Monte Carlo Simulation in Reactor Physics

With the increasing demand for high-fidelity neutronics analysis and the development of computer technology, the Monte Carlo method is becoming increasingly important, especially in the critical analysis of initial core and shielding calculations. This is due to its advantages, such as flexibility in geometry treatment, the ability to use continuous-energy pointwise cross sections, the ease of parallelization, and the high fidelity of simulations. In the last year, many next-generation Monte Carlo codes were developed, including MCNP6, OpenMC, MC21, SHIFT, TRIPOLI, Geant4, Serpent, MCCARD, MCS, RMC, SuperMC, and JMCT. These codes are designed to achieve full core calculations and analyses with high fidelity and efficiency by means of advanced methodologies and algorithms as well as high-performance computing techniques.

The rapid evolution of these sophisticated codes and methodologies has, in turn, fueled a broader and deeper application of the Monte Carlo approach across nearly all facets of reactor physics. Beyond traditional criticality and shielding calculations, its scope now extends to high-fidelity depletion and fuel cycle analysis [1], multi-physics coupling [2], sensitivity and uncertainty quantification [3], and the simulation of advanced reactor [4] concepts where complex geometries and novel materials are the norm. This expanding frontier is characterized by a series of intricate challenges and research opportunities, ranging from managing computational cost and mitigating statistical uncertainties to rigorously validating nuclear data and developing novel variance reduction techniques. It is within this dynamic and challenging context that this Special Issue seeks to present a curated collection of recent advances, highlighting how state-of-the-art Monte Carlo simulations are being leveraged to solve complex problems and push the boundaries of nuclear engineering knowledge.

To capture these advances and catalyze further innovation, we have organized this Special Issue entitled “Monte Carlo Simulations in Reactor Physics” within the Journal of Nuclear Engineering. For this Special Issue, a number of manuscripts were submitted for consideration, all of which were subjected to a rigorous peer-review process. In total, six high-quality research papers were finally accepted for publication and inclusion in this Special Issue. The contributions are listed below.

Niichel et al. [5] introduces a novel open-source MATLAB application designed to overcome the limitations of established codes like MCNP and GADRAS, which are often subject to export controls, steep learning curves, and high computational demands. By implementing a hybrid Monte Carlo method that cleverly integrates stochastic sampling with analytical relationships, the tool achieves remarkable computational efficiency, generating simulated spectra for NaI(Tl) and HPGe detectors in seconds on standard hardware. Benchmarked against experimental data, it maintains reasonable accuracy in replicating key spectral features. This work provides an accessible and practical alternative for educational training and preliminary design studies.

Jia et al. [6] investigate a subtle yet critical issue in high-fidelity reactor analysis: the emergence of nonphysical negative KERMA factors during nuclear data processing. Through a detailed analysis of the RBEC M lead-cooled fast reactor benchmark using cross-section libraries from ENDF/B VII.1 and CENDL 3.2, the authors quantify the resultant deviations in heating rate calculations. The research reveals that while the effect is negligible in fuel regions dominated by fission, deviations of up to 6.46 percent can occur in reflector regions where gamma heating is prevalent. These findings underscore the paramount importance of consistent nuclear data evaluation and provide crucial guidance for improving the accuracy of multi-physics simulations, particularly for the thermal hydraulic design of non-fuel components in advanced reactor systems.

Tuya et al. [7] pioneer a groundbreaking exploration at the intersection of machine learning and neutron transport theory. The authors propose a novel paradigm in which artificial neural networks are employed to estimate a continuous representation of the iterated fission probability—a quantity proportional to the adjoint neutron flux—across the entire phase space. Trained using discrete data generated via a Monte Carlo method for both fast and thermal spectrum systems, the neural network models successfully learn the underlying distribution, albeit with limitations in resolving sharp resonance structures. This research validates neural-network-based methods’ potential to complement conventional techniques, offering a new avenue for obtaining continuous valued observables in complex reactor environments.

Wu et al. [8] addressed a fundamental requirement for the precise design of water-cooled small modular reactors by generating high-fidelity thermal-neutron-scattering data for light water. The authors implemented both the GA and IKE scattering kernel models in their LIPER code to produce temperature-dependent scattering cross sections. The results show excellent agreement with established benchmarks, with negligible reactivity deviations below 0.2 pcm. This study establishes a reliable and high-fidelity foundation for advancing the neutronic and thermal hydraulic modeling of small modular reactor cores, a feat that is particularly vital for the design of systems utilizing supercritical water conditions.

Raposio et al. [9] propose an innovative materials science strategy for enhancing the sustainability and non-proliferation characteristics of molybdenum 99 production. The concept involves substituting a portion of the uranium 238 in UO₂ targets with cerium, an element with similar chemical properties but without the undesirable tendency to produce transuranic isotopes. Detailed MCNP6.2 simulations demonstrate that this substitution drastically reduces the production of the proliferation-sensitive isotope plutonium 239 by orders of magnitude while maintaining the yield of molybdenum 99. The proposed CeO₂-UO₂ composite achieves a high sustainability index while also promising significant economic benefits, outlining a viable pathway towards more environmentally benign and economically competitive radioisotope production.

Chu et al. [10] provide a thorough Monte Carlo-based investigation into the efficiency of fast neutron tracking methods utilizing elastic scattering in silicon and helium 4 targets. Using MCNP simulations, the authors evaluate three distinct methodologies, analyzing key performance parameters such as detection efficiency, scattering distances, and ion recoil energies. The study delivers critical design insights, identifying gaseous time projection chambers as ideal because of their millimeter scale ion tracks, whereas solid-state silicon detectors require challenging sub-micron spatial resolution. This work offers invaluable guidance for optimizing next-generation neutron detectors for applications in nuclear security, non-proliferation, and fundamental science.

The six research papers featured in this Special Issue collectively underscore the vital and expanding role of Monte Carlo simulations across a diverse spectrum of reactor physics applications. These works span detector optimization, nuclear data validation, machine-learning-enhanced flux estimation, and sustainable isotope production, directly addressing pressing challenges in computational efficiency, data accuracy, and model fidelity for advanced nuclear systems. A common theme is the growing reliance on high-fidelity, multi-physics simulation tools capable of supporting the design, safety analysis, and optimization of next-generation reactors, especially in scenarios where experimental data are limited or system complexity challenges traditional deterministic methods.

For the future, researchers should prioritize the development of integrated digital twins that fuse real-time monitoring data, multi-physics coupling, and AI-driven surrogate modeling to achieve predictive and adaptive simulation capacity. Concurrently, further effort is essential to apply Monte Carlo methods to more-extreme environments, such as fusion neutronics, severe accident analysis, and long-term fuel cycle simulations. Bridging the gap between high-fidelity simulation and practical engineering design through robust uncertainty quantification, model reduction techniques, and next-generation high-performance computing will be crucial. These advancements are fundamental to realizing the goal of robust, sustainable, and economically viable nuclear energy systems in the coming decades.