深次临界系统高阶谐波在点堆模型中的机理研究

The point kinetics model is a widely used model in the nuclear reactor systems. It simply considers the largest eigenvalue of the dynamic equation and the fundamental mode of the neuron flux, while it ignores the higher mode eigenvalue or higher mode flux. This can be considered to be right in critical system. However, as the source is stronger for the deep subcritical system, the excitation of higher harmonics will lead to different neutron density distribution compared with that in the critical system, which means the model is unsuitable for subcritical reactors. The subcritical experiments have shown that there is deviation between predicted results given by point kinetics model and the results from the experimental data. One of the main reasons is that the higher harmonics is disturbing the measurement results. Thus, it is significant to study the mechanism of the higher harmonics in both theoretical and experiment aspects. However, there is a lack of theoretical study on the time behaviour and space distribution of the harmonics in the deep subcritical system, where the higher harmonics effects would be stronger. This project is aiming to reveal the law of the influence of higher harmonics in the neuron kinetics for the subcritical systems. The work will be performed based on deep subcritical systems in two aspects: firstly, based on the point kinetics equations, we study the characteristics of spatial distribution and decay behavior for both higher harmonics and fundamental mode, and the effect of source neutrons and fission neutrons; secondly, we express the higher harmonics terms, and build up a new inverse kinetics model. This project is aiming to solve the problem that the traditional point kinetics model is not suitable for the deep subcritical system, and to describe the neuron kinetics in a more accurate way which can be a fundamental study for neutron kinetics characteristics in the deep subcritical system.

点堆模型是在核反应堆中广泛运用的动力学模型。它只考虑点堆方程最大本征值和中子通量密度的基波，忽略高阶本征值和高阶谐波，这在临界系统中近似成立；然而次临界系统有外源项加入，高阶谐波受激发，影响中子通量密度分布，点堆模型不适用。实验上遇到的反应性测量难题，主要原因之一是高阶谐波的扰动。深次临界系统中，高阶谐波重要性加强，研究其性质十分必要；而国际上缺少对各阶谐波的衰变行为和空间分布特征等理论研究。本项目拟通过研究高阶谐波性质，完善深次临界系统点堆动力学理论。拟开展两方面工作：一是基于点堆方程，研究各阶谐波的空间分布和衰变特征，以及外源中子和堆内裂变中子的相互影响机理；二是通过考虑谐波贡献来改进逆动态方程，发展反应性测量方法。本项目旨在解决传统点堆模型不适用于深次临界系统的问题，为精确描述中子动力学特征奠定理论基础。

点堆模型是在核反应堆中广泛运用的动力学模型。它只考虑点堆方程最大本征值和中子通量密度的基波，忽略高阶本征值和高阶谐波，这在临界系统中近似成立；然而次临界系统有外源项加入，高阶谐波受激发，影响中子通量密度分布，点堆模型不适用。实验上遇到的反应性测量难题，主要原因之一是高阶谐波的扰动。深次临界系统中，高阶谐波重要性加强，研究其性质十分必要；而国际上缺少对各阶谐波的衰变行为和空间分布特征等理论研究。.本项目针对深次临界系统中,外源作用增强、高阶谐波受到激发的特点，对高阶谐波在点堆动力学中的作用规律开展深入研究。研究成果包括：(1)获得深次临界系统点堆模型中高阶谐波的衰变规律和空间分布特征。从解析上研究深次临界系统中高阶谐波对点堆动力学的影响机理，实现对各阶谐波和本征值的解析计算，从而从理论上了解了中子通量密度中各阶谐波的行为。（2）总结外源中子和堆内裂变中子的相互影响机制。在日本KUCA反应堆上依照实验方案开展了次临界度测量实验。通过次临界度测量实验，比较实际值与测量值，area method实验测量结果较好，与参考值相差500pcm以内。高阶谐波带来的误差与α的误差密切相关，这来自拟合瞬发中子衰减曲线得来的误差。（3）发展深次临界系统次临界度测量方法。进一步发展适合于深次临界系统的次临界度测量方法——逆动态法。采用逆动态法方法可以考虑高阶谐波的贡献，有效地重建铅基临界反应器的反应性。对于铅基次临界反应堆中，使用该方法仍然可以重建反应性，但受到空间光谱效应和扩散效应的影响，结果偏低。.综上，本项目通过研究高阶谐波在深次临界系统点堆模型中的机理，分析其衰变特性和分布特征，不仅从理论上帮助解释深次临界中子动力学机制，解决传统点堆模型在运用于深次临界系统时不适用的问题，还为模型实际应用于深次临界反应堆测量实验提供支撑条件，对次临界反应堆的反应性测量具有理论意义和工程应用价值。