Journal of Nuclear Engineering

Distributed multisensor networks record multiple data streams that can be used as inputs to machine learning models designed to classify operations relevant to proliferation at nuclear reactors. The goal of this work is to demonstrate methods to assess the importance of each node (a single multisensor) and region (a group of proximate multisensors) to machine learning model performance in a reactor monitoring scenario. This, in turn, provides insight into model behavior, a critical requirement of data-driven applications in nuclear security. Using data collected at the High Flux Isotope Reactor at Oak Ridge National Laboratory via a network of Merlyn multisensors, two different models were trained to classify the reactor’s operational state: a hidden Markov model (HMM), which is simpler and more transparent, and a feed-forward neural network, which is less inherently interpretable. Traditional wrapper methods for feature importance were extended to identify nodes and regions in the multisensor network with strong positive and negative impacts on the classification problem. These spatial-importance algorithms were evaluated on the two different classifiers. The classification accuracy was then improved relative to baseline models via feature selection from 0.583 to 0.839 and from 0.811 ± 0.005 to 0.884 ± 0.004 for the HMM and feed-forward neural network, respectively. While some differences in node and region importance were observed when using different classifiers and wrapper methods, the nodes near the facility’s cooling tower were consistently identified as important—a conclusion further supported by studies on feature importance in decision trees. Node and region importance methods are model-agnostic, inform feature selection for improved model performance, and can provide insight into opaque classification models in the nuclear security domain. Full article

The nations of the world plan to stop burning carbon fuels but have not fixed on any replacement. For social and economic confidence, they need to share a proper picture of the options. The science is simply explained and not in doubt, though widely misunderstood. Energy sources belong to three distinct groups: renewable, chemical and nuclear. Since human life began, it has adopted each of these in turn. In the past, initial disruptions have been more than off-set by the rise in human values that followed. Now, to complete the final step, we confront those who would look backward to the age of renewables. Instead, the world should look forward to a heavy dependence on nuclear energy with a confidence informed by natural science and openly shared in society. Full article

The Nagoya University Accelerator-driven Neutron Source (NUANS) is an accelerator-based neutron source by ⁷Li(p,n)⁷Be reaction with a 2.8 MeV proton beam up to 15 mA. The fast neutrons are moderated and shaped to beam with a Beam Shaping Assembly (BSA). NUANS is aiming at the basic study of the Boron Neutron Capture Therapy (BNCT) such as an in vitro cell-based irradiation experiment using a water phantom. Moreover, the BSA is developed as a prototype of one for human treatment. We have evaluated the radiation field of NUANS by a Monte Carlo code PHITS. It is confirmed that the radiation characteristics at the BNCT outlet meet the requirement of IAEA TECDOC-1223. Additionally, the radiation field in the water phantom located just in front of the BSA outlet is calculated. In the in vitro irradiation experiment, the boron dose of 30 Gy-eq, which is the dose to kill tumor cells, is expected for 20 min of irradiation at the beam current of 15 mA. Full article

The application of the recently developed “nth-order comprehensive sensitivity analysis methodology for nonlinear systems” (abbreviated as “nth-CASAM-N”) has been previously illustrated on paradigm nonlinear space-dependent problems. To complement these illustrative applications, this work illustrates the application of the nth-CASAM-N to a paradigm nonlinear time-dependent model chosen from the field of reactor dynamics/safety, namely the well-known Nordheim–Fuchs model. This phenomenological model describes a short-time self-limiting power transient in a nuclear reactor system having a negative temperature coefficient in which a large amount of reactivity is suddenly inserted, either intentionally or by accident. This model is sufficiently complex to demonstrate all the important features of applying the nth-CASAM-N methodology yet admits exact closed-form solutions for the energy released in the transient, which is the most important system response. All of the expressions of the first- and second-level adjoint functions and, subsequently, the first- and second-order sensitivities of the released energy to the model’s parameters are obtained analytically in closed form. The principles underlying the application of the 3rd-CASAM-N methodology for the computation of the third-order sensitivities are demonstrated for both mixed and unmixed second-order sensitivities. For the Nordheim–Fuchs model, a single adjoint computation suffices to obtain the six 1st-order sensitivities, while two adjoint computations suffice to obtain all of the 36 second-order sensitivities (of which 21 are distinct). This illustrative example demonstrates that the number of (large-scale) adjoint computations increases at most linearly within the nth-CASAM-N methodology, as opposed to the exponential increase in the parameter-dimensional space which occurs when applying conventional statistical and/or finite difference schemes to compute higher-order sensitivities. For very large and complex models, the nth-CASAM-N is the only practical methodology for computing response sensitivities comprehensively and accurately, overcoming the curse of dimensionality in sensitivity analysis of nonlinear systems. Full article

This work presents the n^th-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (n^th-CASAM-N), which enables the most efficient computation of exactly determined expressions of arbitrarily high-order sensitivities of generic nonlinear system responses with respect to model parameters, uncertain boundaries, and internal interfaces in the model’s phase space. The mathematical framework underlying the n^th-CASAM-N is proven to be correct by using mathematical induction. The n^th-CASAM-N is formulated in linearly increasing higher-dimensional Hilbert spaces—as opposed to exponentially increasing parameter-dimensional spaces—thus overcoming the curse of dimensionality in sensitivity analysis of nonlinear systems. Full article

In recent years, there has been a growing interest in the design, development and commercialization of nuclear power Small Modular Reactors (SMRs). Actual SMR designs cover the full spectrum of nuclear reactor technologies, including water-, gas-, liquid-metal-, and molten-salt-cooled. Despite physical and technological differences, SMRs share some relevant design features, such as small size, modularity, inherent and passive safety systems. These features are expected to enhance availability, recoverability, promptness and robustness, thereby contributing to the resilience of power supply. Thanks to the peculiar design features of SMRs, they are likely to satisfy a number of Functional Requirements (FRs) for this objective, namely: (i) low vulnerability to external hazards; (ii) natural circulation of primary coolant; (iii) prompt, unlimited and independent core cooling under shutdown conditions; (iv) shutdown avoidance in response to variations of the offsite power supply quality and electrical load; (v) island mode operation; (vi) robust load-following; (vii) independent, self-cranking start. These make advanced Nuclear Power Plants (aNPPs) comprised of SMRs perfect candidates to withstand a broader range of natural disruptions and to recover faster from them, compared to conventional Nuclear Power Plants (cNPPs), thus rendering them a major potential asset for guaranteeing resilience and security of power supply. The review focuses on Natural Technological (NaTech) events that impact a typical Integrated Energy System (IESs) within which SMRs are embedded: IESs are, indeed, being developed to integrate different power generation plants with gas facilities, through gas and electricity infrastructures, because they are expected to bring increased security and resilience of power supply, as shown in the qualitative case study presented. Full article

Microdosimetry is increasingly adopted in the characterization of proton and carbon ion beams used in cancer therapy. Spectra and mean values of lineal energy calculated in frequency and dose are seen by many as the tools which, by complementing dosimetric measurements, allow for the most complete characterization of the therapeutic radiation fields. The urgency is now to consolidate the experience and converge to commonly accepted methodologies. In this context, the purpose of this work is to study the effects of the energy-loss straggling and the delta-ray escape, considering slab-sensitive volumes; these are, in fact, the typical shapes of solid-state microdosimeters, which are widely used in investigating light ion therapy beams. The method considers the energy distribution of delta rays resulting from the collision of the impinging ion and, taking into account the escape, convolutes it with itself as many times as the expected number of collisions in the sensitive volume thickness. The resulting distribution is compared to the experimental microdosimetric spectrum showing a substantially good agreement. The extension of the methodology to a wider range of ion energy and detector characteristics is instrumental for a detector-independent microdosimetric assessment of the radiation fields. Full article

Fast neutron identification and spectroscopy is of great interest to nuclear physics experiments. Using the neutron elastic scattering, the fast neutron momentum can be measured. Wang and Morris introduced the theoretical concept that the initial fast neutron momentum can be derived from up to three consecutive elastic collisions between the neutron and the target, including the information of two consecutive recoil ion tracks and the vertex position of the third collision or two consecutive elastic collisions with the timing information. Here, we also include the additional possibility of measuring the deposited energies from the recoil ions. In this paper, we simulate the neutron elastic scattering using the Monte Carlo N-Particle Transport Code (MCNP) and study the corresponding neutron detection and tracking efficiency. The corresponding efficiency and the scattering distances are simulated with different target materials, especially natural silicon (92.23%${}^{28}$Si, 4.67%${}^{29}$Si, and 3.1%${}^{30}$Si) and helium-4 (${}^4$He). The timing of collision and the recoil ion energy are also investigated, which are important characters for the detector design. We also calculate the ion traveling range for different energies using the software, “The Stopping and Range of Ions in Matter (SRIM)”, showing that the ion track can be most conveniently observed in ${}^4$He unless sub-micron spatial resolution can be obtained in silicon. Full article

The release of fission products and fuel materials from a molten-salt fast-reactor fuel in hypothetical accident conditions was investigated. The molten-salt fast reactor in this investigation features a fast neutron spectrum, operating in the thorium cycle, and it uses LiF-ThF₄-UF₄ as a fuel salt. A coupling between the severe accident code MELCOR and thermodynamical equilibrium solver GEMS, the so-called cGEMS, with the updated HERACLES database was used in the modeling work. The work was carried out in the frame of the EU SAMOSAFER project. At the beginning of the simulation, the fuel salt is assumed to be drained from the reactor to the bottom of a confinement building. The containment atmosphere is nitrogen. The fission products and salt materials are heated by the decay heat, and due to heating, they are evaporated from the surface of a molten salt pool. The chemical system in this investigation included the following elements: Li, F, Th, U, Zr, Np, Pu, Sr, Ba, La, Ce, and Nd. In addition to the release of radioactive materials from the fuel salt, the formation of aerosols and the vapor-phase species in the modeled confinement were determined. Full article

This work illustrates the application of the fourth-order comprehensive sensitivity analysis methodology for nonlinear systems (abbreviated as “4th-CASAM-N”), which enables the efficient computation of exactly determined 1st-, 2nd-, 3rd-, and 4th-order functional derivatives of results produced by computational models with respect to the model’s parameters. Results produced by computational models are called model “responses” and the respective functional derivatives are called “sensitivities” (with respect) to model parameters. The qualifier “comprehensive” indicates that the 4th-CASAM-N methodology enables the exact and efficient computation not only of response sensitivities with respect to customary model parameters (including computational input data, correlations, initial and/or boundary conditions) but also with respect to imprecisely known material boundaries, as would be caused by manufacturing tolerances. The 4th-CASAM-N enables the hitherto very difficult, if not intractable, exact computation of all of the 1st-, 2nd-, 3rd-, and 4th-order response sensitivities for large-scale systems involving many parameters, as usually encountered in practice. A paradigm model that describes nonlinear heat conduction through a material has been chosen to illustrate the application of the 4th-CASAM-N methodology, as this model enables the derivation of tractable closed-form analytical expressions of representative 1st-, 2nd-, 3rd-, and 4th-order response sensitivities while largely avoiding side-tracking algebraic manipulations. The responses chosen for this paradigm model include not only physically measurable quantities but also a synthetic response designed to illustrate the enormous possible reduction in the number of computation when using the 4th-CASAM-N (rather than other methods) for computing response sensitivities. Full article

This work presents the fourth-order comprehensive sensitivity analysis methodology for nonlinear systems (abbreviated as “4th-CASAM-N”) for exactly and efficiently computing the first-, second-, third-, and fourth-order functional derivatives (customarily called “sensitivities”) of physical system responses (i.e., “system performance parameters”) to the system’s (or model) parameters. The qualifier “comprehensive” indicates that the 4th-CASAM-N methodology enables the exact and efficient computation not only of response sensitivities with respect to the customary model parameters (including computational input data, correlations, initial and/or boundary conditions) but also with respect to imprecisely known material boundaries, caused by manufacturing tolerances, of the system under consideration. The 4th-CASAM-N methodology presented in this work enables the hitherto very difficult, if not intractable, exact computation of all of the first-, second-, third-, and fourth-order response sensitivities for large-scale systems involving many parameters, as usually encountered in practice. Notably, the implementation of the 4th-CASAM-N requires very little additional effort beyond the construction of the adjoint sensitivity system needed for computing the first-order sensitivities. The application of the principles underlying the 4th-CASAM-N to an illustrative paradigm nonlinear heat conduction model will be presented in an accompanying work. Full article

This work discusses challenges and approaches to uncertainty analyses associated with the development of a nuclide inventory benchmark for fuel irradiated in a boiling water reactor. The benchmark under consideration is being developed based on experimental data from the SFCOMPO international database. The focus herein is on how to address missing data in fuel design and operating conditions that are important for adequately simulating the time-dependent changes in fuel during irradiation in the reactor. The effects of modeling assumptions and uncertainties in modeling parameters on the calculated nuclide inventory were analyzed and quantified through computational models developed using capabilities in the SCALE code system. Particular attention was given to the impact of the power history and water coolant density on the calculated nuclide inventory, as well as to the effect of geometry modeling considerations not usually addressed in a nuclide inventory benchmark. These considerations include gap closure, channel bow, and channel corner radius, which do not usually apply to regular reactor operation but are relevant for assessing impacts of potential anomalous operating scenarios. Full article

This work quantifies the impact of the most important 4th-order sensitivities of the leakage response of a polyethylene-reflected plutonium (PERP) reactor physics benchmark with respect to the benchmark’s 180 group-averaged microscopic total cross sections, on the expected value, variance and skewness of the benchmark’s leakage response. This work shows that, as the standard deviations of the cross sections increase, the contributions of the 4th-order sensitivities to the response’s expected value and variance become significantly larger than the corresponding contributions stemming from the 1st-, 2nd- and 3rd-order sensitivities. Considering a uniform 5% relative standard deviation for all microscopic total cross sections, the contributions from the 4th-order sensitivities to the expected value and variance of the PERP leakage response amount to 56% and 52%, respectively. Considering 10% uniform relative standard deviations for the microscopic total cross sections, the contributions from the 4th-order sensitivities to the expected value increase to nearly 90%. Consequently, if the computed value L(a) were considered to represent the actual expected value of the leakage response and the 4th-order sensitivities were neglected, the computed value would represent the actual expected value with an error of 3400%. Furthermore, uniform relative standard deviations of 5% and larger (10%) for the microscopic total cross sections cause the higher-order sensitivities to contribute increasingly higher amounts to the response standard deviation: the contributions stemming from the 4th-order sensitivities are larger than the contributions stemming from the 3rd-order sensitivities, which in turn are larger than those stemming from the 2nd-order sensitivities, which are themselves larger than the contributions stemming from the 1st-order sensitivities. This finding evidently underscores the need for computing sensitivities of order higher than first-order. The results obtained in this work also indicate that the 4th-order sensitivities produce a positive response skewness, causing the leakage response distribution to be skewed towards the positive direction from its expected value. Increasing the parameter standard deviations tends to decrease the value of the response skewness, causing the leakage response distribution to become more symmetrical about the mean value. The results presented in this work highlight the finding that the microscopic total cross section for hydrogen (H) in the lowest (“thermal”) energy group is the single most important parameter among the 180 microscopic total cross sections of the PERP benchmark, as it contributes most to the various response moments. Full article

In this paper, the artificial neural networks (ANN) based deep learning (DL) techniques were developed to solve the neutron diffusion problems for the continuous neutron flux distribution without domain discretization in advance. Due to its mesh-free property, the DL solution can easily be extended to complicated geometries. Two specific realizations of DL methods with different boundary treatments are developed and compared for accuracy and efficiency, including the boundary independent method (BIM) and boundary dependent method (BDM). The performance comparison on analytic benchmark indicates BDM being the preferred DL method. Novel constructions of trial function are proposed to generalize the application of BDM. For a more in-depth understanding of the BDM on diffusion problems, the influence of important hyper-parameters is further investigated. Numerical results indicate that the accuracy of BDM can reach hundreds of times higher than that of BIM on diffusion problems. This work can provide a new perspective for applying the DL method to nuclear reactor calculations. Full article

The safety performance of nuclear power plants (NPPs) is a very important factor in evaluating nuclear energy sustainability. Safety analysis of passive and active safety systems have a positive influence on reactor transient mitigation. One of the common transients is primary coolant leg rupture. This study focused on guillotine large break loss of coolant (LB-LOCA) in one of the reactor vessels, in which cold leg rupture occurred, after establishment of a steady-state condition for the VVER-1000. The reactor responses and performance of emergence core cooling systems (ECCSs) were investigated. The main safety margin considered during this simulation was to check the maximum value of the clad surface temperature, and it was then compared with the design licensing limit of 1474 K. The calculations of event progression used the engineering-level RELAP5/SCDAPSIM/MOD3.5 thermal-hydraulic program, which also provide a more detailed treatment of coolant system thermal hydraulics and core behavior. The obtained results show that actuation of ECCSs at their actuation set points provided core cooling by injecting water into the reactor pressure vessel, as expected. The peak cladding temperature did not overpass the licensing limit during this LB-LOCA transient. The primary pressure above the core decreased rapidly from 15.7 MPa to 1 MPa in less than 10 s, then stabilizes up to the end of transient. The fuel temperature decreased from 847 K to 378 K during the first 30 s of the transient time. The coolant leakage reduced from 9945 kg/s to approximately 461 kg/s during the first 190 s in the transient. Overall, the study shows that, within the design of the VVER-1000, safety systems of the have inherent robustness of containing guillotine LB-LOCA. Full article

Many rate theory models of cavity (void) swelling have been published over the past 50 years, all having the same, or similar, structures. A rigorous validation of the models has not been possible because of the dearth of information concerning the microstructures that correspond with the swelling data. Whereas the lack of microstructure information is still an issue for historical swelling data, in the past 10–20 years data have been published on the evolution of the microstructure (point defect yields from collision cascades, cavity number densities, and dislocation densities/yield strengths) allowing certain gaps in information to be filled when considering historic swelling data. With reasonable estimates of key microstructure parameters, a standard rate theory model can be applied, and the model parameter space explored, in connection with historical swelling data. By using published data on: (i) yield strength as a function of dose and temperature (to establish an empirical expression for dislocation density evolution); (ii) cavity number densities as a function of temperature; and (iii) freely migrating defect (FMD) production as a function of primary knock-on atom (PKA) spectrum, the necessary parameter and microstructure inputs that were previously unknown can be used in model development. This paper describes a rate-theory model for void swelling of 316 stainless steel irradiated in the EBR-2 reactor as a function of irradiation temperature and neutron dose. Full article

This paper presents a new approach to the spent nuclear fuel (SNF) problem, which is uniquely enabled by a liquid fuel form, specifically as in the case of molten salt reactor (MSR) systems. Managing the SNF problem is critical for public acceptance of nuclear power as a climate change solution. An MSR can be refueled while operating by adding more fresh fuel salt, which grows the in-core fuel salt volume. This growth will eventually double the size of the original fuel salt, allowing to start another core with this excess fuel so long as the daughter reactor is of the same design and there is sufficient excess fuel. This study explores how such a “sourdough” strategy would work in MSRs and provides an initial calculation methodology to find the correct refueling rates to match the desired growth curve of power generation. Higher uranium enrichment levels of the refuel salt result in lower refueling rates and thus a longer doubling time. As a result, the refuel salt uranium enrichment can be tailored to match a postulated clean power generation capacity expansion. This approach allows postponing the spent nuclear fuel disposal issue using the sourdough method. Along with the MSR fuel’s unique properties, it suggests a new path towards managing nuclear waste until long-term solutions become economically viable. Full article

Diamond is widely studied and used for the detection of direct and indirect ionizing particles because of its many physical and electrical outstanding properties, which make this material very attractive as a fast-response, high-radiation-hardness and low-noise radiation detector. Diamond detectors are suited for detecting almost all types of ionizing radiation (e.g., neutrons, ions, UV, and X-ray) and are used in a wide range of applications including ones requiring the capability to withstand harsh environments (e.g., high temperature, high radiation fluxes, or strong chemical conditions). After reviewing the basic properties of the diamond detector and its working principle detailing the physics aspects, the paper discusses the diamond as a neutron detector and reviews its performances in harsh environments. Full article