Monte Carlo method with complex-valued weights for frequency domain analyses of neutron noise

Abstract

A Monte Carlo algorithm to solve the transport equation of the neutron noise in the frequency domain has been developed to extend the conventional diffusion theory of the neutron noise to the transport theory. In this paper, the neutron noise is defined as the stationary fluctuation of the neutron flux around its mean value, and is induced by perturbations of the macroscopic cross sections. Since the transport equation of the neutron noise is a complex equation, a Monte Carlo technique for treating complex-valued weights that was recently proposed for neutron leakage-corrected calculations has been introduced to solve the complex equation. To cancel the positive and negative values of complex-valued weights, an algorithm that is similar to the power iteration method has been implemented. The newly-developed Monte Carlo algorithm is benchmarked to analytical solutions in an infinite homogeneous medium. The neutron noise spatial distributions have been obtained both with the newly-developed Monte Carlo method and the conventional diffusion method for an infinitely-long homogeneous cylinder. The results with the Monte Carlo method agree well with those of the diffusion method. However, near the noise source induced by a high frequency perturbation, significant differences are found between the diffusion method and Monte Carlo method. The newly-developed Monte Carlo algorithm is expected to contribute to the improvement of calculation accuracy of the neutron noise.