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247 records · Page 14

Study on Application of Distributed Network of Sensors with List Mode for NMAC Literature Review

Nuclear material accounting and control (NMAC) for nuclear security detects, deters, and resolves questions related to unauthorized removal (i.e. theft) or misuse of nuclear material. NMAC also serves as a key insider threat mitigation measure and aids in recovery of nuclear material that is missing. Effective nuclear security depends on NMAC for timely and accurate information about nuclear material types, quantities, and locations. Bulk nuclear material processing facilities, however, present unique challenges for effective NMAC due to the presence of large quantities of material in-process and the accumulation of residual material holdup within process equipment. These holdup accumulations can obscure accurate physical inventory taking and complicate efforts to resolve NMAC irregularities at the facility level. Bulk material monitoring systems often rely on material balance calculations and indirect measurement techniques, which may mask protracted theft of smaller amounts of nuclear material. These monitoring limitations have generated increased interest in continuous monitoring technologies, including distributed non-destructive assay (NDA) sensor networks capable of providing real-time or near-real-time measurement of material movement and accumulation within bulk processing environments. Recent advancements in distributed networks of NDA radiation detectors and sensing technologies provide an opportunity to address these limitations. Although such distributed sensor networks have been implemented in select facilities for IAEA Safeguards applications, their potential for supporting NMAC functions specifically tailored to nuclear security objectives remains largely unexplored. Furthermore, emerging list-mode data acquisition technologies have reached high technology readiness levels, enabling time-correlated detection of nuclear events across multiple temporal scales. These capabilities provide enhanced opportunities for accurate holdup measurement, continuous process monitoring, and improved detection of material theft or misuse over time. The increasing global expansion of civil nuclear power and development of related bulk material processing facilities, including those supporting high-assay low-enriched uranium (HALEU) and other advanced reactor fuel fabrication, further increases the need for advanced measurement and monitoring strategies for NMAC.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Wellbore Stability and Mud Loss Management in Geothermal Drilling: Optimizing Mud Weight to Mitigate Tensile Wellbore Fracturing at The Geysers, California

As part of a U.S. Department of Energy (DOE) Geothermal Technologies Office-funded initiative, Geysers Power Company, LLC, a subsidiary of Calpine Corporation, has been working to enhance drilling performance at the world’s largest geothermal field, The Geysers, in northern California. In a recent drilling operation of the GDC-36 well, excessive mud losses were encountered, initially addressed through repeated but largely ineffective cement plugging. Ultimately, the most effective strategy was to drill blind through the loss zones, made feasible by the high rate of penetration (ROP) achieved with PDC bits, allowing significant progress before the mud tanks were depleted and water-sensitive argillic formation layers could collapse. In response to these challenges, the project team explored alternative methods to minimize downtime and risks associated with cement plugging and continuous mud loss and to contemplate the driving mechanisms for the losses. Wellbore imaging using Formation MicroImager (FMI) and Ultrasonic Borehole Imager (UBI) tools revealed longitudinal tensile fractures, which were attributed to mud weights exceeding the minimum circumferential stress resulting from the native stress field and formation pressure. This study examines the mud losses encountered and leverages wellbore imaging data to understand the mechanisms behind mud induced tensile fracturing in specific rock facies. Understanding fracture behavior across different lithologies is crucial, as fractures within the reservoir can enhance steam migration throughout the system. The reservoir at The Geysers lies within the Mesozoic Franciscan Assemblage, a tectonic mélange formed by subduction. It consists of metamorphosed turbidite sandstone (greywacke) and mudstone (argillite), oceanic upper crust (including greenstone and chert), and serpentinized ultramafic rocks - each exhibiting distinct geomechanical fracturing properties. The structural fabric of the Franciscan Assemblage was shaped by low-angle Mesozoic thrust faulting and later overprinted by sub-vertical strike-slip structures related to the Pacific-North American plate boundary. A wellbore stability model was developed using core measurements and logs to simulate fracturing scenarios during drilling under varying stress conditions. These simulations guided the development of an optimized mud weight management strategy that should enable adaptive adjustments during drilling, reducing the likelihood of tensile fracturing and mud losses, ultimately improving operational efficiency.

15 GEOTHERMAL ENERGY↗

An Improved Measurement of the Secondary Cosmic Microwave Background Anisotropies from the SPT-SZ + SPTpol Surveys

We report new measurements of millimeter-wave power spectra in the angular multipole range 2000 ≤ ℓ ≤ 11,000 (angular scales ). By adding 95 and 150 GHz data from the low-noise 500 deg 2 SPTpol survey to the SPT-SZ three-frequency 2540 deg 2 survey, we substantially reduce the uncertainties in these bands. These power spectra include contributions from the primary cosmic microwave background, cosmic infrared background, radio galaxies, and thermal and kinematic Sunyaev–Zel'dovich (SZ) effects. The data favor a thermal SZ (tSZ) power at 143 GHz of and a kinematic SZ (kSZ) power of . This is the first measurement of kSZ power at ≥3 σ . However, different assumptions about the CIB or SZ models can reduce the significance down to 2.4 σ in the worst case. We study the implications of the measured kSZ power for the epoch of reionization under the Calabrese et al. model for the kSZ power spectrum and find the duration of reionization to be ( at 95% confidence), when combined with our previously published tSZ bispectrum measurement. The upper limit tightens to if the assumed homogeneous kSZ power is increased by 25% (~0.5 μ K 2 ) and relaxes to if the homogeneous kSZ power is decreased by the same amount.

79 ASTRONOMY AND ASTROPHYSICS↗

Cosmological constraints from DES Y1 cluster abundances and SPT multiwavelength data

We perform a joint analysis of the counts of redMaPPer clusters selected from the Dark Energy Survey (DES) year 1 data and multiwavelength follow-up data collected within the 2500 deg2 South Pole Telescope (SPT) Sunyaev-Zel’dovich (SZ) survey. The SPT follow-up data, calibrating the richness-mass relation of the optically selected redMaPPer catalog, enable the cosmological exploitation of the DES cluster abundance data. To explore possible systematics related to the modeling of projection effects, we consider two calibrations of the observational scatter on richness estimates: a simple Gaussian model which account only for the background contamination (BKG), and a model which further includes contamination and incompleteness due to projection effects (PRJ). Assuming either a ΛCDM+∑mν or wCDM+∑mν cosmology, and for both scatter models, we derive cosmological constraints consistent with multiple cosmological probes of the low and high redshift Universe, and in particular with the SPT cluster abundance data. This result demonstrates that the DES Y1 and SPT cluster counts provide consistent cosmological constraints, if the same mass calibration data set is adopted. It thus supports the conclusion of the DES Y1 cluster cosmology analysis which interprets the tension observed with other cosmological probes in terms of systematics affecting the stacked weak lensing analysis of optically selected low–richness clusters. Finally, we analyze the first combined optically SZ selected cluster catalog obtained by including the SPT sample above the maximum redshift probed by the DES Y1 redMaPPer sample (z=0.65). Besides providing a mild improvement of the cosmological constraints, this data combination serves as a stricter test of our scatter models: the PRJ model, providing scaling relations consistent between the two abundance and multiwavelength follow-up data, is favored over the BKG model.

79 ASTRONOMY AND ASTROPHYSICS↗

Public Reference Data for Megawatt-Scale Hydrogen Electrolysis – Simulated Wind

The U.S. Department of Energy and the National Laboratory of the Rockies (NLR) demonstrate hydrogen electrolysis, hydrogen compression and storage, and variable hydrogen fuel cell power production using megawatt-scale equipment at NLR’s Flatirons Campus as part of the Advanced Research on Integrated Energy Systems (ARIES) initiative. This dataset represents part of that effort and is intended for academic, national laboratory, industrial, and other stakeholders to plan, design, and validate models of megawatt-scale hydrogen technologies and diverse energy infrastructure nationwide. These data provide a baseline for how existing hydrogen electrolysis technologies perform when coupled with various energy technologies. Future datasets will demonstrate how existing hydrogen fuel cell technologies can provide controllable, dispatchable, and variable power output for artificial intelligence (AI) data centers and other variable loads. This dataset entry describes hydrogen production using a single, simulated wind turbine. The electrolyzer is a 1.25-MW proton exchange membrane type MC250 system manufactured by Nel Hydrogen . While the unit supports up to 2.5 MW of electrolysis, NLR only has a single 1.25-MW electrolysis stack. For the simulated wind energy profiles, NLR used OpenFAST to simulate a 3.4-MW International Energy Agency (IEA) reference wind turbine. The hour-long wind energy profiles varied over wind turbulence intensity (Class A or Class C) and average wind speed (5, 7, or 9 m/s). To match the power limits of the 1.25-MW electrolyzer and 3.4-MW IEA wind turbine most effectively and to maximize the efficiency of hydrogen production at a given average wind speed, the profiles were sometimes scaled by two times. This means that, in some cases, the experimental setup assumed two 1.25-MW electrolyzers were coupled with the wind turbine, representing a total maximum electrolysis load of 2.5 MW. Finally, NLR experimented with two settings for the electrolyzer power supply minimum and maximum current ramp rates (gain and slew): 200 and 400 amperes per second. The simulated profiles were translated from power (kilowatts) to current (amperes) using a curve fit with calibration data and sent to the electrolyzer power supply at 1-Hz frequency. These datasets report relevant hydrogen balance-of-plant and system data, all captured at 1 Hz, including hydrogen mass production measured with an Emerson Coriolis flow meter. Each .zip file represents a single wind turbine electrolysis experiment and is formatted as follows: {technology}-{average wind speed}-{turbulence class}_{number of 1.25 MW electrolyzers connected}-{electrolyzer ramp rate in amperes/second} For instance, “windIEA3.4-5ms-C_2-400.zip” represents the hour-long experiment using the IEA 3.4-MW turbine, subjected to an average wind speed of 5 m/s and Class C wind turbulence, and connected to two 1.25-MW electrolyzers with the power supply set to a maximum current ramp rate (gain and slew) of 400 A/s. Each .zip folder contains the following files: A .csv file containing raw data. An .xlsx file explaining all the fields in the raw data. A .png plot showing the time series of hydrogen production in kilograms per hour, electrolysis power consumption, and input wind turbine power. An experiment labeled “characterization_200.zip” demonstrates the MC250 electrolyzer steady-state response with 30 minute load steps for a total duration of 5 hours. Finally, a .csv file is provided with all simulated wind experiments combined into one dataset labeled "combined_wind_experiments.csv". NLR also built an AI/machine-learning predictive model based on these datasets. The model ingests the electrolyzer current command in amperes, as well as various pressures and temperatures across the system, and predicts hydrogen output in kilograms per hour. The complete model can be found at https://huggingface.co/NatLabRockies/ptmelt-hydrogen-electrolysis .

08 HYDROGEN↗

Galaxy Clusters Selected via the Sunyaev–Zel’dovich Effect in the SPTpol 100-square-degree Survey

In this work, we present a catalog of galaxy cluster candidates detected in 100 square degrees surveyed with the SPTpol receiver on the South Pole Telescope. The catalog contains 89 candidates detected with a signal-to-noise ratio greater than 4.6. The candidates are selected using the Sunyaev–Zel'dovich effect at 95 and 150 GHz. Using both space- and ground-based optical and infrared telescopes, we have confirmed 81 candidates as galaxy clusters. We use these follow-up images and archival images to estimate photometric redshifts for 66 galaxy clusters and spectroscopic observations to obtain redshifts for 13 systems. An additional two galaxy clusters are confirmed using the overdensity of near-infrared galaxies only and are presented without redshifts. We find that 15 candidates (18% of the total sample) are at redshift z ≥ 1.0, with a maximum confirmed redshift of ${z}_{\max }=1.38\pm 0.10$. We expect this catalog to contain every galaxy cluster with ${M}_{500c}\gt 2.6\times {10}^{14}{M}_{\odot }{{h}}_{70}^{-1}$ and z > 0.25 in the survey area. The mass threshold is approximately constant above z = 0.25, and the complete catalog has a median mass of approximately ${M}_{500c}=2.7\times {10}^{14}{M}_{\odot }{{h}}_{70}^{-1}$. Compared to previous SPT works, the increased depth of the millimeter-wave data (11.2 and 6.5 μK-arcmin at 95 and 150 GHz, respectively) makes it possible to find more galaxy clusters at high redshift and lower mass.

79 ASTRONOMY AND ASTROPHYSICS↗

Evaluation of FluSight influenza forecasting in the 2021–22 and 2022–23 seasons with a new target laboratory-confirmed influenza hospitalizations

Accurate forecasts can enable more effective public health responses during seasonal influenza epidemics. For the 2021–22 and 2022–23 influenza seasons, 26 forecasting teams provided national and jurisdiction-specific probabilistic predictions of weekly confirmed influenza hospital admissions for one-to-four weeks ahead. Forecast skill is evaluated using the Weighted Interval Score (WIS), relative WIS, and coverage. Six out of 23 models outperform the baseline model across forecast weeks and locations in 2021–22 and 12 out of 18 models in 2022–23. Averaging across all forecast targets, the FluSight ensemble is the 2nd most accurate model measured by WIS in 2021–22 and the 5th most accurate in the 2022–23 season. Forecast skill and 95% coverage for the FluSight ensemble and most component models degrade over longer forecast horizons. In this work we demonstrate that while the FluSight ensemble was a robust predictor, even ensembles face challenges during periods of rapid change.

59 BASIC BIOLOGICAL SCIENCES↗

New insights into Mn 2+ and Mg 2+ inhibition of calcite growth

Impurity ion and isotope partitioning into carbonate minerals provide a window into the molecular processes occurring at the fluid-mineral interface during crystal growth. Here, we employ calcium isotope fractionation together with process-based modeling to elucidate the mechanisms by which two divalent cations with starkly contrasting compatibility, magnesium and manganese, inhibit calcite growth and incorporate into the mineral lattice. Calcite growth inhibition by Mg 2+ is log-linear and K Mg is on the order of 0.02–0.03 throughout the range of {Mg 2+ }/{Ca 2+ } studied here (0.01–2.6). Mn 2+ exhibits much stronger log-linear growth rate inhibition at low Mn 2+ concentrations (fluid {Mn 2+ }/{Ca 2+ } = 0.001–0.02). Mn 2+ is readily incorporated into the calcite lattice to form a calcite-rhodochrosite solid solution, with large partition coefficients (K Mn 4.6–15.6) inversely correlated to growth rate. For both Mn 2+ and Mg 2+ , calcium isotope fractionation is found to be invariant with {Me 2+ }/{Ca 2+ } despite more than an order of magnitude decline in growth rate. This invariant Δ 44/40 Ca suggests that the presence of Mn 2 + or Mg 2+ does not significantly change the relative rates of Ca 2+ attachment and detachment at kink sites during growth, indicative of a dominantly kink blocking inhibition mechanism. Because the partitioning behavior dictates that Mn 2+ must attach to the surface significantly faster than Ca 2+ , attachment of Mn 2+ is likely to be as a non-monomer species such as an ion pair or possibly a larger polynuclear cluster. We propose that calcite growth rate inhibition by Mn is determined by the kinetics of carbonate attachment at Mn-occupied kink sites, potentially due to slow re-orientation kinetics of carbonate ions that have formed an inner-sphere complex with Mn 2+ at the surface but must reorient to incorporate into the lattice. We demonstrate that patterns in Mg 2+ partitioning and inhibition behavior are broadly consistent with growth inhibition driven by slow Mg 2+ -aquo complex dehydration relative to Ca 2+ but argue that this mechanism likely represents one endmember scenario, seen in Mg-calcite growth at low supersaturations and net precipitation rates. During growth at faster net precipitation rates, some portion of Mg 2+ is likely incorporated as a partially hydrated or otherwise complexed species, but calcite growth remains significantly inhibited by the kinetics of CO 3 2- attachment at Mg 2+ kink sites. These findings suggest a hybrid classical/nonclassical growth mechanism whereby Ca 2+ incorporates largely as a free ion at kink sites while Mn 2+ and some portion of Mg 2+ are incorporated via non-monomer attachment. This pattern may be generalizable; trace constituent cations with aquo-complex desolvation rates significantly slower than the mineral growth rate preferentially incorporate as a non-monomer species during otherwise classical crystal growth.

58 GEOSCIENCES↗

SPT-SZ MCMF: an extension of the SPT-SZ catalogue over the DES region

We present an extension to a Sunyaev–Zel’dovich Effect (SZE) selected cluster catalogue based on observations from the South Pole Telescope (SPT); this catalogue extends to lower signal to noise than the previous SPT–SZ catalogue and therefore includes lower mass clusters. Optically derived redshifts, centres, richnesses, and morphological parameters together with catalogue contamination and completeness statistics are extracted using the multicomponent matched filter (MCMF) algorithm applied to the S/N > 4 SPT–SZ candidate list and the Dark Energy Survey (DES) photometric galaxy catalogue. The main catalogue contains 811 sources above S/N = 4, has 91 per cent purity, and is 95 per cent complete with respect to the original SZE selection. It contains in total 50 per cent more clusters and twice as many clusters above z = 0.8 in comparison to the original SPT-SZ sample. The MCMF algorithm allows us to define subsamples of the desired purity with traceable impact on catalogue completeness. As an example, we provide two subsamples with S/N > 4.25 and S/N > 4.5 for which the sample contamination and cleaning-induced incompleteness are both as low as the expected Poisson noise for samples of their size. The subsample with S/N > 4.5 has 98 per cent purity and 96 per cent completeness and is part of our new combined SPT cluster and DES weak-lensing cosmological analysis. We measure the number of false detections in the SPT-SZ candidate list as function of S/N, finding that it follows that expected from assuming Gaussian noise, but with a lower amplitude compared to previous estimates from simulations.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Brightest Cluster Galaxy ellipticity as proxy for halo shape: Orientation bias, assembly bias, and potential selection effects in SZ-selected clusters

The orientation of triaxial galaxy clusters with respect to the line-of-sight is expected to be one of the prime sources of scatter and potential bias in optical observables (e.g., richness and weak-lensing signal) of galaxy clusters. In this work, we use the observed shape of the central Brightest Cluster Galaxy (BCG) as proxy for the orientation along the line-of-sight for clusters selected via the Sunyaev-Zel'dovich (SZ) effect from the South Pole Telescope (SPT) and Atacama Cosmology Telescope (ACT) surveys, matched to optically selected clusters from the Dark Energy Survey Year 3 (DES). We construct two samples of clusters that are designed to be identical in SZ mass estimate and redshift but with the roundest vs. the most elliptical BCGs, which we expect to correspond to BCGs (and clusters) with major axes aligned along the line-of-sight vs. in the plane of the sky, respectively. We find that the optical richness of round-BCG clusters is $\sim 10$% larger than that of elliptical-BCG clusters, in agreement with the expectation from projection effects and presenting the first such detection in data. The density profiles, however, are not in agreement with the expectation from projection effects: the 1-halo term (below $6~h^{-1}\rm{Mpc}$) of both the weak-lensing and galaxy density profiles are the same for the subsamples, contrary to previous studies based on X-ray selected clusters. In the 2-halo regime (above $6~h^{-1}\rm{Mpc}$), we find a significant excess of the elliptical-BCG cluster profiles compared to the round-BCG cluster profiles, which is the opposite of the expectation from numerical simulations. We hypothesize that the intrinsic shape of the BCG reflects not just the orientation angle, but also intrinsic properties of the cluster which can affect both the SZ signal and the amplitude of the 2-halo term.

Srinivasan, Radhakrishnan [SUNY, Stony Brook] (ORC↗

Characterization of the Polarization Beam Response of SPT-3G Using Point Sources

Precise measurements of cosmic microwave background (CMB) polarization require rigorous control of instrumental systematics. For the South Pole Telescope's third-generation camera (SPT-3G), which observes in three bands centered near 95, 150, and 220 GHz, accurate beam characterization is critical for interpreting the polarized mm-wave sky. We present direct measurements of SPT-3G's polarized beam response from observations of 100 bright extragalactic point sources. Previous SPT-3G power spectrum analyses introduced a phenomenological parameter, $β_{\rm pol}$, to describe the polarization preserved in beam sidelobes, and found evidence for significant depolarization from the requirement of inter-frequency polarization power spectrum consistency. Our direct measurements yield $β_{\rm pol}=0.89\pm0.10$ at 95 GHz, $1.08\pm0.10$ at 150 GHz, and $0.90\pm0.22$ at 220 GHz, indicating minimal sidelobe depolarization. We validate these results with systematic tests of posterior sampling versus bootstrap resampling, real-space versus Fourier-space analysis, temperature-to-polarization leakage handling, covariance determination, and source selection. Compared to values inferred from previous cosmological analyses, our results differ by an effective $1.3σ$. This apparent discrepancy is model dependent, because the point source analysis derives much of its $β_{\rm pol}$ constraining power from higher multipoles than the power spectrum analysis. These measurements therefore admit three explanations for the frequency-dependent residuals observed in the power spectrum analysis: a statistical fluctuation, the need for more sophisticated polarized beam models, or systematics other than beam depolarization.

de Haan, T. [KEK, Tsukuba]↗

Cosmology From CMB Lensing and Delensed EE Power Spectra Using 2019-2020 SPT-3G Polarization Data

From CMB polarization data alone we reconstruct the CMB lensing power spectrum, comparable in overall constraining power to previous temperature-based reconstructions, and an unlensed E -mode power spectrum, with clear detections of the third through tenth acoustic peaks. The observations, taken in 2019 and 2020 with the South Pole Telescope (SPT) and the SPT-3G camera, cover 1500 deg 2 at 95, 150, and 220 GHz with arcminute resolution and roughly 4.9 µ K-arcmin coadded noise in polarization. The power spectrum estimates, together with systematic parameter estimates and a joint covariance matrix, follow from a Bayesian analysis using the Marginal Unbiased Score Expansion (MUSE) method. The E -mode spectrum at ℓ > 2000 and lensing spectrum at L > 350 are the most precise to date. Assuming the ΛCDM model, and using only these SPT data and priors on τ and absolute calibration from Planck, we find H 0 = 66.81 ± 0.81 km/s/Mpc, comparable in precision to the Planck determination and in 5.4 σ tension with the most precise H 0 inference derived via the distance ladder. We also find S 8 ≡ σ 8 (Ω m /0.3) 0.5 = 0.850 ± 0.017, providing further independent evidence of a slight tension with low-redshift structure probes. The ΛCDM model provides a good simultaneous fit to the combined Planck, ACT, and SPT data, and thus passes a powerful test. Combining these CMB datasets with BAO observations, we explore extensions to the ΛCDM model. We find that the effective number of neutrino species, spatial curvature, and primordial helium fraction are consistent with standard model values, and that the 95% confidence upper limit on the neutrino mass sum is 0.075 eV, close to the minimum sum expected from observations of solar and atmospheric neutrino oscillations. The SPT data are consistent with the somewhat weak (< 3 σ ) preference for excess lensing power seen in Planck and ACT data relative to predictions of the ΛCDM model given the combined Planck, ACT, and BAO data sets. Finally, we also detect at greater than 3 σ the influence of non-linear evolution in the CMB lensing power spectrum and discuss it in the context of the S 8 tension. Forthcoming SPT-3G analyses will feature deeper and wider observations in temperature and polarization, providing even tighter constraints and more powerful tests of the ΛCDM model.

79 ASTRONOMY AND ASTROPHYSICS↗

SPT-3G D1: A Measurement of Secondary Cosmic Microwave Background Anisotropy Power

We report new measurements of millimeter-wave temperature power spectra in the angular multipole range $1700 \le \ell \le 11,000$ (wavelengths $13^\prime \gtrsim λ\gtrsim 2^\prime$). We use two years of data in three observing bands centered near 95, 150, and 220 GHz from the SPT-3G receiver on the South Pole Telescope that cover a 1646 deg$^2$ region of the Southern sky. Using the measured power spectra, we present constraints on the thermal and kinematic Sunyaev-Zel'dovich (SZ) effects, radio galaxies, and cosmic infrared background (CIB). We find that inferred SZ powers are dependent on the detailed modeling of the thermal SZ-CIB correlation, and to a lesser extent on the assumed angular dependence of the SZ spectra. We report constraints for simulation-based model templates as well as fits where the angular dependencies of the SZ and CIB power spectra are allowed to vary. In the latter case at $\ell=3000$, we find thermal SZ power at 143 GHz of $D_{3000}^{\rm tSZ} = 4.91\pm0.37\, μ{\rm K}^2$ and kinematic SZ power of $D_{3000}^{\rm kSZ} =1.75\pm0.86\, μ{\rm K}^2$. We use the measured kinematic SZ power to estimate the duration of reionization, noting that the reionization inferences are sensitive to the model choices and assumed level of homogeneous kinematic SZ power from the late-time universe. We find a 95% limit on the duration from an ionization fraction of 25% to 75% of $Δ^{50} z_{\rm re} <\,3.8$ based on a semi-analytic model, or a limit on the duration from an ionization fraction of 5% to 95% of $Δ^{90} z_{\rm re} <\,6.1$ based on the AMBER simulations.

Chaubal, P. [Melbourne U.]↗