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

IF 3.2 3区工程技术 Q1 NUCLEAR SCIENCE & TECHNOLOGY

Progress in Nuclear Energy Pub Date : 2025-09-08 DOI:10.1016/j.pnucene.2025.106007

Taro Ueki

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引用次数: 0

Abstract

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.

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随机傅立叶级数和不完全随机Weierstrass函数的随机媒介临界性分析

连续混合随机介质的临界性分析对燃料碎片的安全回收至关重要。一个关键的第一步是建立一些蒙特卡罗（MC）方法，以单模反幂律功率谱为特征的随机介质，用不完全随机Weierstrass函数（IRWF）建模。然而，图像分析显示，氧化物碎片模型的功率谱不能完全由单一因素解释。这导致了寻找一种新的随机函数，其功率谱能够捕获比单模定律更复杂的情况。为此，一种称为随机傅立叶级数（RFS）的函数被开发出来表示任意形状的功率谱。在这里，RFS的功能是如此广泛，以至于它能够表示从测量中获得的功率谱，包括布朗运动的karhunen - lo展开的相位随机形式，并允许反应堆物理学家和临界安全工程师分析各种场景。给出了中子有效倍增因子（keff）在RFS独立生成的随机介质副本上波动的数值结果。RFS的尺度是线性的，而IRWF的尺度是对数的，因此IRWF也给出了数值结果来识别对keff波动影响最大的光谱范围。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Progress in Nuclear Energy 工程技术-核科学技术

CiteScore

5.30

自引率

14.80%

发文量

331

审稿时长

3.5 months

期刊介绍： Progress in Nuclear Energy is an international review journal covering all aspects of nuclear science and engineering. In keeping with the maturity of nuclear power, articles on safety, siting and environmental problems are encouraged, as are those associated with economics and fuel management. However, basic physics and engineering will remain an important aspect of the editorial policy. Articles published are either of a review nature or present new material in more depth. They are aimed at researchers and technically-oriented managers working in the nuclear energy field. Please note the following: 1) PNE seeks high quality research papers which are medium to long in length. Short research papers should be submitted to the journal Annals in Nuclear Energy. 2) PNE reserves the right to reject papers which are based solely on routine application of computer codes used to produce reactor designs or explain existing reactor phenomena. Such papers, although worthy, are best left as laboratory reports whereas Progress in Nuclear Energy seeks papers of originality, which are archival in nature, in the fields of mathematical and experimental nuclear technology, including fission, fusion (blanket physics, radiation damage), safety, materials aspects, economics, etc. 3) Review papers, which may occasionally be invited, are particularly sought by the journal in these fields.