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209 records · Page 12

Reaction-in-flight neutrons as a diagnostic for hydrodynamical mixing in double shell inertial confinement fusion capsules

We examine reaction-in-flight (RIF) neutrons as diagnostics for hydrodynamical mixing of high-Z shell material into the hotspot of double shell capsules that are designed for the National Ignition Facility. In particular, we consider the effects of different levels of mixing of tungsten shell material into the DT gas on RIF spectra. Using a set of 1D simulations from the radiation hydrodynamic code xRAGE to determine the temperature and density profiles of the mixed W-DT gas, we find that increasing the mass of mix systematically reduces the ratio of RIF neutrons to primary 14 MeV neutrons. The shape of the RIF spectrum also changes with mix, with the predicted spectrum softening in energy with increasing mix.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

High-Speed and High-Quality Field Welding Repair Based on Advanced Non-Destructive Evaluation and Numerical Modeling

Creep strength-enhanced ferritic (CSEF) steels such as Grade 91 (9Cr-1Mo-V) and Grade 92 (Fe-9Cr-2W-0.5Mo) steels are widely used in the fossil-fuel-fired and nuclear power plants. The weld integrity of these steels is crucial for power plants' safe and reliable operations. Due to harsh service conditions, the steel weld can become susceptible to environmental degradation. Field welding repair is used to restore the degraded weld’s performance where a controlled temper-bead welding technique is commonly used to temper the freshly formed martensite during welding. However, knowledge of weld repairability is limited and experimental trial and error optimization to achieve desired microstructure and joint properties is expensive and time-consuming. Many existing computational models, e.g., finite element models, are limited to solving heat conduction equation and ignoring convective heat transfer due to molten metal flow. These models can result in over-prediction of peak temperatures of weld pool and heat-affected zone (HAZ), which in turn can affect the accuracy of tempering prediction. Moreover, these finite element models require an input of the deposit profiles in advance and thus limits the usability of these models. Here, a molten pool-based, multi-pass multi-layer model has been developed based on computational fluid dynamics (CFD) approach with the Volume of Fluid (VOF) method. The model calculates the bead formation, thereby eliminating the need for pre-determined bead profiles required by finite element models. For computational efficiency, a coordinate system attached to the moving heat source is utilized. A subroutine is developed to convert the temperature profiles in the reference frame stationary to the heat source to that stationary to the workpiece. The converted thermal cycles are then imported into a microstructure model to compute the tempering kinetics and resultant hardness using a Johnson-Mehl-Avrami-Kolmogorov (JMAK), and modified Grange-Baughman parameter. The modeling approach is first developed and validated on single- and multi-pass deposition of stainless steel filler metal onto a SA-533 high strength steel substrate. The models are then applied to a multi-pass V-groove repair weld of Grade 91 steel plate as well as directed energy deposition of Grade 92 steel. Non-destructive characterization of microstructures was performed on Grade 91 and 92 steel welds. Two welding processes, cold metal transfer (CMT) and flux-cored arc welding (FCAW), were investigated for the Grade 91 steel weld samples. For the Grade 92 weld samples, three different heat inputs (low, medium, and high) of gas tungsten arc welding (GTAW) were utilized to replicate traditional field welding processes. The non-destructive evaluation (NDE) method used for this research was immersion ultrasonic testing (UT) using a micro-resolution ultrasonic imaging methodology specifically designed to operate in the through-transmission configuration operating at 20 MHz of frequency. The system used a focused ultrasonic beam spot size diameter between 250-300 μm, and a 6 μm laser vibrometer spot size for detection, to produce highly defined images with longitudinal and mode-converted shear waves. From the micro-resolution ultrasonic C-scan images, three microstructural regions, i.e., weld metal (WM), HAZ, and base metal (BM), were clearly identifiable. Various levels of ultrasonic amplitudes distributed over the three regions were correlated with electron beam backscattered diffraction (EBSD) images using grain size, grain boundaries, and dislocation densities. The results showed that areas with relatively higher ultrasonic amplitude levels were associated with smaller grains and higher dislocation densities, while areas with lower amplitude levels were associated with larger grains and lower dislocation densities. In addition, ultrasonic velocity data obtained across the three different weld microstructural regions of Grade 91 test samples were correlated with optical metallographic images and hardness measurements. The results showed distinctive decreases in ultrasonic velocity and hardness over the HAZ region, where weld failures often occur during service.

36 MATERIALS SCIENCE↗

Probing late-stage hadronic interactions at high baryon density via $K^{⁎0}$ production in the RHIC beam energy scan program

A precision measurement of the $K^{⁎0}$ meson yield is reported in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7, 11.5, 14.6, 19.6, and 27 GeV using the high-statistics data sample collected by the STAR experiment during the Beam Energy Scan II (BES-II) program at RHIC. The transeverse momentum (p T )-integrated yield ratios $\large{(}K^{⁎0} + \overline{K^{⁎0}}\large{)}/(K^+ + K^{-})$ in central collisions show a suppression relative to peripheral collisions at the (1.7–3.6) σ level, while a thermal model without final-stage rescattering overpredicts this ratio with a deviation of (6.9–8.2) σ. These results indicate a loss of the measured $K^{⁎0}$ signal in central collisions due to re-scattering of its hadronic decay products in the hadronic phase. The p T -integrated yield of charged kaons exhibits an approximate scaling with charged-particle multiplicity, independent of collision energy and system size. A similar trend is observed for the short-lived $K^{⁎0}$ resonance, although significant deviations emerge at lower energies. At BES energies, the $K^{⁎0}/K$ ratio shows stronger suppression than at the highest RHIC and LHC energies within a given multiplicity bin, particularly in central and mid-central collisions. This behavior is consistent with changes in the effective hadronic interaction cross section and is supported by transport model calculations, which indicate dominant meson–baryon interactions at lower energies and meson–meson interactions at higher energies.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Search for cascade decays of charged sleptons and sneutrinos in final states with three leptons and missing transverse momentum in 𝑝⁢𝑝 collisions at $\sqrt{𝑠} = 13$ TeV with the ATLAS detector

A search for cascade decays of charged sleptons and sneutrinos using final states characterized by three leptons (electrons or muons) and missing transverse momentum is presented. The analysis is based on a dataset with 140 fb −1 of proton-proton (pp) collisions at a center-of-mass energy of $\sqrt{𝑠} = 13$ TeV recorded by the ATLAS detector at the Large Hadron Collider. This paper focuses on a supersymmetric scenario that is motivated by the muon anomalous magnetic moment observation, dark-mattter relic density abundance, and electroweak naturalness. A mass spectrum involving light Higgsinos and heavier sleptons with a bino at intermediate mass is targeted. No significant deviation from the Standard Model expectation is observed. This search enables us to place stringent constraints on this model, excluding at the 95% confidence level charged slepton and sneutrino masses up to 450 GeV when assuming a lightest neutralino mass of 100 GeV and mass-degenerate selectrons, smuons and sneutrinos.

extensions of Higgs sector↗

Compositing and Characterization of SE Quadrant Waste Exemplars

This report outlines the experimental investigation and characterization of transport properties in Hanford SE quadrant High-Level Waste (HLW). The goal of the study was to establish baseline behaviors of bulk composite rheology and settling characteristics to facilitate waste treatment process design for the Waste Treatment and Immobilization Plant (WTP) and avoid waste conditions and properties favorable to bubble cascade gas release events. The study focused on two major objectives: 1) identifying, obtaining, and preparing relevant Hanford tank waste samples for evaluation and 2) quantifying the “as-received” rheology and transport properties of the samples. Twenty-three centrifuged core segments originating from tanks AN-101, AN-106, and AW-105 were selected based on compositional relevance to SE quadrant PUREX cladding waste. These materials were composited into five waste composites enriched with target analytes: aluminum (Al), iron (Fe), phosphate (PO 4 ), uranium (U), and zirconium (Zr). Physical property and transport testing examined particle size distributions, bulk densities, settling behaviors, rheological properties, shear strengths, and just-suspended mixing speeds (NJS). Testing revealed two distinct composite classifications based on rheological characteristics: non-Newtonian composites (Fe and PO 4 ) and Newtonian composites (Al, U, and Zr). The Fe and PO 4 composites exhibited slow settling rates and reduced mobilization proclivity, attributable to strong particle-particle interactions and the formation of yield structures within non-Newtonian slurries. In contrast, the Al, U, and Zr composites displayed rapid settling and dense compaction behaviors, indicative of minimal structuring and interactions. Shear strengths for all composites were generally low relative to prior studies of SE quadrant waste, with only the U composite showing elevated strength approaching values reported in previous literature. Repeat shear strength measurements revealed contributions from dense granular material in the U composite and stronger cohesive properties in the Al composite. Settling data highlighted hindered settling behavior, with rates falling more than one order of magnitude below estimates based on Stokes’ law and rate decreasing as composite UDS content increased. NJS testing demonstrated different mobilization behaviors between cohesive and granular composites. The Fe composite required the highest mixing rate for resuspension, while the Al composite was the easiest to resuspend. Comparison of measured NJS against predictions made using the Zwietering correlation suggests non-Newtonian behavior alters resuspension mechanics, rendering non-Newtonian systems more stable against resuspension lift forces relative to their granular counterparts.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Testing of High S Matrix Glasses to Expand DFHLW Glass Compositional Ranges (Rev.1)

Gaps in glass composition-property data for direct-feed high-level waste (DFHLW) have recently been identified. One such gap is the region of high sulfur solubility since previous, pretreated, high-level wastes contained very little sulfur. Filling this data gap will significantly broaden the range of process flowsheet options including minimal washing and will allow for optimized waste loading in DFHLW glasses. This report summarizes the data collected during the characterization of the DFHLW High S Glass Matrix (HS24). A glass matrix of 50 glass compositions was developed to evenly cover the DFHLW composition region for high sulfur glass. Matrix glasses were designed to expand the composition region outside the current component concentration and property limits so as to reduce uncertainties at the limits. The 50 matrix glasses were fabricated and tested for properties important to the success of DFHLW vitrification including: compositions, canister centerline cooling (CCC) crystallinity and isothermal crystallinity, density, viscosity, electrical conductivity (EC), product consistency test (PCT) response, toxicity, and sulfate solubility. Melter materials corrosion testing is reported elsewhere. These glasses were intentionally designed to have high SO 3 solubilities (0.7 to 2.2 SO 3 wt%) in compositional regions that had not been previously explored. Forty-eight glasses showed the measured SO 3 content retained >80% of the target SO 3 and the densities of all the glasses ranged from 2.49 g·cm -3 to 2.74 g·cm -3 . While the model predicted nepheline formation in 5 glasses, one of the tested 50 CCC glasses formed nepheline, and 35 glasses formed Cr-containing phases such as spinels and eskolaite. Only five glasses were amorphous after CCC treatment where 44 glasses with detectable crystals contained =10 wt% crystals and only one glass had > 10 wt% crystals. None of the glasses exceeded the allowable T 2% for spinel crystal formation at 950 ºC (i.e., no glasses had >2 wt% spinel at 950 ºC) during isothermal crystal fraction tests where 10 glasses showed no crystalline phases at or below 950 ºC. All the glasses (except one which failed being slightly lower than the target) satisfied the SO 3 constraint while 98 glasses did not meet the viscosity constraints and 4 failed the EC constraints. Six quenched (Q) and six CCC glasses failed the Defense Waste Processing Facility (DWPF) Environmental Assessment (EA) glass PCT threshold and 3 Q and 4 CCC failed the PCT design constraint. One glass exceeded the WTP delisting limits for Cr via EPA Method 1311 (i.e., Toxicity Characteristic Leaching Procedure, TCLP). It should be emphasized that some of these glasses were specifically designed to approach or even exceed certain property constraints, as filling data gaps in these regions will provide the greatest benefit for future model development by improving accuracy and reducing uncertainties. These insights will ultimately support the development of more robust glass formulation strategies, enabling higher waste loading, reducing operational risks, and expanding the processing envelope.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Atacama Cosmology Telescope DR6 and DESI: Structure growth measurements from the cross-correlation of DESI legacy imaging galaxies and CMB lensing from ACT DR6 and 𝑃⁢𝑙⁢𝑎⁢𝑛⁢𝑐⁢𝑘 PR4

We measure the growth of cosmic density fluctuations on large scales and across the redshift range 0.3 < 𝑧 < 0.8 through galaxy clustering and the cross-correlation of the ACT data release 6 cosmic microwave background (CMB) lensing map and galaxies from the Dark Energy Spectroscopic Instrument Legacy Survey, using three galaxy samples spanning the redshifts of 0.3 ≲ 𝑧 ≲ 0.45, 0.45 ≲ 𝑧 ≲ 0.6, 0.6 ≲ 𝑧 ≲ 0.8. We adopt a scale cut where nonlinear effects are negligible, so that the cosmological constraints are derived from the linear regime. We determine the amplitude of matter fluctuations over all three redshift bins using Atacama Cosmology Telescope (ACT) data alone to be 𝑆 8 ≡ 𝜎 8 ⁢(Ω 𝑚 /0.3) 0.5 =0.772 ± 0.040 in a joint analysis combining the three redshift bins and ACT lensing alone. Using a combination of ACT and Planck data we obtain 𝑆 8 = 0.765 ± 0.032. The lowest redshift bin used is the least constraining and exhibits a ∼2⁢𝜎 tension with the other redshift bins; thus we also report constraints excluding the first redshift bin, giving 𝑆 8 = 0.785 ± 0.033 for the combination of ACT and Planck. This result is in excellent agreement at the 0.3⁢𝜎 level with measurements from galaxy lensing, but is 1.8⁢𝜎 lower than predictions based on Planck primary CMB data. Understanding whether this hint of discrepancy in the growth of structure at low redshifts arises from a fluctuation, from systematics in data, or from new physics is a high priority for forthcoming CMB lensing and galaxy cross-correlation analyses.

cosmic microwave background↗

MOSCATO Development and Integration in Fiscal Year 2025: Implementation of Multiphase, Multiphysics Modeling Capabilities for Molten Salt Systems

MOSCATO (Molten Salt Chemistry and Transport) is a multiphysics code that provides high-fidelity, coupled simulations of fluid flow, heat transfer, mass transfer, chemistry, electrochemical phenomena, and alloy corrosion for molten salt systems. In FY25, significant developments were made to the code package, enhancing its capabilities for modeling all relevant phenomena within operating moltens salt reactors (MSRs). The developments and activities in FY25 included: 1. Implementation of Level-Set methods to enable modeling of single-bubble behavior in molten salts. In FY25, the Level-Set two-phase flow modeling implementation was improved to simulate single bubble behavior with molten salt media. The large density and viscosity ratios between typical gases and molten salt liquids present challenges for these types of numerical solvers. With enhancements to the pressure projection method, MOSCATO’s Level-Set solver was able to be successfully validated to experiments related to helium bubble rise in stagnant molten salt. The simulated bubble rising velocity showed reasonable good agreement with experimental measurements. The bubble shape and dynamics were also visually compared with experimental snapshots, demonstrating a good qualitative match. 2. Generation of mass transfer correlations for multiphase flow systems. To enable calculations of the tritium transport across the interface between gas bubbles and salt, we modeled high- Schmidt-number mass transfer around a sphere across a broad range of Reynolds numbers. The mesh near the sphere surface was highly refined to resolve steep concentration gradients caused by the low diffusion coefficient. Literature-based mass transfer correlations were compared with the numerical results, and modifications were proposed to improve agreement, particularly at higher Schmidt numbers. These mass transfer correlations were subsequently provided to other national laboratories to help enable high quality mass transfer simulations using lower-order solvers under development within the NEAMS program. 3. Preliminary implementation of a bubbly flow solver. To model bubbly flow in molten salt, we implemented a bubbly flow solver for void fractions less than 5%. To do so, an algebraic relative velocity model that assumes small bubbles with rapid momentum equilibration was added to MOSCATO to compute bubble velocities. Preliminary comparisons with experimental data showed reasonable agreement, and further improvements are underway. 4. Generation of mass transfer correlations for MSRE subchannel The Molten-Salt Reactor Experiment (MSRE) was a landmark historical project that demonstrated the feasibility of molten-salt reactor technology. The MSRE campaign also generated a significant body of experimental data and reports that continue to support molten-salt–related research. In this report, the MSRE core subchannel was used as the reference geometry for a mass transfer study performed with MOSCATO. The geometry and computational mesh were adapted from a previous study, providing adequate resolution for the relatively low Reynolds number in this case. Additional mesh refinement was applied to reach higher Schmidt numbers, enabling the derivation of a reliable mass-transfer correlation for the present scenario. 5. Simulations of oxygen ingressions into molten salt. In the previous fiscal year, we initiated a study to simulate oxygen ingression in stagnant salt. As oxygen enters the salt through its surface, it reacts with Ce 3+ to form solid CeO 2 and other reaction products. To more fully capture the complex diffusion-convection-reaction mechanisms, capabilities for modeling natural convection in the salt vessel were added. These were needed as the flow of the ingressed gas induced flow in the salt caused by surface shear and non-isothermal effects. With these updated physics in place, we were able to successfully reproduce the experimental results for the rate of change of CeCl 3 concentrations versus time. 6. Flow corrosion model validation. In FY24, MOSCATO’s corrosion model was validated against static corrosion experiments. In FY25, this work was extended to a flow corrosion experiment, where FLiNaK salt was driven by natural convection, with initial salt impurities to initiate corrosion. Despite uncertainties in parameters such as elemental diffusion coefficients in the alloy and unknown H + concentrations, the simulations achieved good agreement with experimental results, especially in predicting sample mass losses.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DESI 2024: Constraints on physics-focused aspects of dark energy using DESI DR1 BAO data

Baryon acoustic oscillation data from the first year of the Dark Energy Spectroscopic Instrument (DESI) provide near percent-level precision of cosmic distances in seven bins over the redshift range z=0.1–4.2. Here, this paper is the follow-up to the original DESI BAO cosmology paper [A. G. Adame et al. (DESI Collaboration), arXiv:2404.03002], which considered the conventional w 0 w a cold dark matter (CDM) model. We use the novel DESI data, together with other cosmic probes, to constrain the background expansion history using some well-motivated physical classes of dark energy. In particular, we explore three physics-focused behaviors of dark energy from the equation of state and energy density perspectives: the thawing class (matching many simple quintessence potentials), emergent class (where dark energy comes into being recently, as in phase transition models), and mirage class [where phenomenologically the distance to cosmic microwave background (CMB) last scattering is close to that from a cosmological constant Λ despite dark energy dynamics]. All three classes fit the data at least as well as Λ ⁢CDM, and indeed can improve on it by Δ⁢χ 2 ≈ –5 to –17 for the combination of DESI BAO with CMB and supernova data while having one more parameter. The mirage class does essentially as well as w 0 ⁢w a CDM and exhibits moderate to strong Bayesian evidence preference with respect to Λ⁢ CDM. These classes of dynamical behaviors highlight worthwhile avenues for further exploration into the nature of dark energy.

79 ASTRONOMY AND ASTROPHYSICS↗

DECOVALEX-2023: Task D Final Report

Task D of DECOVALEX-2023 is focused on the simulation of the coupled thermal hydraulic-mechanical (THM) behaviour in the full-scale engineered barrier system (EBS). The Horonobe EBS experiment is the demonstration of the full-scale EBS in the underground research laboratory (URL) (performed by JAEA in the Horonobe URL in Japan). Task D consisted of the three steps, a preliminary step (Step 0), simulation of the laboratory tests (Step 1) and simulation of the in-situ full-scale EBS experiment (Step 2). Since the Horonobe EBS experiment demonstrates the vertical emplacement option of the EBS, the experiment gallery is also backfilled with the backfill material. Therefore, interaction between the EBS and the backfill material can also be demonstrated, such as deformation (change of density) of the buffer material. The underground water in the Horonobe URL is saline. This fact adds chemical processes to THM behaviour. For example, mechanical properties (such as swelling pressure of the buffer material and backfill material) and hydraulic properties (such as permeability of the buffer material and backfill material) change depending on the water chemistry. Task D was therefore a challenging Task focused on not only the relatively simple THM behaviour but also complex THM behaviour including chemical processes. Six research teams (BGR, CAS, JAEA, KAERI, SNL and Taipower) participated the Task D. BGR, CAS, JAEA, KAERI and Taipower research teams selected a THM approach, while the SNL research team selected a TH approach. Step 1 involved the simulation of laboratory test results and was important to check the numerical codes developed by the research teams. Step 1 was divided into four sub steps. The simulation results through the Step 1 identified the parameters for simulation of the Step 2. Basic parameters of the materials (buffer material, backfill material, rock mass, concrete, sand) were provided by JAEA. Special parameters which research team needed were identified by back analysis of Step 1. Most notably the mechanical behaviour of swelling and displacement depended on the applied model (elastic model or elastoplastic model). Parameters such as Young’s modulus were found to need smaller values than characterised in the fundamental laboratory test results (Step 1-1, 1-2) for the elastic model. Although laboratory experiments are usually simple, test results contained some error. For example, if the saturation level is 100 % or higher, it should be considered an error. This situation was presented in the Step 1-3. A possible reason is that the buffer material is a mixture of bentonite and silica sand. When a specimen is cut to measure volume or weight, sand grains will affect the measurement data. In Step 2, boundary conditions such as temperature on the surface of the simulated overpack, heater power of the electrical heaters installed in the simulated overpack, injection pressure and inflow rate of the test water, were applied. The outer boundary conditions can be selected using measured data (injection pressure and inflow rate of the test water that is controlled by the injection systems installed in the sand layer around the buffer material and in the boundary between backfill material and concrete support). Since such measured data has some noise, research teams developed their own simplified boundary conditions. Inner boundary conditions can be selected using measured data as heater power and temperature on the surface of the simulated overpack. These data also contain some noise, so research teams developed their own simplified developed boundary conditions. Task D validated various approaches thorough the simulation of the in-situ full scale EBS system including backfill of the gallery: variations in the coupling processes (THM or THC), analysis codes, and boundary conditions. Temperature distribution in the buffer material was simulated well by all research teams. This means thermal behaviour is not sensitive to the simulation approaches. Although the water content distribution on the outside of the buffer material was well simulated by all research teams, the simulation results differ from the measured values inside the buffer material (at the centre and inside, near the simulated overpack). The buffer material is made from tap water, but in the in-situ experiment, saline groundwater infiltrates the buffer material. Therefore, the selection of the hydraulic parameters of the buffer material greatly affects the simulation results of the re saturation behaviour of the buffer material. In the Horonobe EBS experiment, measured values suitable for validating the simulation results were not obtained near the simulated overpack. When simulating the pressure and deformation of the buffer material, the measurement data is easily affected by the installation conditions of the measurement sensors, so verifying the measurement data itself remains an issue. Mechanical simulation results differ depending on whether they are considered as elastic or elastoplastic phenomena. The accuracy of measured in-situ data can be assessed by detailed analysis comparing sampling specimen analysis and measured data. The Horonobe EBS experiment is scheduled to be dismantled in the future (FY2026 and 2027). This detailed dismantling investigation will finally confirm the measured data.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Dark Energy Survey Year 6 results: cell-based coadds and METADETECTION weak lensing shape catalogue

We present the metadetection weak lensing galaxy shape catalogue from the 6-yr Dark Energy Survey (DES Y6) imaging data. This data set is the final release from DES, spanning 4422 deg 2 of the southern sky. We describe how the catalogue was constructed, including the two new major processing steps, cell-based image coaddition, and shear measurements with metadetection. The DES Y6 M etadetection weak lensing shape catalogue consists of 151 922 791 galaxies detected over riz bands, with an effective number density of n eff = 8.22 galaxies per arcmin 2 and shape noise of σ e = 0.29. We carry out a suite of validation tests on the catalogue, including testing for point spread function (PSF) leakage, testing for the impact of PSF modelling errors, and testing the correlation of the shear measurements with galaxy, PSF, and survey properties. In addition to demonstrating that our catalogue is robust for weak lensing science, we use the DES Y6 image simulation suite to estimate the overall multiplicative shear bias of our shear measurement pipeline. We find no detectable multiplicative bias at the roughly half-per cent level, with m = (3.4 ± 6.1) x 10 –3 , at 3σ uncertainty. This is the first time both cell-based coaddition and Metadetection algorithms are applied to observational data, paving the way to the Stage-IV weak lensing surveys.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗