等价理论的偏差分析与改进研究

Deviation Analysis and Improvement of Equivalence Theory

等价理论是通过建立均匀问题和非均匀问题的等价关系产生有效共振截面的传统共振计算方法,有着广泛应用。由于等价理论引入了多种近似处理,包括平通量假设、逃脱概率有理近似、窄共振近似等,其结果与严格共振计算方法(超细群方法,连续能量方法)存在一定偏差。本文基于等价理论计算程序和超细群计算程序,对各近似处理带来的偏差进行了定量分析。结果表明,平通量假设和窄共振近似是等价理论偏差的主要因素。针对这些因素,本文对传统等价理论的模型和计算流程进行改进,提出了一种新的等价理论模型。结果表明,新的等价理论模型实现了对传统等价理论方法偏差的非经验、系统的修正。新的等价理论模型继承了传统模型简便、高效的特点,未引入额外的计算,可在保证效率的基础上提高等价理论共振计算程序的精度。

The conventional resonance calculation generates the effective resonance cross section by between heterogeneous and homogeneous system. method known as equivalence theory setting up the equivalent relationship It is widely utilized in lattice physics calculation. Several approximations involved in equivalence theory including spatially constant flux approximation, rational approximation of the neutron escape probability and narrow resonance approximation cause considerable deviation of effective cross sections compared to those generated by rigorous method, such as ultra-fine-group method and Monte Carlo method. The deviation caused by each approximation was analyzed using resonance calculation codes based on equivalence theory and ultra-finegroup method. Results show that spatially constant flux approximation and narrow resonance approximation are the main source of the deviation. A new derivation of effective cross section by equivalence theory was proposed to improve the conventional method and calculation flow. And the deviation caused by conventional equivalence theory is corrected systematically by the new method. Because the new method is simple and efficient, it is convenient to be implemented into the existing codes to utilize the equivalence theory.