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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

First results of the NEXT-100 detector using $^{83m}$Kr decays

The NEXT collaboration is investigating the double beta decay of $ ^{136}\mathrm Xe$ using high-pressure gas electroluminescent time projection chambers, which provide excellent energy resolution together with a robust topological signature. Operating at the Laboratorio Subterráneo de Canfranc (LSC) and building on the success of the NEXT-White detector, the NEXT-100 apparatus began commissioning in May 2024 and started operation with xenon at a pressure of 4 bar in October 2024. We report here the first results obtained with NEXT-100 using low-energy calibration data from $^{83\text {m}}\textrm{Kr}$ decays, which allow mapping of the detector response in the active volume and monitoring of its stability over time. After homogenizing the light response, we achieve an energy resolution of 4.37% FWHM at 41.5 keV for $^{83\text {m}}\textrm{Kr}$ point-like energy deposits contained in a radius of 425 mm. In a fiducial region representing the operating conditions of NEXT-100 at 10 bar we obtain an improved energy resolution of 4.16% FWHM. These results are in good agreement with that obtained in NEXT-White, and an $E^{-1/2}$ extrapolation to $Q_{\beta \beta }$ yields an energy resolution close to 0.5% FWHM, well below the 1% FWHM design target.

Martínez-Lema, G. [Donostia Intl. Phys. Ctr., San ↗
DOE OSTI2023

Calibration of Single-Crystal TATB EOS

An equation of state (EOS) for the single-crystal TATB (C 6 H 6 N 6 O 6 , molar mass 258.15 g/mol) is calibrated using the experimental/computational calibration data uploaded to the caldata repository. The thermodynamically complete EOS is given by the Helmholtz free energy as a single-valued almost analytical function of the specific volume and temperature. The cold curve is taken to be of the MACAW form. The vibrational contribution to the Helmholtz free energy is described by a weighted sum of three Debye oscillators in the quasi-harmonic approximation. The calibration data suggests the range of reliable applicability of the EOS from the ambient conditions to temperatures of ∼ 3000 K and pressures of ∼ 50-70 GPa.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Predicting Geologic Behavior in Carbon Storage Projects Using Graph Neural Network

This study was invited to presented at NVIDIA's GTC conference to highlight the potential of Graph Neural Network as a novel and promising methodology for predicting pressure and saturation evolution in carbon storage projects. Carbon capture and storage (CCS) technology plays a pivotal role in mitigating greenhouse gas emissions, facilitating the transition to a low-carbon future. Effective management of subsurface reservoirs is essential to ensure the safe and efficient storage of captured carbon dioxide (CO₂). Accurate predictions of pressure and saturation over time are critical for evaluating the long-term performance and integrity of CCS projects. In recent years, Graph Neural Network (GNN) has emerged as a powerful framework for analyzing complex data in graph-structured domains. This abstract explores the application of GNN to forecast pressure and saturation evolution in carbon storage projects. Traditional numerical simulations of subsurface reservoirs have proven successful in providing pressure and saturation forecasts. However, these simulations involve massive amounts of computational effort and require extensive domain expertise for proper model calibration and validation. Graph Neural Operator offers an alternative approach that harnesses the inherent graph structure of reservoirs, where nodes represent reservoir grid cells and edges represent the geological connectivity between them.

Shih, Chung Yan↗
DOE OSTI2023

Tomographic optical emission spectroscopy of atmospheric pressure plasma interacting with complex surfaces

Plasma distribution in 3D space is heavily influenced by complex surfaces and the coupling interactions between plasma properties and interfacing material properties. For example, guided streamers that transition to surface ionization waves (SIWs) and propagate over structured dielectrics experience field enhancements that can lead to localized increases in ionization rates and complex 3D configurations that are difficult to analyze. Investigating these configurations requires techniques than can provide a more complete 3D picture. To help address this capability gap, a tomographic optical emission spectroscopy (tomo-OES) diagnostic system has been developed at Sandia National Laboratories that can resolve SIWs. The system includes four intensified cameras that measure the angular projections of the plasma light emission through bandpass filters. A dot calibration target co-registers each angular projection to the same voxel grid and an algebraic reconstruction technique (ART) recovers the light intensity at each voxel. An atmospheric pressure plasma jet (APPJ), provided by Peter Bruggeman, has been investigated and representative results are shown in Figure 1. Here, a bandpass filter was used to isolate emission from the N 2 second positive system (SPS) at 337.1 nm to capture the transition of the streamer to SIW on a planar dielectric surface (relative permittivity 3.3) located 3 mm below the APPJ [3]. The surface wave velocity was 3.5x10 4 (m/s), consistent with measurements made by Steven Shannon. Characterization of this APPJ will support the group effort of standing up a reproducible APPJ across institutions for applications such as liquid treatment, catalysis, and plasma aided combustion. Future work will investigate non-planar surfaces and eventually develop tomographic laser-induced fluorescence (tomo-LIF) approaches.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Reactive Transport Modeling of Hydrogen Production from Serpentinization of Olivine

Hydrogen production from serpentinization of ultramafic rocks represents a promising natural pathway for generating carbon-free energy, yet its kinetics and controlling factors remain incompletely understood. A key challenge in advancing serpentinization research lies in the heterogeneity of porosity and permeability in rocks, which leads to nonuniform fluid velocity fields, as well as uncertainties in estimating reactive surface area and identifying appropriate mineral reaction equilibria. Additional complexities arise from the role of dissolved SiO 2 , Fe 2+ /Fe 3+ partitioning, and the limited effect of pH variations within the strongly alkaline regime on hydrogen yields. These challenges hinder straightforward extrapolation from laboratory tests to practical applications of hydrogen production from natural rocks. Here, in this work, we address these questions using a simulation-based reactive transport modeling framework calibrated against controlled laboratory experiments reported elsewhere. The model couples geochemical kinetics, multiphase flow, and mineralogical feedbacks, enabling systematic evaluation of how surface area, dissolved silica concentration, Fe redox state, temperature, and pressure govern serpentinization and H2 generation. We find that surface area exerts the strongest control on reaction rates and hydrogen yields, while Fe 2+ /Fe 3+ ratios act as secondary modulators. Elevated dissolved silica concentrations suppress hydrogen production but accelerate serpentine precipitation, whereas increasing pH beyond 12 within the strongly alkaline regime produces only marginal gains. Finally, we demonstrate that integrating targeted experiments with calibrated simulations offers a powerful and efficient approach for predicting hydrogen yields and assessing parameter trade-offs in industrial-scale applications. This integration can substantially reduce the experimental burden while improving predictive capability, thereby enhancing both the mechanistic understanding and the practical feasibility of hydrogen production from serpentinization.

08 HYDROGEN↗
DOE OSTI2022

Emrgy 2022 Hydrokinetic Turbine Data - TEAMER Post Access Submission

The data herein contains all data collected and used for the Performance Characterization Testing and Model Calibration of a Vertical Axis Hydrokinetic Turbine. The data includes performance data and durability data for the Hydrokinetic Turbine. The device performance data contains shaft RPM, turbine RPM, power output, flow velocity, pressure, and pressure drop across the turbine. The mechanical durability data includes stress and strain at varied depths and velocities. There is also an FEA analysis included. This TEAMER project was awarded to Emrgy, Inc.in collaboration with Alden Research Laboratory LLC.

16 TIDAL AND WAVE POWER↗
DOE OSTI2024

Establishing ZIF‐8 as a reference material for hydrogen cryoadsorption: An interlaboratory study

Abstract Hydrogen storage by cryoadsorption on porous materials has the advantages of low material cost, safety, fast kinetics, and high cyclic stability. The further development of this technology requires reliable data on the H 2 uptake of the adsorbents, however, even for activated carbons the values between different laboratories show sometimes large discrepancies. So far no reference material for hydrogen cryoadsorption is available. The metal‐organic framework ZIF‐8 is an ideal material possessing high thermal, chemical, and mechanical stability that reduces degradation during handling and activation. Here, we distributed ZIF‐8 pellets synthesized by extrusion to 9 laboratories equipped with 15 different experimental setups including gravimetric and volumetric analyzers. The gravimetric H 2 uptake of the pellets was measured at 77 K and up to 100 bar showing a high reproducibility between the different laboratories, with a small relative standard deviation of 3–4 % between pressures of 10–100 bar. The effect of operating variables like the amount of sample or analysis temperature was evaluated, remarking the calibration of devices and other correction procedures as the most significant deviation sources. Overall, the reproducible hydrogen cryoadsorption measurements indicate the robustness of the ZIF‐8 pellets, which we want to propose as a reference material.

08 HYDROGEN↗
DOE OSTI2020

Leveraging operational information from wastewater injection wells to evaluate CO 2 injection performance for carbon storage applications in the Appalachian Basin

Abstract Geologic parameters, geophysical logging, injection testing, and operational metrics from wastewater injection wells were integrated to develop a preliminary design of a carbon storage facility in the Appalachian Basin. A scattered group of 10–20 commercial wastewater injection wells dispose off produced water from oil and gas wells in the region, utilizing a sequence of stacked deep saline formations for injection zones. These wastewater injection wells provide practical benchmarks for understanding the feasibility of carbon dioxide (CO 2 ) storage. Geologic models were developed based on characterization data from the wastewater injection wells. Reservoir simulations were calibrated according to injection testing and operational data from the wastewater injection wells. Long‐term operational data on injection flow rates and pressures measured in the wastewater injection wells were especially useful to evaluate the performance of carbon storage applications. The simulations were used to estimate injection pressures, radius of CO 2 saturation, and pressure response for industrial scale CO 2 storage applications. Results were also used to provide a design basis in terms of number of injection wells, well spacing, area of review, injection system components, monitoring plan, and CO 2 pipeline distribution system. The analysis demonstrates that there is sufficient injectivity in the deep saline formations in the west‐central Appalachian Basin to store commercial volumes of anthropogenic CO 2 . The geologic system appears suitable for supporting CO 2 injection rates of 0.5–1.0 million metric tons per year at injection pressures below formation fracture pressure in a single well. The long‐term operational data of wastewater injection wells within the study area suggested a lower permeability‐thickness values than indicated by initial reservoir tests. A workflow for developing realistic permeability values for input into reservoir simulations is presented. © 2020 Society of Chemical Industry and John Wiley & Sons, Ltd.

Valluri, Manoj↗
DOE OSTI2022

Estimation of pipe failure frequencies in the absence of operational experience data: A pilot study

Probabilistic failure metrics such as leak frequency and rupture frequency are commonly used to characterize piping reliability. The methodologies for calculating the failure metrics rely on a complex set of input parameters. Operating experience data and experimental data play an important role in informing the different input parameters. The paper describes results and conclusions of a coordinated research project to benchmark three different reliability models using a four-step procedure: reference case definition of relevance to advanced reactor designs, input parameter calibration, validation of results, and application of different methodologies upon completion of the calibration and validation steps. The reference case is a weld consisting of nickel-base alloy 152/52 and located within a primary pressure boundary of an advanced reactor. This alloy is a class of structural materials known to be highly resistant to stress corrosion cracking. Synergies between the different methods are noted and the importance of a multi-disciplinary approach to input parameter development is underscored. A key conclusion is that the three methods are equally suitable for estimating failure frequencies. In any specific application, a selection of the most practical or effective computational tool can be considered. The comparison of alternative models confirms and helps to gain confidence in the computed failure frequency estimates. The study was part of a coordinated research project organized by the International Atomic Energy Agency.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

Soil water content, matric potential, carbon dioxide and oxygen concentrations, Oct 2018-Dec 2021, Slate River Floodplain, Crested Butte, Colorado

This data package includes a time series of soil sensor data (temperature, water content, bulk electrical conductivity, porewater dissolved oxygen and porewater dissolved carbon dioxide) in a vertical profile from the Slate River floodplain outside Crested Butte, Colorado, a focus field site for the SLAC Floodplain Hydro-Biogeochemistry SFA. The data was generated as part of the work targeting the overarching research question for the SLAC SFA: How do ubiquitous subsurface interfaces mediate molecular-scale biogeochemical processes and groundwater quality in floodplains and watersheds? The package includes: (1) soil temperature, volumetric water content and electrical conductivity at 40, 60 and 82.5 cm depth; (2) soil matric potential at 40, 60, 79 and 100 cm depth; (3) soil CO2 concentrations at 40, 60 and 82.5 cm depth; and (4) soil oxygen concentrations at 60, 82.5, 100, 135, 170 and 182 cm depth. Both the carbon dioxide and oxygen sensors are optical sensors that can measure the partial pressure of oxygen in both saturated and unsaturated conditions. Unfortunately, soil CO2 in the profile is unexpectedly high and above the sensor calibration range (0-25,000 ppm). In addition, soil CO2 sensors failed within a year of deployment, so we only report CO2 data from 2019-2020.Within the data package, "FLMD.csv" describes file-level metadata and "dd.csv" defines column headers and universal terms across the dataset. The data package includes 4 "*data.csv" files, one for each calendar year in the dataset. Each "*data.csv" file has a corresponding "*_InstallationMethods.csv" file that describes the location, sensor model, sensor serial number and other metadata corresponding for each measured parameter. Because sensors have been added over time, not every sensor has data dating back to Oct 2018. Note that there is a data gap over winter 2019-2020 due to a power outage. While this repository currently only contains data through December 2021, the dataset will be updated as additional years are collected and processed.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Water-based Ria Testing in TREAT: Commissioning and Early Results

We have completed a series of reactivity-initiated accident commissioning tests with the static water capsule in the Transient Reactor Test Facility and completed some visual and non-destructive post-irradiation examinations on the fuel rods. The test campaign included a calibration test followed by five tests in the Static Environment Rodlet Transient Test Apparatus capsule. The conditions varied from room temperature and pressure up to 200°C and 2.5 MPa, with energy depositions varying between ~500–1100 J/gUO2. The series of tests allowed for a number of instrumentation qualifications and demonstrations, including cladding thermometry, rodlet plenum pressure, cladding elongation, and an electro-impedance boiling detector. This paper documents the design of the capsule and highlights some results from the commissioning tests and post-transient examination.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Overview of the Water-Based RIA Testing in TREAT

We have completed a series of reactivity-initiated accident commissioning tests with the static water capsule in the Transient Reactor Test Facility. The test campaign included a calibration test followed by five tests in the Static Environment Rodlet Transient Test Apparatus capsule. The conditions varied from room temperature and pressure up to 200°C and 2.5 MPa, with energy depositions varying between ~500–1100 J/gUO2. The series of tests allowed for a number of instrumentation qualifications and demonstrations, including cladding thermometry, rodlet plenum pressure, cladding elongation, and an electro-impedance boiling detector. This paper documents the design of the capsule and highlights the results from the commissioning tests.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

An integrated approach to derive relative permeability from capillary pressure

Surface tension affects all aspects of fluid flow in porous media. Through measurements of surface tension interaction under multiphase conditions, a relative permeability curve can be determined. Relative permeability is a numerical description of the interaction between two or more fluids and the porous media. It is a critical parameter for various tools that characterize subsurface multiphase flow systems, such as numerical simulation for carbon sequestration, oil and gas development, and groundwater contamination remediation. Therefore, it is critical to get a good statistical distribution of relative permeability in the porous media under study. Empirical formula for determining relative permeability from capillary pressure are already well established but do not provide the needed flexibility that is required to match laboratory-derived relative permeability curves. By expanding the existing methods for calculating relative permeability from capillary pressure data, it is possible to create both two and three-phase relative permeability curves. Mercury intrusion capillary pressure (MICP) data from the Morrow 'B' Sandstone coupled with interfacial tension and contact angle measurements were used to create a suite of relative permeability curves. Furthermore, these curves were then calibrated to a small sample of existing laboratory curves to elucidate common fitting parameters for the formation that were then used to create relative permeability curves from MICP data that does not have an associated laboratory-measured relative permeability curve.

58 GEOSCIENCES↗
DOE OSTI2025

Computationally efficient subglacial drainage modelling using Gaussian process emulators: GlaDS-GP v1.0

Subglacial drainage models represent water flow at the ice–bed interface through coupled distributed and channelized systems to determine water pressure, discharge, and drainage system geometry. While they are used to understand processes such as the relationship between surface melt and ice flow, the number of uncertain model parameters and the computational cost of running models makes it difficult to adequately explore the high-dimensional parameter space and evaluate uncertainty in model predictions. Here, we develop Gaussian process (GP) emulators that make fast predictions with associated uncertainty of subglacial drainage model outputs. Using a truncated principal component (PC) basis representation, we construct a GP emulator for diurnally averaged subglacial water pressure. We also explore emulation of scalar variables describing drainage efficiency and configuration. We train the emulators using ensembles of up to 512 simulations varying eight parameters of the Glacier Drainage System (GlaDS) model on a synthetic domain intended to represent an ice-sheet margin. The emulators make predictions ∼ 1000 times faster than GlaDS simulations, with errors <3 % for the water pressure field and ∼ 5 %–9 % for drainage efficiency and configuration. We apply the emulators to explore the eight-dimensional parameter space by computing variance-based parameter sensitivity indices, finding that three parameters (ice flow coefficient, bed bump aspect ratio, and the subglacial cavity system conductivity) explain 90 % of the variance in modelled water pressure in response to parameter changes. The GP emulator approach described here is well suited to integrating observational data with models to make calibrated, credible predictions of subglacial drainage.

58 GEOSCIENCES↗
DOE OSTI2021

Overview of the Water-Based RIA Testing in TREAT

A series of reactivity-initiated accident (RIA) commissioning tests have been completed with the static water capsule in the Transient Reactor Test (TREAT) Facility. The test campaign included a calibration test followed by five tests in the Static Environment Rodlet Transient Test Apparatus (SERTTA) capsule. The conditions varied from room temperature and pressure up to 200°C and 2.5 MPa with energy depositions varying between ~500-1100 J/gUO2. The series of tests allowed for a number of instrumentation qualifications and demonstrations including cladding thermometry, rodlet plenum pressure, cladding elongation, and an electro-impedance boiling detector. This paper documents the design of the capsule and highlight the results from the commissioning tests.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

A Multi-Objective Bayesian Optimization Approach Using the Weighted Tchebycheff Method

Abstract Bayesian optimization (BO) is a low-cost global optimization tool for expensive black-box objective functions, where we learn from prior evaluated designs, update a posterior surrogate Gaussian process model, and select new designs for future evaluation using an acquisition function. This research focuses upon developing a BO model with multiple black-box objective functions. In the standard multi-objective (MO) optimization problem, the weighted Tchebycheff method is efficiently used to find both convex and non-convex Pareto frontiers. This approach requires knowledge of utopia values before we start optimization. However, in the BO framework, since the functions are expensive to evaluate, it is very expensive to obtain the utopia values as a prior knowledge. Therefore, in this paper, we develop a MO-BO framework where we calibrate with multiple linear regression (MLR) models to estimate the utopia value for each objective as a function of design input variables; the models are updated iteratively with sampled training data from the proposed MO-BO. These iteratively estimated mean utopia values are used to formulate the weighted Tchebycheff MO acquisition function. The proposed approach is implemented in two numerical test examples and one engineering design problem of optimizing thin tube geometries under constant loading of temperature and pressure, with minimizing the risk of creep-fatigue failure and design cost, along with risk-based and manufacturing constraints. Finally, the model accuracy with frequentist, Bayesian and without MLR-based calibration are compared to true Pareto solutions.

Engineering↗
DOE OSTI2024

DECOVALEX-2023: Task C Final Report

The Full-scale Emplacement (FE) heater experiment at the Mont Terri Underground Rock Laboratory (URL) was designed and conducted by Nagra to replicate an emplacement tunnel of Nagra’s reference repository design at 1:1 scale. Alongside testing the technical feasibility of constructing disposal tunnels, emplacing waste containers in the tunnels and then backfilling them, the main goals of the FE experiment are (1) to obtain a better understanding of the coupled effects of induced thermo-hydro-mechanical (THM) processes that may occur and (2) to validate existing coupled THM models (Müller et al., 2017). A key aspect of ensuring safety for repositories located in low-permeability rock involves minimizing any damage to the rock itself, thereby preserving its integrity and promoting a stable environment Amongst a number of processes that could damage the rock is the increase in pore pressure due to thermal loading caused by heat emitted from the waste. To reduce the potential damage of the rock, it is important to analyse the evolution of heat over time due to the heat load of the containers and assess possible consequences by coupled THM models. The aim of Task C of DECOVALEX-2023 was to build 3D numerical models of the FE experiment, focussing in particular on the heating induced pore pressure change in the Opalinus Clay. Data from a large number of sensors were available from the FE experiment for model comparison. These sensors measured temperature and relative humidity in the bentonite around the heaters, and temperature, pressure and displacement/strain in the surrounding Opalinus clay. Data were available from the start of excavation (April 2012) up to August 2020 for most sensors (more than 5 years from the start of heating in December 2014). To fulfil the overall aim of the task, the work was broken down into a number of steps, starting with simpler models to build confidence in each team’s approach and then moving to more complex models that better represent the FE experiment. Step 0 consisted of 2D benchmark models, gradually increasing the number of processes that are represented from thermal (T) only models in Step 0a, to coupled thermal hydraulic (TH) models in Step 0b with a representation of changing porosity, to coupled thermo-hydro-mechanical (THM) models in Step 0c, where porosity changes are calculated by the mechanical model. A detailed specification of processes, parameters, initial and boundary conditions was provided for this step, with the ambition that all teams would work towards close agreement in their model results, thus building confidence in the model implementations. vi It was not straightforward to achieve agreement between the teams, so additional steps (Step 0b2, 0b3, 0c2, 0c3) were added along with derivation of some analytical solutions against which the models could be compared. The reasons for the differences between teams were investigated and found to be caused primarily by different conceptual model assumptions (including temperature dependence of the thermal expansion of water), different model formulations (including porosity evolution) and differences in modelled domain sizes, boundary conditions and grid discretisation. This demonstrates that comparisons between multiple modelling teams and/or comparison with analytical results and experimental data are highly beneficial in providing an indication of uncertainty in model predictions. At the conclusion of Step 0, almost all teams had achieved a close agreement in model results and those that had not achieved an agreement knew the reason for this. Step 1 moved from 2D models to 3D models of the FE experiment without adding technical features like shotcrete or EDZ, and only considering the heating phase. Initially the 3D model was tightly specified to continue to build confidence in the model implementations (Step 1a). The results of Step 1a were compared to the data from the FE-experiment without the teams seeing the data. The teams were then provided with a sub-set of the data from the FE-experiment and invited to consider how best to use the large dataset for model comparison (Step 1b). Teams were then asked to use the data provided to calibrate their models, only changing material property values rather than adding features or processes to their models (Step 1c). In Step 1, teams were asked to only model the heating phase of the experiment, so pressure in the Opalinus Clay was reported as change in pressure since the initial conditions were specified rather than modelled. The change from 2D to 3D models was accompanied by an increase in the dispersion of results between the teams. Some of this was resolved during the task, but some remained and is potentially due to model discretisation. Calibration of parameters was useful in improving the fit of the models to the data but the remaining differences indicated that the models were missing features or processes. In Step 2, the teams were asked to update their models with additional features and processes as well as calibrating parameters to try and improve the fit of the models to the data. Teams were encouraged to represent ventilation of the open FE tunnel prior to backfilling with heaters and bentonite and in Step 2, the absolute pressure in the Opalinus Clay was compared between the teams. Teams took different approaches, but there was consideration of adding shotcrete and an EDZ into the model, representing stress change during excavation and different approaches to modelling ventilation of the FE tunnel. Overall, the documented results showed a very good agreement for temperature. The results for porewater pressure evolution showed a significant improvement for most teams compared to Step 1c with a good agreement to the measurements for several teams whereas some teams overpredicted the pressure increase and others overpredicted the drainage effect especially for the sensors close to the heater. Step 3 was an opportunity for teams to use the models developed in Step 1 and Step 2 to make predictions about the temperature and pressure changes that will be expected at the FE experiment over the next few years in light of the planned changes in thermal output of the heaters.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗