Fission source stationarity diagnostics using the Fourier fundamental mode coefficient

• Published in: Progress in nuclear energy (New series) 2022-04, Vol.146, p.104164, Article 104164
• Main Authors: Omar, M.R., Karim, J.A.
• Format: Article
• Language: English
• Subjects: Eigenvalues; Entropy; Entropy (Information theory); Fission source convergence; Fourier series; Fourier transforms; k-eigenvalue calculation; Mathematical analysis; Mathematical models; Monte Carlo criticality calculation; Monte Carlo simulation; Series expansion; Shannon entropy; Spectrum analysis; Stationarity diagnostics
• ISSN: 0149-1970; 1878-4224
• DOI: 10.1016/j.pnucene.2022.104164

We present the complete mathematical analysis of using Fourier fundamental mode coefficient (FFMC) as a useful posterior stationary diagnostics of the Monte Carlo k-eigenvalue calculation. It is well understood that the traditional Shannon entropy calculation requires space discretization, and the decision on choosing the number of spatial bins is subjective and based on users experience. In our previous work, we suggested that the fundamental mode of the Fourier series expansion of the source distribution will be the last mode to equilibrate as soon as stationarity is achieved. Unfortunately, a complete mathematical analysis that justifies such a postulate is yet to be outlined. This paper will deliver such an analysis and will also discuss the detailed spectral analysis of Fourier modes to support our argument. •Monte Carlo source convergence is determined using Fourier analysis.•The Fourier fundamental mode coefficient is a useful stationarity diagnostic tool.•The computation of the proposed indicator avoids spatial discretization.