Patchy Nuclear Chain Reactions

Maintaining a deterministic neutron population within a nuclear reactor is critical for safety, especially during startup and shutdown. Automatic safety systems rely on predictable neutron behavior to detect and respond to power excursions. To understand the conditions where fluctuations vanish, experiments were designed and executed at the Rensselaer Polytechnic Institute Reactor Critical Facility (RCF) in 2017. Prior research on fission-induced correlations and simulations had shown strong non-Poissonian patterns, including spontaneous neutron clustering, in decoupled systems. This phenomenon, observed in other areas like life sciences (epidemics, bacteria growth), arises from the asymmetry between particle death (occurring everywhere) and birth (localized near parent particles). Diffusion mitigates these patterns. The question was whether this clustering was a simulation artifact or experimentally observable. This international collaboration aimed to design experiments and detectors to measure neutron fluctuations below saturation thresholds; create a numerical reactor twin for validation and extrapolation; and interpret results through stochastic branching processes. The experiments utilized in-core and ex-core detectors at the RCF, complemented by simulations using the MORET6 Monte Carlo neutron transport code. This paper presents experimental findings, the stochastic model's role in interpreting them, and the implications for reactor safety.

Extensive research has explored fission-induced correlations in nuclear systems, leading to the development of sophisticated simulation capabilities using high-performance computing to characterize fluctuations and correlations. Several numerical simulations have reported strong non-Poissonian patterns affecting neutron spatial distributions, particularly in decoupled systems larger than the neutron mean free path. The occurrence of spontaneous neutron clustering has been a focus of recent studies, raising questions about its experimental observability. The phenomenon of clustering is known to be prevalent in systems where particles diffuse, reproduce, and die, as seen in various life science contexts. The crucial aspect is the asymmetry between ubiquitous death and birth localized near parent particles; diffusion plays a smoothing role. Previous studies have suggested that neutron clustering could occur experimentally in low-power reactors due to the similarities between neutron population dynamics and branching random walks. However, this hypothesis lacked experimental confirmation until this research.

The experimental setup at the RCF involved in-core and ex-core detectors to capture neutron spatial distributions. In-core detectors measured at low power, while ex-core Neutron Multiplicity ³He Array Detectors (NoMAD) measured higher power, preventing saturation. The MORET6 Monte Carlo code served as a numerical twin, simulating the reactor, detection system, and neutron transport. The code incorporated detailed nuclear data, including correlated fission secondaries from 235U and 238U (for both neutron-induced and spontaneous fissions) from the Lawrence Livermore National Laboratory Fission Library. This ensured high-fidelity simulation of the stochastic neutron transport. Massively parallel computing was used to simulate the reactor's startup until neutron population convergence. Data analysis involved comparing experimental and simulated results, characterizing fluctuations using the variance-to-mean ratio, and quantifying spatial correlations via a two-point correlation function. A simplified stochastic model, based on branching random walks, was developed to interpret the findings, incorporating key mechanisms: diffusion, fissions, captures, and leakages. This model incorporated both induced and spontaneous fissions, along with the effect of delayed neutrons.

The experiments and simulations revealed several key findings. First, neutron fluctuations persisted up to surprisingly high reactor powers, showing a "blinking" behavior of the reactor power. The variance-to-mean ratio of the neutron population remained bounded and independent of power for a 1 ms time-gate width, contradicting the unbounded growth predicted by the critical catastrophe model (neglecting spontaneous fissions). The stochastic model, incorporating spontaneous fissions, explained this bounded behavior. However, increasing the time-gate width to 1 s resulted in a variance-to-mean ratio scaling with P², suggesting a recovery of the "critical catastrophe" regime at higher powers. This effect is attributed to delayed neutrons, whose longer emission times allow for increased stochastic noise at large time-gate widths. Secondly, significant spatial correlations were observed, indicating neutron clustering. The spatial correlation function exhibited a linear decay with distance, and its slope was inversely proportional to reactor power. This was again consistent with the stochastic model. The cluster size increased linearly with power, up to the core size. Finally, 2D visualizations of neutron flux confirmed the non-Poissonian distribution in snapshots of the reactor core, visually showing clustered neutron distributions, which confirms the clustering phenomena.

The findings address the research question by demonstrating that neutron fluctuations and spatial correlations can be significant, even at unexpectedly high reactor powers. The bounded fluctuations observed at small time-gate widths are explained by the inclusion of spontaneous fissions in the stochastic model. This contrasts with the critical catastrophe prediction, which does not account for spontaneous fissions. The power-dependent noise and power-independent fluctuations observed depend on the time-gate width used for measurements. The significant spatial correlations and neutron clustering demonstrate the limitations of deterministic descriptions at low powers. The inverse relationship between the slope of the spatial correlation function and reactor power further confirms the clustering effect and its sensitivity to the reactor state. This work extends previous studies by providing experimental evidence of clustering and offering a more comprehensive theoretical framework for understanding neutron behavior in low-power reactors.

This research demonstrates that neutron fluctuations and spatial correlations significantly affect reactor behavior at low power, even in regimes where the reactor should be considered deterministic. The findings highlight the limitations of deterministic models at low powers and the importance of considering the stochastic nature of the nuclear chain reaction. Further research should investigate the impact of burnup effects on the balance between induced and spontaneous fissions and explore the relationship between spatial correlations and reactor power tilts in larger reactors. The development of improved models and advanced detection systems is vital for enhancing nuclear reactor safety and control.

The study is limited by the use of a zero-power reactor (RCF) for experimentation. While the RCF was ideal for the low-power conditions required, extrapolating these findings directly to high-power reactors may require caution. The simplified stochastic model, while successfully interpreting the main results, incorporates several assumptions (homogeneous infinite medium, diffusion approximation) which may not perfectly reflect the complex geometry and heterogeneous composition of real reactors. Finally, the experimental data are not publicly available due to export control regulations on codes and associated simulations, potentially restricting external validation of the results.