计算α本征值的蒙特卡罗期望估计方法

Monte Carlo expected estimation method for α eigenvalue calculation

从齐次中子输运方程出发,推导了计算α本征值的数学表达式,并给出了三种蒙特卡罗期望估计式,它们分别是:径迹长度期望估计;碰撞期望估计;逃逸期望估计。不同模型的计算结果表明,期望估计方法的计算效率可比MCNP中的(α,k)回归迭代方法有量级的提高。尤其对含慢化材料的次临界模型,期望估计方法有着特殊的优势。

From the basic homogeneous integro-differential equation of neutron transport, three Monte Carlo expected estimator formulations of a based on the eigen-solution are derived. They are Collision estimator, Path-length estimator and Escaping estimator respectively. The unbiased estimation values can be calculated in the process of Monte Carlo simulation. Related numerical results are shown about a specific model and a benchmark model. The calculation efficiency of the Expected Estimation Method is higher than （α,k） iteration method. In special, the new method has advantages in the calculation of sub-critical model with hydrogen material.