Random media criticality analysis using randomized Fourier series and incomplete randomized Weierstrass function

Criticality analysis of continuously-mixed random media is essential for the safe retrieval of fuel debris. A key first approach to it is to establish some Monte Carlo (MC) method for the random media characterized by a single-mode inverse power law power spectrum, modelled using the Incomplete Randomized Weierstrass Function (IRWF). However, image analysis reveals that the power spectrum of an oxide debris mock-up cannot be fully explained by a single contributing factor. This has led to the search for a new randomized function with a power spectrum capable of capturing more complexity than a single-mode law. To this end, a function called a Randomized Fourier Series (RFS) has been developed to represent a power spectrum of arbitrary shape. Here, the repertoire of RFS is so broad that it is capable of representing power spectra obtained from measurements, includes a phase-randomized form of the Karhunen-Loève expansion of Brownian motion, and allows reactor physicists and criticality safety engineers to analyse various scenarios. Numerical results are presented for the fluctuation of neutron effective multiplication factor (k_eff) over the random media replicas independently generated via RFS. The scale of RFS is linear, while that of IRWF is logarithmic, therefore numerical results are also presented for IRWF to identify a spectral range most influential on the k_eff fluctuation.