Journal of Nuclear Engineering

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

The minimum mass for a critical reactor is well studied whereas the minimum heat production from a nuclear reactor has received little attention. The thermal power of a (sub)critical reactor originates from fission as well as radioactive decay. Fission includes neutron-induced and spontaneous fission. For an idealized critical core, we find that the minimum theoretical power is E_R/Λ, whereas for a subcritical reactor comprising fissionable material undergoing spontaneous fission, the minimum power is dictated by subcritical multiplication. Interestingly, radioisotopic heat generation exceeds the minimum theoretical fission power for most of the fissile materials examined in this study. Full article

Scientific issues that draw international attention from the public and experts during the last 10 years after the Fukushima accident are discussed. An assessment of current severe accident analysis methodology, impact on the views of nuclear reactor safety, dispute on the safety of fishery products, discharge of radioactive water to the ocean, status of decommissioning, and needs for long-term monitoring of the environment are discussed. Full article

Rapid search and localization for nuclear sources can be an important aspect in preventing human harm from illicit material in dirty bombs or from contamination. In the case of a single mobile radiation detector, there are numerous challenges to overcome such as weak source intensity, multiple sources, background radiation, and the presence of obstructions, i.e., a non-convex environment. In this work, we investigate the sequential decision making capability of deep reinforcement learning in the nuclear source search context. A novel neural network architecture (RAD-A2C) based on the advantage actor critic (A2C) framework and a particle filter gated recurrent unit for localization is proposed. Performance is studied in a randomized $20\times 20$ m convex and non-convex simulation environment across a range of signal-to-noise ratio (SNR)s for a single detector and single source. RAD-A2C performance is compared to both an information-driven controller that uses a bootstrap particle filter and to a gradient search (GS) algorithm. We find that the RAD-A2C has comparable performance to the information-driven controller across SNR in a convex environment. The RAD-A2C far outperforms the GS algorithm in the non-convex environment with greater than $95\%$ median completion rate for up to seven obstructions. Full article

The EBR-II benchmark, which was recently included in the International Handbook of Evaluated Reactor Physics Benchmark Experiments, served as a basis for assessing the performance of the SCALE code system for fast reactor analyses. A reference SCALE model was developed based on the benchmark specifications. Great agreement was observed between the eigenvalue calculated with this SCALE model and the benchmark eigenvalue. To identify potential gaps and uncertainties of nuclear data for the simulation of various quantities of interest in fast spectrum systems, sensitivity and uncertainty analyses were performed for the eigenvalue, reactivity effects, and the radial power profile of EBR-II using the two most recent ENDF/B nuclear data library releases. While the nominal results are consistent between the calculations with the different libraries, the uncertainties due to nuclear data vary significantly. The major driver of observed uncertainties is the uncertainty of the ${}^{235}$U (n,$\gamma$) reaction. Since the uncertainty of this reaction is significantly reduced in the ENDF/B-VIII.0 library compared to ENDF/B-VII.1, the obtained output uncertainties tend to be smaller in ENDF/B-VIII.0 calculations, although the decrease is partially compensated by increased uncertainties in ${}^{235}$U fission and $\overline{\nu }$. Full article

Coarse Mesh Finite Difference (CMFD) is a widely-used iterative acceleration method for neutron transport problems in which nonlinear terms are introduced in the derivation of the low-order CMFD diffusion equation. These terms, including the homogenized diffusion coefficient, the current coupling coefficients, and the multiplicative prolongation constant, are subject to numerical instability when a scalar flux estimate becomes sufficiently small or negative. In this paper, we use a suite of contrived problems to demonstrate the susceptibility of CMFD to failure for each of the vulnerable quantities of interest. Our results show that if a scalar flux estimate becomes negative in any portion of phase space, for any iterate, numerical instability can occur. Specifically, the number of outer iterations required for convergence of the CMFD-accelerated transport problem can increase dramatically, or worse, the iteration scheme can diverge. An alternative Linear Diffusion Acceleration (LDA) scheme addresses these issues by explicitly avoiding local nonlinearities. Our numerical results show that the rapid convergence of LDA is unaffected by the very small or negative scalar flux estimates that can adversely affect the performance of CMFD. Therefore, our results demonstrate that LDA is a robust alternative to CMFD for certain sensitive problems in which CMFD can exhibit reduced effectiveness or failure. Full article

The Evaluated Nuclear Data File (ENDF)/B-VIII.0 data library was released in 2018. To assess the new data during development and shortly after release, many validation calculations were performed with static, room-temperature benchmarks. Recently, when performing validation of ENDF/B-VIII.0 for pressurized water reactor depletion calculations, a regression in performance compared to ENDF/B-VII.1 was observed. This paper documents extensive benchmark calculations for light-water reactors performed using continuous energy Monte Carlo code with ENDF/B-VII.1 and -VIII.0 and neutronic characteristics of ENDF/B-VIII.0 are discussed and compared to those of ENDF/B-VII.1. It is our recommendation that ENDF/B data library assessment should include reactor-specific benchmark assessments, including depletion cases, such that these types of regressions may be caught earlier in the data development cycle. Full article