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加速器驱动次临界系统中非齐次中子扩散方程的一种解析解
An Analytical Solution to Inhomogeneous Neutron Diffusion Equation in Accelerator Driven System
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摘要: 利用傅里叶方法得到了非齐次中子扩散方程格林函数的解析形式，通过格林函数计算了当外源在堆芯任意位置时的中子通量密度分布，分析了在次临界反应堆系统中，次临界倍增系数ks与外源位置和相同次临界深度下堆芯尺寸的依赖关系。发现，ks随着堆芯尺寸的增加而减小，这点变化虽小，但能量增益对ks以及堆芯尺寸是相当敏感的，加速器驱动的次临界系统(ADS)设计时应必须予以考虑。Abstract: The analytical form of the Green’s functions of the inhomogeneous diffusion equation for neutrons are obtained using the Fourier method. The neutron flux distributions with the external neutron source located at arbitrary positions are calculated from the Green’s functions. In a subcritical system, the dependences of the subcritical multiplication factor ks on the source position and the core size with the fixed subcriticality keff are analyzed based on the series solution. It is found that ks decreases with the core size. Although this variation is small, the energy gain is sensitive to ks and then the core size, which has to be taken into account in the design of the source driven subcritical system.
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