Abstract Spectrum unfolding is a key tool used together with diagnostics in the determination of nuclear fields that are associated with a range of nuclear technologies spanning fusion, fission, nuclear medicine and accelerator domains. The underlying process requires a mathematical method for solving the Fredholm integral equation of the first kind. This paper discusses the development, testing and comparison of the modern combined framework of methods for performing neutron spectrum unfolding SPECTRA-UF, which includes the UF_G and UF_M subroutines, based on the underlying mathematics of the GRAVEL and MAXED methods respectively, along with a custom parameterised subroutine, UF_P. We compared the behaviour of each method using a set of synthetic data. We discuss the challenges associated with unfolding fusion spectra, and the behaviour of each subroutine along with the feasibility of using general parameterised spectra as initial a priori spectra. The UF_M, UF_G and UF_P methods showed reasonable agreement where good a priori was supplied and all improved on the a priori spectrum given, but behaved poorly where less accurate a priori was provided, with UF_G showing itself to rely more heavily on the a priori spectrum given. The UF_M subroutine performed most favourably, producing the lowest mean fractional deviation across the majority of spectra. The UF_P was able to represent the fusion peaks and relatively smooth epi-thermal regions, but performed less well where the flux spanned many orders of magnitude. The modelling of the down-scatter component of the fusion peaks was also challenging to reliably model using simple distributions.

中文翻译：

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SPECTRA-UF中子能谱展开方法的开发、测试和比较

摘要 频谱展开是与诊断一起使用的关键工具，用于确定与一系列核技术相关的核场，这些核技术涵盖聚变、裂变、核医学和加速器领域。底层过程需要一种数学方法来求解第一类 Fredholm 积分方程。本文分别基于 GRAVEL 和 MAXED 方法的基础数学，讨论了用于执行中子谱展开 SPECTRA-UF 的现代组合框架的开发、测试和比较，其中包括 UF_G 和 UF_M 子程序，以及自定义参数化子程序，UF_P。我们使用一组合成数据比较了每种方法的行为。我们讨论与展开融合光谱相关的挑战，以及每个子程序的行为以及使用通用参数化光谱作为初始先验光谱的可行性。UF_M、UF_G 和 UF_P 方法在提供良好先验的情况下表现出合理的一致性，并且在给定的先验频谱上都得到了改进，但在提供的先验精度较低的情况下表现不佳，UF_G 表明自己更依赖于先验频谱给。UF_M 子程序表现最出色，在大多数光谱中产生最低的平均分数偏差。UF_P 能够代表聚变峰和相对平滑的超热区，但在通量跨越多个数量级的情况下表现不佳。融合峰的向下散射分量的建模对于使用简单分布进行可靠建模也具有挑战性。