Calculating Criticality

By Owen Summerscales | November 1, 2023

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Since its foundation in 1943, Los Alamos has been designing experiments and crunching numbers to determine nuclear criticality parameters. At the time, it was blazing a trail into the terra incognita of nuclear science, a brand-new discipline that opened doors to both nuclear power and powerful weapons. Today, the Laboratory is still hard at work improving its knowledge of critical and sub-critical systems and collaborates with national and international partners to improve the safety and efficiency of nuclear systems by combining modern data science techniques with advanced experimental capabilities.

Criticality safety is a paramount consideration in the handling of fissile and fissionable materials such as plutonium-239. Uncontrolled nuclear chain reactions can result in dangerous bursts of high energy radiation and when these reactions are triggered accidentally, injuries or even fatalities may result. The Los Alamos report A Review of Criticality Accidents (McLaughlin et al. 2000) details 60 criticality accidents from 1944 to 1999 that caused 21 deaths globally (see Actinide Research Quarterly, 2022, First Quarter, for more information on the Demon Core criticality accidents during the Manhattan Project). Of these 60 incidents, 22 occurred in process environments outside nuclear reactor cores or experimental assemblies, 21 of which occurred with solutions, and 38 in small experimental reactors and other test assemblies. The discipline of criticality safety has consequently been shaped by these accidents and is now based on prevention with careful system analysis and prediction.

Researchers at Los Alamos have recently identified potential improvements to the criticality limits used in the aqueous chloride (AQCL) operations at the Plutonium Facility (PF-4), which are part of the plutonium recovery efforts. These improvements should reduce both worker radiation dose and operational costs, and could also increase batch processing rates in fundamental work tied to pit production. To meet mission requirements to produce a minimum of 30 pits per year by 2026, it is essential that all the manufacturing steps involving plutonium are examined in detail and streamlined while maintaining criticality safety standards.

How criticality parameters are developed 

Nuclear chain reactions are affected by a range of parameters summarized by the acronym MAGIC MERV (mass, absorption, geometry, interaction, concentration, moderation, enrichment, reflection, and volume); temperature is also a factor. These parameters are carefully controlled and used as inputs in computer models. Calculations are performed using advanced neutron transport codes, such as the Monte Carlo N-Particle® (MCNP®) code developed at Los Alamos (read about the history of the Monte Carlo method at Los Alamos on p35). These models, which approximate the properties of a nuclear system or operation, are combined with credible unfavorable conditions to give a set of operational limits that govern the bounds of safe work with fissile materials. This includes mass limits, volume restrictions, and handling practices which are incorporated into operator training.

Although fissile solids have been successfully modeled with the above method, aqueous fissile solutions pose a different and more complex challenge that has not yet been adequately solved. Even simple properties such as density are not well known for fissile solutions relevant to nuclear energy and security. Furthermore, chemical solutions are inherently variable in ways that counterintuitively affect criticality risk—these factors include container geometry,* concentration, chemical speciation/

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Figure 1. José Benito Vigil IV and Nathan Robbins (PT-1) working at TA-55 using a metal chlorination process. Courtesy: Nathaniel Madlem.

reactivity, and light element neutron moderators (which slow down fast neutrons and make them more effective in the fission chain reaction). *Thin slab tanks, small diameter pencil tanks, annular tanks, and other designs have been used for criticality safety for solutions.

At present, limits at PF-4 for aqueous chloride processing are calculated without accounting for chlorine, although chlorine-35 is known by differential measurements to have high thermal neutron capture. The aqueous mixture density is simply extrapolated from the density of solid α-plutonium (19.8 g/cm3; for comparison, the density of water is defined as 1 g/cm3) and includes only plutonium and water. These assumptions represent an overly conservative approach, currently allowing for a maximum of 520 g of plutonium in solution. Furthermore, criticality is attenuated by the presence of chlorine-35 in hydrochloric acid and metal salts, which are physically required for the plutonium to be dissolved in solution. In the available nuclear data, there are very few experimental benchmarks used for code validation that are sensitive to chlorine-35 (n,γ), and of these few benchmarks, the sensitivity is much lower than the application.

Improving the models 

Researchers at Los Alamos have recently asked themselves, how can we improve the accuracy of our solution models? To answer this question, they designed a series of experiments with the aid of machine learning protocols that characterize key features of aqueous plutonium chloride solutions. The experiments had two main objectives: (i) benchmarking neutron absorption from chlorine, and (ii) determining plutonium solution densities.

The research team investigated chlorine neutron absorption in the Chlorine Worth Study (CWS), which included critical experiments using a fissile fuel and chlorine-containing material. These experiments were designed using machine learning methods to match the chlorine absorption sensitivities for AQCL operations at PF-4. The CWS experiments took place at the National Criticality Experiments Research Center (NCERC), owned and operated by Los Alamos at the Nevada

Nuclear Security Site (NNSS), over three weeks in December 2021. Experiments were performed by a team including co-leads Theresa Cutler (NEN-2) and Travis Grove (NEN-2), along with Kelsey Amundson (NEN-2), Jesson Hutchinson (NEN-2), Noah Kleedtke (XCP-5), and Nicholas Wynne (NEN-2). The concluding task of integrating the data to generate a final benchmark is underway and is intended to be completed by spring 2023.

Plutonium solution characteristics were investigated for a ternary mixture of plutonium chloride, hydrochloric acid, and water (PuClx/HCl/H2O) by measuring water activity and solution density. This work is ongoing and aims to incorporate experimental density data into a function density law using the semi-empirical Pitzer equation, which then would be implemented in the MCNP model. The team who performed this work include the following: Kelly Aldrich (C-AAC) and Dung Vu (C-AAC) as project lead and co-lead; Laura Worl* (DPO-MRR) as funding manager; Kimberly Bonilla (C-AAC) and Justin Cross (C-AAC) as contributing researchers; Steve Willson (C-AAC), Jennifer Alwin* (XCP-7), Riley Bulso* (NCS), Alicia Salazar Crockett* (NCS), Theresa Cutler* (NEN-2), David Kimball* (AMPP-4), and James Bunsen* (AMPP-4) in advisory roles. *Contributed to both CWS and solution density experiments.

Effective neutron multiplication factor 

In nuclear reactor theory, the neutron multiplication factor k is a key ratio that represents the average number of neutrons from one fission that causes another fission. If k is less than 1, the system is subcritical and cannot sustain a chain reaction; the neutron population will exponentially decay. If k = 1, the reaction is critical, and the neutron population will remain constant. Finally, if k is greater than 1, the reaction is supercritical, and the neutron population will grow exponentially.

For criticality safety, k must always be less than 1 when handling fissile materials. There is an additional margin of around 0.05 below this cutoff for all normal and credible abnormal process conditions, but the exact figure varies based on the circumstances. MCNP codes produce the effective neutron multiplication factor keff as an output eigenvalue, which informs scientists of the criticality risk. This parameter is defined as the ratio of the number of free neutrons in a generation to the number of neutrons in the previous generation, accounting for all fission contributions and losses due to scattering, absorption, and leakage.

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Chlorine-35: Neutron sink 

Aqueous chloride operations involve significant quantities of chlorine, largely in the form of hydrochloric acid, chloride salts, and plutonium chloride in aqueous solution. Previous differential experiments have characterized a large thermal neutron cross section for the stable isotope chlorine-35 (76% natural abundance) in an (n,γ) reaction, giving chlorine-36 (half-life 3 × 105 years) as the product along with gamma radiation.†

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† Historically, large amounts of chlorine-36 were produced by neutron irradiation of seawater (containing sodium chloride) in the Pacific during atmospheric testing of nuclear weapons by the US, UK, and France in the 1940s–1990s.

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Nuclear data: Benchmarking and the ICSBEP 

Benchmarks underpin the science of criticality: they comprise complete collections of experimental data, along with fully documented details and complete uncertainty analysis of the experiments that produced them. Benchmarks are used to validate codes such as MCNP and also serve to adjust nuclear data. Los Alamos has designed and executed critical and subcritical benchmarks since 1945 and continues this work today at NCERC. In 1992, in order to standardize this nuclear data, the US Department of Energy (DOE) established what would become the International Criticality Safety Benchmark Evaluation Project (ICSBEP) under the intergovernmental Nuclear Energy Agency (NEA), allowing criticality safety analysts to validate calculation tools and cross-section libraries.

The ICSBEP handbook contains over 5,000 critical and subcritical configurations, which all undergo extensive peer review before publication. Benchmarks are also used by the Los Alamos Nuclear Criticality Safety Division (NCSD) for validation of their codes, which ensure that fissile material operations can be performed without risk of criticality. The intent is for the current CWS experiments to be evaluated and submitted to the ICSBEP as a recognized criticality safety benchmark for chlorine-35. This is a significant undertaking: a benchmark report of this type will often weigh in at around 500 pages and undergo a much more thorough peer review process than a typical academic publication.

The cross section of the chlorine-35 (n,γ) reaction is known from differential experiments, however the data still needs to be validated in the thermal neutron regime using integral experiments. In other words, researchers have the neutron absorption data for chlorine-35 in isolation, but how it behaves in a complex fissile environment needs to be investigated. These types of integral experiments, such as CWS, measure neutron period and use this data to calculate keff.

Coincidentally, work is underway by a different team at the Los Alamos Neutron Science Center (LANSCE) to calculate the cross section for the chlorine-35 (n,p) reaction in a fast neutron energy regime. This effort is being supported by TerraPower as part of their work to develop a molten chloride fast reactor. They hope that by obtaining high-quality measurements of chlorine-35 and chlorine-37 cross sections and re-evaluating the corresponding nuclear data libraries, they can reduce regulatory uncertainty for these new types of advanced reactors (see article on p28).

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Figure 2.1 The Chlorine Worth Study team at NCERC. Left to right: Gabrielle Ambrosio, Leah Berman, Theresa Cutler, Jesson Hutchinson, Christopher Lopez, David Kimball.
Figure 2.2 Theresa Cutler (left) assists as Leah Berman (right) loads plutonium plates for experiment.Inset, bottom right: ZPPR plates in a 5-by-4 array. 

Part 1: Chlorine Worth Study 

Design considerations 

For the design of these experiments, researchers had to make several important choices regarding fuel type, type of chlorine-containing material, concentration range to match, and type of additional moderating materials. Aqueous solutions containing fissile materials are not considered safe for experiments at NCERC, therefore the solution environment had to be emulated using solid materials that contained both chlorine and hydrogen atoms (the latter being important as a neutron moderator that is present in water). The experiments were designed such that the chlorine absorption sensitivities in the experiment model matched the solution application in PF-4.

Multiple fuel types were considered, including both high-enriched uranium as well as plutonium, but ultimately plutonium was chosen in the form of the Plutonium-Aluminum No-Nickel (PANN) Zero Power Physics Reactor (ZPPR) plates, which have been used in several recently published ICSBEP benchmarks. These are steel-clad weapons-grade plutonium plates roughly 2 × 3 × 0.125 in with a mass of approximately 100 g plutonium-239 per plate and used in a 5-by-4 array (i.e., 20 plates, see Fig. 2).

When examining possible chlorine-containing moderating materials for use in the CWS experiments, the team used several metrics, including chlorine content, safety, neutron moderation (i.e., how much the material will mimic chlorine in solution), scattering data availability, lack of competing reactions, and other practical considerations such as low cost and room temperature solid state. Organic materials examined were polyvinyl chloride (PVC), chlorinated polyvinyl chloride (CPVC), dechlorane plus (DCP), and tris(2-chloroethyl) phosphate (TCEP). Inorganic materials examined were potassium chloride, sodium chloride, magnesium chloride, and magnesium chloride hexahydrate. While all the listed materials have high chlorine content, the organic materials were of more interest than the inorganic materials, mainly due to the competing reactions metric. Of the organic materials, TCEP is a carcinogen and DCP has environmental impact issues. Therefore, the chlorine-containing materials that were chosen for use in the CWS experiments were PVC and CPVC.

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Figure 3. Anniversary challenge coin issued in 2021 celebrating 10 years of operations at NCERC. Over the past decade, NCERC has executed more than 50 experiments using its unique critical assemblies.

High-density polyethylene (HDPE) was chosen as reflector and additional moderating material. This was needed to thermalize (slow down) the neutrons without capturing them, as chlorine-containing materials absorb too many neutrons to thermalize the system on their own. Thermal neutrons are needed to simulate the type of environment found in AQCL operations (“thermal” refers not to a high temperature but that the neutrons are in thermal equilibrium with the medium they are interacting with, i.e., the reactor’s fuel, moderator, and structure, which is much lower energy than the fast neutrons initially produced by fission).

Three different plutonium concentration ranges were chosen that cover most of the practical possibilities and where the sensitivities are similar. One representative model per range was chosen: 20–90, 200–400, and 500–600 g/L, corresponding to 30, 300, and 600 g/L models, respectively. To recreate these three different plutonium concentrations, three different material geometries were designed. For this, machine learning techniques developed during the ARCHIMEDES Laboratory Directed Research and Development (LDRD) Reserve project were used in combination with MCNP and other codes to calculate the partial ck similarity coefficient for chlorine-35 (n,γ) reactions of the proposed designs compared to the application models (ck and partial ck are similarity coefficients that use model sensitivities for nuclear data and uncertainties associated with that data).

The intrinsic heat generated from the plutonium fuel plates was also considered in the design. The team modeled this aspect with predictive calculations using the COMSOL® Multiphysics software, which showed that leaving heat dissipation to air convection alone would increase the steady-state temperatures in the experiment to well over 75 °C. Therefore, heat conduction was achieved using interlocking aluminum frames that conducted heat to two primary heat sinks—the bottom stack conducted heat to the moveable platen, and the top stack transferred heat to the top plate. With this amendment in the design, the model indicated that the maximum steady-state temperature would be much safer at approximately 33 °C, compared to greater than 75 °C in the original design.

Chlorine Worth Study: Final design 

The three final design configurations all featured approximately three inches of HDPE as an outer reflector and a series of layers which each include 20 ZPPR plates in a 5-by-4 array, aluminum trays and frames to support each unit of the configuration as well as provide heat transfer out to the top plate and platen, internal absorbers (PVC/CPVC), and an internal moderator (HDPE). Twelve resistance temperature detector (RTD) inputs were slotted into the aluminum trays to provide temperature monitoring.

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Figure 4. Final unit designs for (a) configuration 1 and (b) configurations 2 and 3 (chlorine-containing moderator is PVC in configuration 2, CPVC in configuration 3). Not to scale.
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Figure 5. In-situ images of the two halves of the final experimental configurations and the combined critical configurations for all three experiments at 30, 300, and 600 g Pu/L.
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Figure 6. CWS team members at the NCERC critical assembly control center.

The three configurations, corresponding to 30, 300, and 600 g/L applications, are shown in Figs. 4 and 5. Configuration 1 contains PVC as the chlorine-containing material sandwiched between two thicker layers of HDPE, all sitting on a layer of ZPPR plates. Configurations 2 and 3 share the same geometry, with a circular layer of chlorine-containing material (PVC in configuration 2, CPVC in configuration 3) surrounded by HDPE as an outer reflector, all on top of ZPPR plates. These configurations are assembled as two separate halves, split horizontally using the “1/M approach,” with each portion having less than three-quarters of the predicted critical mass. This point is called the handstack limit, which is when researchers transition from local to remote operations. Using the Planet assembly machine, the two parts of the critical configuration are brought together mechanically with remote control (Fig. 6).

The team performed the CWS experiments at NCERC over a three-week period in December 2021. During the second week, AQCL operations personnel attended, participating in the 1/M approach-to-critical process and loading fuel into the experimental configurations (Fig. 2). The group included a full range of workers from simulation experts, experimentalists, and engineers through to on-the-floor process operators who would directly benefit from increased limits. Involvement of these AMPP (Actinide Materials Processing & Power) employees was a unique aspect of the project—normally, the research would have been performed solely by a small core team at NCERC—and significantly contributed to the esprit de corps felt by the team for their mission-critical work.

The team is currently processing the data to produce a final benchmark, taking extraordinary effort to best understand the system and minimize overall uncertainty. Error margins associated with the critical configurations include uncertainties from many factors: material composition, physical dimensions, reactor period measurement, temperature effect, and nuclear data, among others.

This painstaking operation includes details down to sending samples of plastics used for detailed chemical analysis. Benchmarking will officially take place in the spring (2023) at the ICSBEP technical review group meeting in Paris, France. In addition to this benchmark evaluation, the data will be given to the Los Alamos NCSD to be used in future criticality safety evaluations to reassess fissile mass limits in PF-4 processes.

Critical assembly machine: Planet

One of four critical assembly machines located at NCERC, Planet is a general-purpose vertical-lift assembly machine that was used in the CWS experiments. Critical experiments are conducted on Planet by remotely bringing two halves of a critical assembly together into a critical configuration using a hydraulic lift mechanism. Planet’s simple design, which operates at essentially zero power (less than a watt), allows for a wide variety of experimental configurations, and measures subcritical neutron multiplication and critical reactor periods as a function of separation between experimental components. Planet uses gravity as a passive shutdown mechanism—it fails in an “open state.” This mechanism has been in wide use since the “demon core” criticality accidents at Los Alamos in the 1940s.

Currently located at NCERC (at the NNSS in Nevada), Planet was previously housed at TA-18 as part of the Los Alamos Critical Experiments Facility (LACEF). Following more than 20 years of operation during which it conducted 30 ICSBEP benchmarks, it was moved in 2008 as part of the de-inventory operations of LACEF and became fully functional again in 2011 (note: “de-inventory” is the process of removing fissionable material with the goal of eliminating the need for criticality safety control).

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Planet critical assembly machine without experimental setup. This is a general purpose vertical assembly machine designed to accommodate experiments in which neutron multiplication is measured as a function of separation distance between experimental components. Courtesy: Sanchez et al., Nuclear Science and Engineering, June 2021.

Planet loaded with CWS critical assembly. Note the configuration is split into two pieces to keep the assembly from becoming critical while workers are in the room. The lower platen is raised remotely to lock in with the stationary upper stack to achieve criticality (see Figs. 5 and 6 on previous spread).


In the last three years, two machine learning projects have been funded through the LDRD program at Los Alamos that aim to improve the nuclear data pipeline: ARCHIMEDES (Application Relevant Critical/Subcritical HEU/Pu-based Integral Measurements for Enhancing Data and Evaluating Sensitivities) in 2019–2020 and EUCLID (Experiments Underpinned by Computational Learning for Improvements in Nuclear Data) in 2021–2023. These projects use machine learning algorithms to first identify where compensating errors or gaps exist in nuclear data libraries and then use separate algorithms to design and optimize experiments to address these issues. Such improvements to nuclear data have potential applications in weapons, advanced reactors, and criticality safety.

ARCHIMEDES has four steps. First, the application is chosen, and a model of the process is generated using MCNP. Next, the radiation transport code is used to determine cross-section sensitivities both for the application model and for over 1,000 existing benchmark models. In the third step, these models are compared using the nuclear data covariance, and gaps are identified. Finally, machine learning algorithms are applied to optimize experiments, aiming to achieve a higher similarity coefficient to the application than existing ICSBEP benchmarks. These experiments can then be performed using the capabilities at NCERC. This overall process is how the CWS experiments described in this article were designed. In addition to designing improved experiments, these calculations should result in a better understanding of cross-section sensitivities for specific applications and help determine which existing criticality benchmarks are most relevant for such applications.

EUCLID expands on ARCHIMEDES and aims to reduce compensating errors in nuclear data libraries, lead to faster impact of integral experiments on nuclear data, and improve validation-experiment design with machine learning. This will create a valuable library of cross-section sensitivities as well as other computational tools which will be made available to data scientists. Error reduction will be achieved by using a suite of measurement types beyond keff for configurations that are optimally designed using machine learning. Advances in the ARCHIMEDES and EUCLID projects make it possible to design targeting experiments to answer specific application questions through nuclear data validation on a timescale much faster than previously achievable.

Team members: ARCHIMEDES: Jennifer Alwin* (XCP-7), Rian Bahran (GS-NNS), Travis Grove (NEN-2), Jesson Hutchinson* (NEN-2), Joel Kulesza (XCP-3), Robert Little* (XCP-3), Isaac Michaud* (CCS-6), Alexander McSpaden (NEN-2), Michael Rising* (XCP-3), Travis Smith* (NEN-2), Nicholas Thompson* (NEN-2). EUCLID: Brian Bell (XCP-5), Alexander Clark (XCP-3), Theresa Cutler (NEN-2), Michael Grosskopf (CCS-6), Wim Haeck (XCP-5), Michal Herman (T-2), Noah Kleedtke (XCP-5), Juliann Lamproe (NEN-2), Denise Neudecker (XCP-5), Scott Vander Wiel (CCS-6), Nicholas Wynne (NEN-2). *Contributed to both ARCHIMEDES and EUCLID.

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Figure 7. Left: Anton Paar DMA 1001 Precision density meter in a glovebox. The U-shaped sample chamber shown with plutonium chloride solution loaded using syringe. Right: AquaLab 4TE water activity meter with the sample compartment open, showing the sample chamber.

Part 2: Determining solution density and water activity 

The second thrust of the experimental work, performed by a separate team led by Kelly Aldrich (C-AAC), was to determine both the density and the water activity of aqueous plutonium/hydrochloric acid solutions. These characteristics were investigated using an Anton Paar 1001 density meter and an AquaLab 4TE water activity meter (Fig. 7), varying three parameters: (i) plutonium concentration, (ii) hydrochloric acid concentration, and (iii) plutonium oxidation state. Water activity, a value between 0 and 1, is defined as the partial vapor pressure of water in a solution divided by the standard state partial vapor pressure of water. It is a measure of the ideality of the solution behavior, which informs modeling parameters.

Varying plutonium and hydrochloric acid concentration 

Plutonium concentrations were examined in the range in which they typically demonstrate optimized moderation and have historically posed the highest risk for accidental criticality (30–100 g/L in detail; however, the model incorporates data in the range 0–260 g/L). Density measurements were taken at four different temperatures in the 20–40 °C range. The results showed that solution density increases significantly as plutonium content increases, as anticipated, and that it is inversely proportional to temperature.

For hydrochloric acid concentration, a set plutonium concentration of 60 g/L (Pu, 0.257 mol/kg) was chosen with varying concentrations of HCl (0.5–10 M range). The plutonium concentration chosen is a typical concentration for AQCL batches in PF-4 and happens to be in the optimally moderated portion of the criticality curve.

The density of plutonium solutions was found to increase with increasing HCl concentration, as would be expected. By subtracting the plutonium contribution from the data, researchers in C-AAC were interested to note a deviation from ideal behavior at higher concentrations, i.e., activity coefficient ≠ 1. Unfortunately, they found that water activity measurements of the ternary plutonium solution showed a higher degree of error relative to density measurements. However, a statistically significant decrease in water activity, and consequently the activity coefficient, was observed at higher plutonium or HCl concentrations.

A successful working density law model was developed (an eight-parameter Pitzer model), which showed less than 2% error between the predicted and measured solution density values over the concentration ranges studied, with the average error even smaller. Future work under a wider range of experimental conditions is planned (examining low-acid and high-plutonium concentrations) that will establish bounding limits of the “simple solution” behavior of this ternary system to verify the binary plutonium chloride parameters.

Plutonium oxidation states and effects on solution measurements 

A known complication of aqueous plutonium chemistry is the presence of variable oxidation states. Researchers examined the solutions described above using UV-visible spectroscopy and found a mixture of Pu(III) and Pu(IV) (Fig. 8). In the plutonium concentration experiments, the two states were found in a 1:1 ratio, whereas in the hydrochloric acid concentration experiments, Pu(IV) was the major species (~75%). Using ascorbic acid as a reductant, density measurements were performed on solutions containing purely Pu(III) ions, and no significant differences were found in the mixed oxidation state solutions, which has been confirmed by more recent experiments. This means that a conservative estimate can be confidently used when crediting chlorine in the models using the experimentally derived density equation (i.e., 3:1 versus 4:1 chlorine-to-plutonium).

MCNP calculations 

Initial calculations were made using the MCNP code to test the effect of using a more realistic (i.e., lower) value for solution density and accounting for chlorine. The model was created with 600 g of plutonium-239 at 60 g/L concentration and infinitely reflected with water and HCl concentration varied. The crucial variable of solution density was initially calculated using the old density model (the volume and mass of alpha-plutonium are added to the volume and mass of the remaining liquid as water). The results then showed that the calculated keff was substantially reduced when a small amount of chlorine is accounted for in the model and an experimental solution density value is used.

The team concluded that even conservative chloride crediting—for example a 3:1 chlorine-to-plutonium stoichiometric ratio—could yield dramatic operational improvements while maintaining high confidence in subcriticality. By substituting the previously assumed solution density with a far more relevant experimental value, the models showed an approximate 10% decrease in keff at the optimal moderation concentration. This could lead to a change of almost 100 g in the allowable mass limit under which plutonium AQCL systems can safely remain subcritical.

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Figure 8. Plutonium can adopt several different oxidation states in solution. Here three permutations of oxidation state of plutonium chloride in aqueous hydrochloric acid solution are shown: Pu(III), Pu(III/IV), Pu(IV).



Safely handling fissile materials is an essential requirement for completing a portion of the Los Alamos pit production mission and getting it right means having high-fidelity measurements and models. Los Alamos scientists have recently examined aqueous chloride operations in PF-4 for potential improvements to criticality models and have diagnosed several gaps between assumptions made for calculations and real-world experimental conditions. They found that the models use inaccurate estimates of solution densities and that they also disregard the influence of chlorine-35, which is a thermal neutron absorber that would be expected to reduce neutron flux under reaction conditions. For the latter, there were no appropriate benchmarks sensitive to chlorine-35 (n,γ) for the application available in the nuclear data, therefore experimental work was initiated to obtain and benchmark this vital information.

Using designs originating from machine learning algorithms as part of the ARCHIMEDES and EUCLID projects, a set of criticality experiments was performed at NCERC in December 2021 to ascertain the precise influence of chlorine on the neutron multiplication factor, keff. A detailed benchmark evaluation is currently underway, which is intended to be submitted to the ICSBEP at the spring 2023 technical review group meeting and distributed to the Los Alamos Nuclear Criticality Safety Division to begin the process of reviewing the data in the context of PF-4 operations. This will include detailed modeling with new inputs using MCNP codes.

Supporting this work, an ongoing experimental effort has focused on determining accurate solution characteristics for ternary plutonium chloride/hydrochloric acid/ water systems; in particular, solution density, water activity (i.e., solution ideality), and oxidation state/speciation. A broadly applicable density law has been designed for the system, which shows a high degree of accuracy and can be incorporated into the criticality models. Scoping studies have been performed to expand this work from plutonium chloride to oxalate (a species also present in AQCL operations, as described in the article on p16).

Combining the initial data indicates that by crediting for chlorine and using a more realistic value for solution density, significant increases in the operational limits of plutonium can be made while remaining safely subcritical. This could yield dramatic improvements for aqueous chloride operations at PF-4 and its current pit production mission.


I would like to thank Theresa Cutler, Kelly Aldrich, Jesson Hutchinson, Nic Lewis, Maureen Lunn, and David Kimball for their help in the writing of this article, and Nathaniel Madlem, Theresa, and Kelly for providing photos. The TA-55 work was supported by the Plutonium Program Office (NA-191) under the Office of Production Modernization (NA-19), funded and managed by the NNSA for the DOE. NCERC is supported by the DOE Nuclear Criticality Safety Program, funded and managed by the NNSA for the DOE.

Further reading: 

1. T. Cutler, K. Amundson, J. Hutchinson, N. Kleedtke, N. Wynne, “The CWS Experiments – An Experimental Study of the Effects of Chlorine on Thermal Neutron Absorption,” 2022 ANS Annual Meeting, Nuclear Criticality Safety Division Topical Meeting (NCSD 2022), Anaheim, CA (United States), 12-16 Jun. 2022, LA-UR-22-20549. 

2. K.E. Aldrich, D.M. Vu, K.M. Bonilla, J.N. Cross, S.P. Willson, J. Alwin, D. Kimball, J. Bunsen, T. Cutler, 15 L. Worl, R. Bulso, A. Salazar-Crockett, “Experimental steps toward a density law for chlorine-crediting criticality models of aqueous plutonium solutions,” 2022 ANS Annual Meeting, Nuclear Criticality Safety Division Topical Meeting (NCSD 2022), Anaheim, CA (United States), 12-16 Jun. 2022. 

3. R. Sanchez, T. Cutler, J. Goda, T. Grove, D. Hayes, J. Hutchinson, G. McKenzie, A. McSpaden, W. Myers, R. Rico, J. Walker, R. Weldon, “A New Era of Nuclear Criticality Experiments: The First 10 Years of Planet Operations at NCERC,” Nucl. Sci. Eng., 2021, 195, S1–S16, S1. 

4. J. Hutchinson, J. Alwin, R. Bahran, T. Grove, R. Little, I. Michaud, A. McSpaden, W. Myers, M. Rising, T. Smith, N. Thompson, D. Hayes, “Criticality testing of recent measurements at the National Criticality Experiments Research Center,” 11th International Conference on Nuclear Criticality Safety, Sept. 15–20, 2019, Paris, France. 

5. T.P. McLaughlin, S.P. Monahan, N.L. Pruvost, V.V. Frolov, B.G. Ryazanov, V.I. Sviridov, “A Review of Criticality Accidents,” LA-13638, 2000.