Stochastic analysis of the neutron transport equation and applications to nuclear safety

中子输运方程的随机分析及其在核安全中的应用

• 批准号: EP/P009220/1
• 负责人: Andreas Kyprianou
• 金额: $ 56.35万
• 依托单位: University of Bath
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2017
• 资助国家: 英国
• 起止时间: 2017 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FP009220%2F1
• 关键词: Stochastic; analysis; neutron; transport; equation

The technical basis of this proposal pertains to the Neutron Transport Equation (NTE), which is used to describe neutron density in a physical environment where nuclear fission is taking place, such as a reactor core. This equation is of prime importance in the nuclear industry as it is used to construct models of reactor cores, nuclear medical equipment (e.g. for proton therapy) and other industrial scenarios where irradiation occurs. Primarily these models are used to assess safety and inform regulatory procedure when handling radioactive materials. Although the NTE can be derived through physical considerations of mass transport, it can also be derived using entirely probabilistic means. To be more precise, the NTE can be derived from the stochastic analysis of a spatial branching process. The latter models the evolution of neutron particles as they behave in reality, incorporating the features of random scattering and random fission, with increasing numbers of particles as time evolves. The derivation using spatial branching processes has been known since the 1960/70s, however, since then, very little innovation in the literature has emerged through probabilistic analysis. This mirrors a general lull in fundamental mathematical research contributing to modelling of nuclear fission after the 1980s. In recent years, however, the nuclear power and nuclear regulatory industries have a greater need for a deep understanding the spectral properties of the NTE. Such analytical quantities help e.g. engineers model the criticality and density of nuclear fission activity within a reactor core. In turn this informs optimal reactor design from several different view points (safety, energy production, efficiency etc.) as well as address regulatory constraints. With the decommissioning of old and the construction of new, more efficient and environmentally friendly nuclear power stations the demand for mathematical modelling using the NTE was never greater. The inhomogeneous nature of the NTE as it is used in practice has seen industry turn to Monte-Carlo techniques based on the underlying probabilistic treatment from 40-50 years ago. Many of the associated algorithms can only be run on supercomputers as they boil down to costly Monte-Carlo cycles of the entire fission processes, in essence replicating a virtual physical reality in a computer. This has the huge drawback that computational parallelization is not possible. In the decades that new probabilistic developments have been absent from the treatment of the NTE, there has been a significant evolution in the mathematical theory of spatial branching processes and related stochastic processes. The research in this proposal aims to re-align the understanding of the NTE with the modern theory of spatial branching processes. This is principally motivated by the implication that a whole suite of completely new Monte-Carlo techniques can be developed, as desired by industry, which are, fundamentally, of a lower order of complexity than existing algorithms. The overall aim of this project is to develop a `proof of concept' for this completely new approach, providing the theoretical basis and a stochastic numerical analysis that quantifies relative efficiency. In particular, the most important feature of the new algorithms that will emerge is the ability to parallelize computations.The project will be carried out in close scientific collaboration with industrial partner Amec-Foster-Wheeler, a major UK-based energy consultancies and one of the global leaders in servicing the nuclear energy and nuclear medical industries with simulation software for safety and regulatory purposes.All research output will be made open source on a webpage dedicated to the project.

该提案的技术基础与中子传输方程（NTE）有关，该方程用于描述发生核裂变的物理环境中的中子密度，例如反应堆核心。该方程在核工业中至关重要，因为它用于构建反应堆核心模型，核医疗设备（例如，用于质子治疗）以及发生辐射的其他工业场景。这些模型主要用于评估安全程序时，在处理放射性材料时。尽管可以通过大规模运输的物理考虑来得出NTE，但也可以使用完全概率的手段来得出。更确切地说，可以从空间分支过程的随机分析中得出NTE。后者模拟了中子颗粒在现实中行为的演变，并结合了随机散射和随机裂变的特征，随着时间的发展，颗粒数量的增加。自1960/70年代以来，使用空间分支过程的推导就已经知道，但是，从那时起，文献中很少有创新通过概率分析而出现。这反映了基本数学研究的一般平息，该研究促进了1980年代以后的核裂变建模。然而，近年来，核电和核监管行业更需要深入了解NTE的光谱特性。这样的分析量有助于例如工程师对反应堆核心内的核裂变活性的关键性和密度建模。反过来，这从几个不同的观点（安全性，能源生产，效率等）以及地址监管限制中介绍了最佳反应堆设计。随着旧，更高效，更环保的核电站的建设，使用NTE对数学建模的需求永远不会更大。 NTE在实践中使用的NTE的不均匀性质已看到行业转向40-50年前的基础概率治疗的蒙特卡洛技术。许多相关的算法只能在超级计算机上运行，​​因为它们归结为整个裂变过程的昂贵的蒙特卡洛周期，从本质上讲，在计算机中复制了虚拟物理现实。这具有巨大的缺点，即计算并行化是不可能的。在NTE的处理中缺乏新的概率发展的几十年中，空间分支过程和相关随机过程的数学理论已经存在显着的演变。该提案中的研究旨在通过空间分支过程的现代理论重新对准NTE。这主要是由于行业所需的全新蒙特卡洛技术的整体套件的主要含义，从根本上讲，这比现有算法的复杂性低。该项目的总体目的是为这种全新的方法开发“概念验证”，提供量化相对效率的理论基础和随机数值分析。特别是，将出现的新算法的最重要特征是能够并行计算。该项目将与工业合作伙伴AMEC-Foster-Wheeler紧密合作，这是英国主要的能源咨询公司，并且在核能和核能医疗行业方面的全球领导者之一，通过Sautean和Suckulations的核能进行了努力。

项目成果

Yaglom limit for critical nonlocal branching Markov processes

• DOI: 10.1214/22-aop1585
• 发表时间: 2022-11
• 期刊: The Annals of Probability
• 作者: S. Harris;E. Horton;A. Kyprianou;Minmin Wang

Multi-species Neutron Transport Equation

• DOI: 10.1007/s10955-019-02307-2
• 发表时间: 2018-09
• 期刊: Journal of Statistical Physics
• 影响因子: 1.6
• 作者: A. Cox;S. Harris;E. Horton;A. Kyprianou

Asymptotic moments of spatial branching processes

• DOI: 10.1007/s00440-022-01131-2
• 发表时间: 2022-04
• 期刊: Probability Theory and Related Fields
• 影响因子: 2
• 作者: I. González;E. Horton;A. Kyprianou

Stochastic Methods for Neutron Transport Equation III: Generational many-to-one and $k_\texttt{eff}$

中子输运方程 III 的随机方法：分代多对一和 $k_ exttt{eff}$

• DOI: 10.48550/arxiv.1909.00581
• 发表时间: 2019
• 作者: Cox A

Stochastic methods for the neutron transport equation II: Almost sure growth

• DOI: 10.1214/20-aap1574
• 发表时间: 2019-01
• 期刊: The Annals of Applied Probability
• 作者: S. Harris;E. Horton;A. Kyprianou