Monte Carlo perturbation methods using “virtual density” theory for calculating reactivity due to geometry change

The “virtual density” theory in the field of neutronics is a method to quantify reactivity of a reactor core due to geometry changes by altering the material density or nuclear cross section instead of explicitly changing the geometry. The Monte Carlo perturbation methods-differential-operator sampling (DOS) and correlated sampling (CS)-can efficiently yield accurate small reactivity for cross section changes. However, Monte Carlo perturbation methods have weakness in their inability to deal with geometry changes. This study incorporates the virtual-density theory into the Monte Carlo perturbation methods. When an entire core expands or swells uniformly, keff of the perturbed core can be calculated by simply changing the material density without changing the geometry. Regarding uniform expansion or swelling, conventional Monte Carlo perturbation methods-where cross sections change proportionally to the material density-can predict the altered keff. According to the virtual-density theory, keff perturbed due to a uniform anisotropic expansion or swelling can be predicted by stretching or shrinking the mean free path of neutrons in only one direction without changing the geometry. A new Monte Carlo algorithm is developed to incorporate the path length-stretching or -shrinking in only one direction into a random-walk process in a Monte Carlo keff-eigenvalue calculation. The new Monte Carlo algorithm provides accurate keff values for uniform anisotropic expansion and swelling regardless of the perturbation degree. New formulations of the Monte Carlo perturbation methods are derived to predict the change in keff due to a uniform anisotropic expansion or swelling. Both Monte Carlo perturbation methods can accurately and efficiently predict changes in keff for a small uniform anisotropic expansion or swelling.