Monte Carlo criticality analysis of random media under bounded fluctuation driven by normal noise

In Monte Carlo criticality analysis under material distribution uncertainty, it is necessary to evaluate the response of neutron effective multiplication factor (k_eff) to the space-dependent random fluctuation of volume fractions within a prescribed bounded range. Normal random variables, however, cannot be used in a straightforward manner since the normal distribution has infinite tails. To overcome this issue, a methodology has been developed via forward-backward-superposed reflection Brownian motion (FBSRBM). Here, the forward-backward superposition makes the variance of fluctuation spatially constant and the reflection Brownian motion confines the fluctuation driven by normal noise in a bounded range. In addition, the power spectrum of FBSRBM remains the same as that of Brownian motion. FBSRBM was implemented using Karhunen-Loève expansion (KLE) and applied to the fluctuation of volume fractions in a model of UO₂-concrete media with stainless steel. Numerical results indicate that the non-negligible and significant fluctuation of k_eff arises due to the uncertainty of media formation and just a few number of terms in KLE are enough to ensure the reliability of criticality calculation. (author)