脉冲堆有限裂变链长的数学期望值分析(英文)

Expected Value of Finite Fission Chain Lengths of Pulse Reactors

摘要: 讨论了在一个增殖系统引发一个持续裂变链所需要的平均中子数。在点堆模型基础上, 考虑了在 t0 时刻系统引入一个源中子, 在 t 时刻产生 n 个中子的概率(n, t0, t), 推导了概率生成函数 G(z; t0, t)所满足的偏微分方程, 并得到了近似解。用近似解计算了GodivaII脉冲堆的有限裂变链长数学期望值, 有限裂变链期望值反比于脉冲堆的反应性。

Abstract: The average neutron population necessary for sponsoring a persistent fission chain in a multiplying system, is discussed. In the point reactor model, the probability function (n, t0, t) of a source neutron at time t0 leading to n neutrons at time t is dealt with. The nonlinear partial differential equation for the probability generating function G(z; t0, t) is derived. By solving the equation, we have obtained an approximate analytic solution for a slightly prompt supercritical system. For the pulse reactor GodivaⅡ, the mean value of finite fission chain lengths is estimated in this work and shows that the estimated value is reasonable for the experimental analysis.