次临界系统中α本征值与k本征值的关系

Relationship between the α eigenvalue and the k eigenvalue in subcritical systems

以Godiva临界模型为基础,建立了两种次临界模型,并计算了两种模型中不同易裂变核材料含量的k本征值和α本征值。结果表明,并非k越小,α就会越小。对于含氢介质较多的系统,即使k很小,由于瞬发中子寿命很大,α也会接近于0,因而α不能直观地表征系统的临界特性,而k比α更适合这样的系统。对瞬发中子寿命较小的次临界系统,α绝对值较大,能直观地显示系统中子随时而间的衰减行为,对这种系统,使用α是合适的。

Two subcritical fission models were developed based on the Godiva critical system to calculate the variation of the k eigenvalues and the α eigenvalues with mass variations of fissile material.The results show that the α eigenvalue does not increase linearly with the k eigenvalue.Even though the k eigenvalue is very small,the α eigenvalue is close to zero in subcritical system with many hydrogen nuclei,which has a very long prompt neutron removal lifetime.For such systems,the k eigenvalue is a much more convenient criteria than the α eigenvalue for describing criticality.The α eigenvalue can usually describe neutron decay in subcritical systems which have a short prompt neutron removal lifetime and a large absolute value of α.