循环燃料反应堆在完美混合近似下的随机点动力学模型
Stochastic Point Kinetics Model of Circulating-Fuel Reactors under Perfect Mixing Approximation
AI总结：
本文提出了一种随机框架，用于模拟循环燃料反应堆中低人口动态，捕捉延迟中子前体运输而不引入延迟项，通过改进的点动力学模型和Itô随机微分方程系统，展示了AMC和半隐式Milstein求解器在瞬态基准中的有效性，揭示了SDE方法在某些情况下低估了前体方差。
摘要：
我们提出了一种随机框架，用于低人口动态的循环燃料反应堆（CFRs），该框架捕捉延迟中子前体（DNP）运输而不引入延迟项。从一个改进的点动力学模型出发，该模型包含两个完美混合的体积，推导出等效的离散事件动力学和Itô随机微分方程（SDE）系统。实现了两种求解器：类比蒙特卡罗（AMC）引擎和半隐式Milstein SDE求解器。瞬态基准测试显示，AMC/SDE的均值与确定性解完美一致，同时揭示SDE方法在某些情况下低估了DNP的方差，可能由于忽略了DNP噪声。我们进一步将由于前体漂移导致的反应性损失重新表述为这种随机设置，并显示其估计器存在负偏倚。总体而言，所开发的框架提供了一个最小但具有代表性的CFR低人口动力学模型。未来的工作将重新推导和测试SDE噪声项，并将该框架应用于选定的瞬态应用，如CFR的启动分析。
英文摘要：
We present a stochastic framework for low-population dynamics in circulating-fuel reactors (CFRs) that captures delayed-neutron precursor (DNP) transport without delay terms. Starting from a modified point-kinetics model with two perfectly-mixed volumes, we derive equivalent discrete-event dynamics and an Itô stochastic differential equation (SDE) system. Two solvers are implemented: an analog Monte Carlo (AMC) engine and a semi-implicit Milstein SDE solver. Transient benchmarks demonstrate perfect agreement of AMC/SDE means with deterministic solutions, while revealing that the SDE approach underestimates DNP variances in selected regimes, potentially due to the neglect of DNP noise. We further recast reactivity loss due to precursor drift in this stochastic setting and show that its estimator is negatively biased. Overall, the developed framework provides a minimal yet representative model for CFR low-population kinetics. Future work will re-derive and test SDE noise terms and apply the framework to selected transient applications such as start-up analyses of CFRs.
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