nuclear reactors中子布居的逾渗特性
Percolation properties of the neutron population in nuclear reactors
摘要：
反应堆物理学的目的是研究反应堆堆芯在反馈机制（如多普勒温度效应）影响下的中子数量。然而，计算这种耦合随机系统的宏观性质的数值方案需要定义中间量（例如温度场），这是随机中子场和确定性反馈之间的差距。通过将裂变介质中中子在反馈机制影响下的分支随机行走解释为定向渗流过程，并利用生灭过程的统计场论，我们将建立中子输运理论和反应堆物理的随机模型。这个模型的临界指数，结合到所得到的场方程的分析，涉及一个分数拉普拉斯算子将表明，临界扩散方程不能充分描述的空间分布的中子人口和转移，而不是一个临界超扩散方程。对该方程的分析将揭示，在反应堆堆芯中可能会出现不可忽略的偏离平均场行为，这对核工业目前使用的数值方案的可达到的精度提出了质疑。
英文摘要：
Reactor physics aims at studying the neutron population in a reactor core under the influence of feedback mechanisms, such as the Doppler temperature effect. Numerical schemes to calculate macroscopic properties emerging from such coupled stochastic systems however require to define intermediate quantities (e.g. the temperature field), which are bridging the gap between the stochastic neutron field and the deterministic feedback. By interpreting the branching random walk of neutrons in fissile media under the influence of a feedback mechanism as a directed percolation process and by leveraging on the statistical field theory of birth death processes, we will build a stochastic model of neutron transport theory and of reactor physics. The critical exponents of this model, combined to the analysis of the resulting field equation involving a fractional Laplacian will show that the critical diffusion equation cannot adequately describe the spatial distribution of the neutron population and shifts instead to a critical super-diffusion equation. The analysis of this equation will reveal that non-negligible departure from mean field behavior might develop in reactor cores, questioning the attainable accuracy of the numerical schemes currently used by the nuclear industry.
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