Random media criticality analysis using the Randomized Fourier Series for arbitrary-shaped power spectrum

Ueki, Taro  

The criticality analysis of continuously mixed random media is essential to the safe retrieval of fuel debris. Image analysis of an oxide debris mockup reveals that the power spectrum cannot be fully explained by a single factor alone, but instead requires consideration of the complexity of multiple factors. This highlights the need for a randomized function capable of representing complex power spectra. To address this, we developed a new function called the Randomized Fourier Series (RFS), which introduces randomization in amplitude and phase. RFS allows the representation of power spectra with arbitrary shapes, facilitating realistic Monte Carlo (MC) simulations of random continuous material mixtures. For demonstration, taking the Lorentz power spectrum as an example, the spectrum flatness at low wavenumbers is analyzed to understand how the transition to white noise influences the fluctuation in neutron effective multiplication factor across independently generated random media replicas. Numerical results are presented for a mixture of 4 materials, along with the root mean-squared mass deviation over the constituent materials. The MC solver Solomon is employed with a partial volume pairing feature.