[论文解读] Stochastic Point Kinetics Model of Circulating-Fuel Reactors under Perfect Mixing Approximation

Lubomír Bureš, Valeria Raffuzzi|arXiv (Cornell University)|Jan 30, 2026

Nuclear reactor physics and engineering被引用 0

一句话总结

该论文为循环燃料反应堆的低人口动态建立了一个随机框架，推导出从两体积完全混合点动力学模型得到的 Itô SDE，并实现了模拟自然蒙特卡洛与 Milstein 基于求解器。结果显示平均轨迹与确定性解一致，但在某些制度下 DNP 方差被低估，原因是忽略了 DNP 噪声，同时再活性损失估计量存在负偏差。

ABSTRACT

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.

研究动机与目标

• Motivate and model low-population dynamics in circulating-fuel reactors (CFRs) without delay terms.
• Extend modified point kinetics to two perfectly mixed volumes to capture precursor transport between core and ex-core regions.
• Develop and compare two stochastic solvers (AMC and SDE Milstein) for CFR dynamics.
• Benchmark stochastic methods against deterministic solutions and assess variance behavior and bias in estimators.

提出的方法

• Formulate a stochastic process equivalent to the two-volume modified point-kinetics model with neutron and delayed neutron precursor populations in core and ex-core regions.
• Derive an Itô SDE system for N, C_c, and C_e incorporating a diffusion term D(t) and a Milstein-type discretization.
• Implement an analog Monte Carlo (AMC) solver (MARS) that explicitly simulates events from Table 1.
• Implement a semi-implicit Milstein SDE solver with non-uniform time stepping based on a deterministic initial solution.
• Benchmark the AMC and SDE solvers against deterministic solutions using ramp reactivity transients and examine variance and bias.
• Discuss reactivity loss due to precursor drift and its negative estimator bias within the stochastic CFR framework.

实验结果

研究问题

• RQ1 Can a two-volume perfectly mixed CFR model replicate low-population stochastic dynamics without explicit delay terms?
• RQ2 How do AMC and Itô SDE Milstein solvers compare in terms of mean trajectories and variance for CFR dynamics?
• RQ3 Does neglecting DNP noise in the SDE formulation lead to underestimation of DNP variance, and under what regimes does this occur?
• RQ4 What is the behavior of reactivity loss estimators based on stochastic CFR dynamics, and is there a bias introduced by averaging?

主要发现

• Mean neutron and precursor trajectories from AMC and SDE solutions match deterministic solutions.
• Variance from the SDE solver underestimates DNP variance in some regimes compared to AMC.
• Negative bias is observed in the reactivity loss estimator due to DNP drift when computed on-the-fly.
• Reactivity loss estimator converges to the deterministic value as O(1/N0^2), with variance behaving roughly as O(1/N0) in certain analyses.
• For large populations, variances from AMC and SDE align, but discrepancies arise in specific precursor configurations (in-core vs ex-core).
• The DNP noise omission in the SDE formulation is identified as a potential cause for variance underestimation and is highlighted as a topic for future refinement.