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.

该提案的技术基础涉及中子输运方程（NTE），该方程用于描述发生核裂变的物理环境（例如反应堆堆芯）中的中子密度。该方程在核工业中至关重要，因为它用于构建反应堆堆芯、核医疗设备（例如用于质子治疗）和发生辐射的其他工业场景的模型。这些模型主要用于评估安全性并为处理放射性材料时的监管程序提供信息。虽然 NTE 可以通过质量传输的物理考虑来推导，但它也可以使用完全概率的方法来推导。更准确地说，NTE 可以从空间分支过程的随机分析中推导出来。后者模拟中子粒子在现实中的行为演化，结合了随机散射和随机裂变的特征，随着时间的推移，粒子数量不断增加。使用空间分支过程的推导自 20 世纪 60/70 年代以来就已为人所知，然而，从那时起，通过概率分析在文献中出现的创新很少。这反映出 20 世纪 80 年代后核裂变建模基础数学研究普遍陷入停滞。然而，近年来，核电和核监管行业更加需要深入了解 NTE 的光谱特性。这样的分析量有助于例如工程师对反应堆堆芯内核裂变活动的临界度和密度进行建模。反过来，这可以从几个不同的角度（安全、能源生产、效率等）为最佳反应堆设计提供信息，并解决监管限制。随着旧核电站的退役和新的、更高效、更环保的核电站的建设，对使用 NTE 进行数学建模的需求从未如此之大。 NTE 在实践中的不均匀性使得业界转向基于 40-50 年前的潜在概率处理的蒙特卡罗技术。许多相关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罗循环，本质上是在计算机中复制虚拟物理现实。这有一个巨大的缺点，即计算并行化是不可能的。在 NTE 的治疗中缺乏新的概率发展的几十年里，空间分支过程和相关随机过程的数学理论发生了重大演变。本提案中的研究旨在重新调整对 NTE 的理解与现代空间分支过程理论。这主要是因为这样的含义：可以根据行业的需要开发一整套全新的蒙特卡罗技术，从根本上讲，这些技术的复杂性比现有算法要低。该项目的总体目标是为这种全新方法开发“概念验证”，提供理论基础和量化相对效率的随机数值分析。特别是，即将出现的新算法的最重要特征是并行计算的能力。该项目将与工业合作伙伴 Amec-Foster-Wheeler 密切科学合作进行，Amec-Foster-Wheeler 是一家英国主要能源咨询公司，也是为核能和核医疗行业提供安全和监管模拟软件服务的全球领导者之一。所有研究成果都将在该项目专用的网页上开源。

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

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

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 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