameters. Deterministic and stochastic methods to obtain the sensitivity coefficient of neutron noise with respect to the abovementioned parameters are proposed. As a deterministic method, a diffusion equation for the first derivative of neutron noise with respect to a cross section or kinetic parameter is derived by differentiating the neutron noise diffusion equation. As a stochastic method, the differential operator sampling method, which is a well-established Monte Carlo technique, is applied to calculate the sensitivity coefficient. Neither method requires adjoint mode calculations and can be expanded to higher-order derivatives. Based on verifications performed in this study, it is discovered that these techniques yield accurate sensitivity coefficients. The methods developed in this study eliminates a large number of calculations that need to be performed in the random sampling method.