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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

QUIJOTE scientific results – IV. A northern sky survey in intensity and polarization at 10–20 GHz with the multifrequency instrument

ABSTRACT We present QUIJOTE intensity and polarization maps in four frequency bands centred around 11, 13, 17, and 19 GHz, and covering approximately 29 000 deg2, including most of the northern sky region. These maps result from 9000 h of observations taken between May 2013 and June 2018 with the first QUIJOTE multifrequency instrument (MFI), and have angular resolutions of around 1°, and sensitivities in polarization within the range 35–40 µK per 1° beam, being a factor ∼2–4 worse in intensity. We discuss the data processing pipeline employed, and the basic characteristics of the maps in terms of real space statistics and angular power spectra. A number of validation tests have been applied to characterize the accuracy of the calibration and the residual level of systematic effects, finding a conservative overall calibration uncertainty of 5 per cent. We also discuss flux densities for four bright celestial sources (Tau A, Cas A, Cyg A, and 3C274), which are often used as calibrators at microwave frequencies. The polarization signal in our maps is dominated by synchrotron emission. The distribution of spectral index values between the 11 GHz and WMAP 23 GHz map peaks at β = −3.09 with a standard deviation of 0.14. The measured BB/EE ratio at scales of ℓ = 80 is 0.26 ± 0.07 for a Galactic cut |b| > 10°. We find a positive TE correlation for 11 GHz at large angular scales (ℓ ≲ 50), while the EB and TB signals are consistent with zero in the multipole range 30 ≲ ℓ ≲ 150. The maps discussed in this paper are publicly available.

Astronomy & Astrophysics↗
DOE OSTI2023

Dark matter axion search using a Josephson Traveling wave parametric amplifier

Here, we describe the first implementation of a Josephson Traveling Wave Parametric Amplifier (JTWPA) in an axion dark matter search. The operation of the JTWPA for a period of about two weeks achieved sensitivity to axion-like particle dark matter with axion–photon couplings above 10 -13 Ge V -1 over a narrow range of axion masses centered around 19.84 µeV by tuning the resonant frequency of the cavity over the frequency range of 4796.7–4799.5 MHz. The JTWPA was operated in the insert of the axion dark matter experiment as part of an independent receiver chain that was attached to a 0.56-l cavity. The ability of the JTWPA to deliver high gain over a wide (3 GHz) bandwidth has engendered interest from those aiming to perform broadband axion searches, a longstanding goal in this field.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

The Atacama Cosmology Telescope: A Catalog of >4000 Sunyaev–Zel’dovich Galaxy Clusters

Here, we present a catalog of 4195 optically confirmed Sunyaev–Zel’dovich (SZ) selected galaxy clusters detected with signal-to-noise ratio >4 in 13,211 deg 2 of sky surveyed by the Atacama Cosmology Telescope (ACT). Cluster candidates were selected by applying a multifrequency matched filter to 98 and 150 GHz maps constructed from ACT observations obtained from 2008 to 2018 and confirmed using deep, wide-area optical surveys. The clusters span the redshift range 0.04 < z < 1.91 (median z = 0.52). The catalog contains 222 z > 1 clusters, and a total of 868 systems are new discoveries. Assuming an SZ signal versus mass-scaling relation calibrated from X-ray observations, the sample has a 90% completeness mass limit of M 500 c > 3.8 × 10 14 M ⊙ , evaluated at z = 0.5, for clusters detected at signal-to-noise ratio >5 in maps filtered at an angular scale of 2.'4. The survey has a large overlap with deep optical weak-lensing surveys that are being used to calibrate the SZ signal mass-scaling relation, such as the Dark Energy Survey (4566 deg 2 ), the Hyper Suprime-Cam Subaru Strategic Program (469 deg 2 ), and the Kilo Degree Survey (825 deg 2 ). We highlight some noteworthy objects in the sample, including potentially projected systems, clusters with strong lensing features, clusters with active central galaxies or star formation, and systems of multiple clusters that may be physically associated. The cluster catalog will be a useful resource for future cosmological analyses and studying the evolution of the intracluster medium and galaxies in massive clusters over the past 10 Gyr.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

BASS XXXII: Studying the Nuclear Millimeter-wave Continuum Emission of AGNs with ALMA at Scales ≲100–200 pc

To understand the origin of nuclear (≲100 pc) millimeter-wave (mm-wave) continuum emission in active galactic nuclei (AGNs), we systematically analyzed subarcsecond resolution Band-6 (211–275 GHz) Atacama Large Millimeter/submillimeter Array data of 98 nearby AGNs (z < 0.05) from the 70 month Swift/BAT catalog. The sample, almost unbiased for obscured systems, provides the largest number of AGNs to date with high mm-wave spatial resolution sampling (~1–200 pc), and spans broad ranges of 14–150 keV luminosity {$40\lt \mathrm{log}[{L}_{14-150}/(\mathrm{erg}\,{{\rm{s}}}^{-1})]\lt 45$}, black hole mass $[5\lt \mathrm{log}({M}_{\mathrm{BH}}/{M}_{\odot })\lt 10$], and Eddington ratio ($-4\lt \mathrm{log}{\lambda }_{\mathrm{Edd}}\lt 2$). We find a significant correlation between 1.3 mm (230 GHz) and 14–150 keV luminosities. Its scatter is ≈0.36 dex, and the mm-wave emission may serve as a good proxy of the AGN luminosity, free of dust extinction up to N H ~ 10 26 cm –2 . While the mm-wave emission could be self-absorbed synchrotron radiation around the X-ray corona according to past works, we also discuss different possible origins of the mm-wave emission: AGN-related dust emission, outflow-driven shocks, and a small-scale (<200 pc) jet. The dust emission is unlikely to be dominant, as the mm-wave slope is generally flatter than expected. Also, due to no increase in the mm-wave luminosity with the Eddington ratio, a radiation-driven outflow model is possibly not the common mechanism. Furthermore, we find independence of the mm-wave luminosity on indicators of the inclination angle from the polar axis of the nuclear structure, which is inconsistent with a jet model whose luminosity depends only on the angle.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Experimental realization of linearly polarized x-ray detected ferromagnetic resonance

We present the first theoretical and experimental evidence of time-resolved dynamic x-ray magnetic linear dichroism (XMLD) measurements of GHz magnetic precessions driven by ferromagnetic resonance in both metallic and insulating thin films. Our findings show a dynamic XMLD in both ferromagnetic Ni 80 Fe 20 and ferrimagnetic Ni 0.65 Zn 0.35 Al 0.8 Fe 1.2 O 4 for different measurement geometries and linear polarizations. A detailed analysis of the observed signals reveals the importance of separating different harmonic components in the dynamic signal in order to identify the XMLD response without the influence of competing contributions. In particular, RF magnetic resonance elicits a large dynamic XMLD response at the fundamental frequency under experimental geometries with oblique x-ray polarization. The geometric range and experimental sensitivity can be improved by isolating the 2ω Fourier component of the dynamic response. These results illustrate the potential of dynamic XMLD and represent a milestone accomplishment toward the study of GHz spin dynamics in systems beyond ferromagnetic order.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Analysis of Polarized Dust Emission Using Data from the First Flight of SPIDER

Using data from the first flight of Spider and from the Planck High Frequency Instrument, we probe the properties of polarized emission from interstellar dust in the Spider observing region. Component-separation algorithms operating in both the spatial and harmonic domains are applied to probe their consistency and to quantify modeling errors associated with their assumptions. Analyses of diffuse Galactic dust emission spanning the full Spider region demonstrate (i) a spectral energy distribution that is broadly consistent with a modified-blackbody (MBB) model with a spectral index of β d = 1.45 ± 0.05 (1.47 ± 0.06) for E (B)-mode polarization, slightly lower than that reported by Planck for the full sky; (ii) an angular power spectrum broadly consistent with a power law; and (iii) no significant detection of line-of-sight polarization decorrelation. Tests of several modeling uncertainties find only a modest impact (~10% in σ r ) on Spider's sensitivity to the cosmological tensor-to-scalar ratio. The size of the Spider region further allows for a statistically meaningful analysis of the variation in foreground properties within it. Assuming a fixed dust temperature T d = 19.6 K, an analysis of two independent subregions of that field results in inferred values of β d = 1.52 ± 0.06 and β d = 1.09 ± 0.09, which are inconsistent at the 3.9σ level. Furthermore, a joint analysis of Spider and Planck 217 and 353 GHz data within one subregion is inconsistent with a simple MBB at more than 3σ, assuming a common morphology of polarized dust emission over the full range of frequencies. This evidence of variation may inform the component-separation approaches of future cosmic microwave background polarization experiments.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Beam combining of high-power terahertz lasers with semiconductor metasurface gratings

Spectral beam combining (SBC) of an array of single-mode lasers has the potential for realizing a chip-scale electrically tunable multispectral laser source without any moving parts and with emission at closely spaced discrete frequencies. Here, we demonstrate SBC of an array of single-mode THz quantum-cascade lasers (QCLs) with small frequency spacing. Semiconductor-based metasurface THz blazed gratings are developed for integration with QCLs in a compact cryocooler setup. Single-lobed beams of four QCLs emitting around 3.2 THz and spectrally separated by ~14 GHz are combined to achieve collinear propagation of spatially overlapped and collimated beams in the far field with ≲ 0.1° of pointing error. Peak optical power in the range 50–100 mW is detected from each of the QCLs after combining. The dense frequency spacing in our method provides a pathway to incorporate tens of QCLs on a chip to realize a high-power discretely tunable THz laser source for applications in THz spectroscopy.

Jia, Fei [Lehigh Univ., Bethlehem, PA (United Stat↗
DOE OSTI2023

BICEP/Keck. XVI. Characterizing Dust Polarization through Correlations with Neutral Hydrogen

We characterize Galactic dust filaments by correlating BICEP/Keck and Planck data with polarization templates based on neutral hydrogen (H i) observations. Dust polarization is important for both our understanding of astrophysical processes in the interstellar medium (ISM) and the search for primordial gravitational waves in the cosmic microwave background (CMB). In the diffuse ISM, H i is strongly correlated with the dust and partly organized into filaments that are aligned with the local magnetic field. We analyze the deep BICEP/Keck data at 95, 150, and 220 GHz, over the low-column-density region of sky where BICEP/Keck has set the best limits on primordial gravitational waves. We separate the H i emission into distinct velocity components and detect dust polarization correlated with the local Galactic H i but not with the H i associated with Magellanic Stream i. We present a robust, multifrequency detection of polarized dust emission correlated with the filamentary H i morphology template down to 95 GHz. For assessing its utility for foreground cleaning, we report that the Hi morphology template correlates in B modes at a ~10%–65% level over the multipole range 20 < ℓ < 200 with the BICEP/Keck maps, which contain contributions from dust, CMB, and noise components. We measure the spectral index of the filamentary dust component spectral energy distribution to be β = 1.54 ± 0.13. We find no evidence for decorrelation in this region between the filaments and the rest of the dust field or from the inclusion of dust associated with the intermediate velocity H i. Finally, we explore the morphological parameter space in the H i-based filamentary model.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

High-volume tunable resonator for axion searches above 7 GHz

In this research, we present results from an experimental demonstration of a tunable thin-shell axion haloscope whose geometry decouples its overall volume from its resonant frequency, thereby evading the steep sensitivity degradation at high frequencies. An aluminum 2.6-l (41⁢λ 3 ) prototype, which tunes from 7.1 to 8.0 GHz, was fabricated and characterized at room temperature. An axion-sensitive, straightforwardly tunable TM 010 mode is clearly identified with a room-temperature quality factor, Q, of approximately 5000. The on-resonance E-field distribution is mapped and found to agree with numerical calculations. Anticipating future cryogenic operation, we develop an alignment protocol relying only on rf measurements of the cavity, maintaining a form factor of 0.57 across the full tuning range. These measurements demonstrate the feasibility of cavity-based haloscopes with operating volume V $\gg$ λ 3 . We discuss plans for future development and the parameters required for a thin-shell haloscope exploring the postinflationary axion parameter space (approximately 4 to 30 GHz) at Dine-Fischler-Srednicki-Zhitnitsky sensitivity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

The Material Plasma Exposure eXperiment: Mission and conceptual design

Mastering Plasma Material Interactions (PMI) is key for obtaining a high performance, high duty-cycle and safe operating fusion reactor. Numerous gaps exist in PMI which have to be addressed before a reactor can be built. In particular the lack of data at high ion fluence, fusion reactor divertor relevant plasma conditions and neutron displacement damage requires new experimental devices to be able to develop plasma facing materials and components. This has been recognized in the community and the U.S. fusion program is addressing this need with a new linear plasma device—the Material Plasma Exposure eXperiment (MPEX). MPEX will be a superconducting linear plasma device with magnetic fields of up to 2.5 T. The plasma source is a high-power helicon source (200 kW, 13.56 MHz). The electrons will be heated via Electron Bernstein Waves with microwaves using multiple 70 GHz gyrotrons (up to 600 kW in total). Ions will be heated via ion cyclotron heating in the so-called “magnetic beach heating” scheme in the frequency range of 6–9 MHz (up to 400 kW in total). An overview of the conceptual design and the project/design requirements is given in this paper.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Broadband Nonreciprocity Enabled by Strong Coupling of Magnons and Microwave Photons

Nonreciprocity of signal transmission enhances the capacity of communication channels and protects the transmission quality against possible signal instabilities, thus becoming an important component for ensuring coherent information processing. However, nonreciprocal transmission requires breaking time-reversal symmetry (TRS), which poses challenges of both practical and fundamental character that hinder progress. Here we report an alternative scheme for achieving broadband nonreciprocity using a specially engineered hybrid microwave cavity. The TRS breaking is realized via strong coherent coupling between a selected chiral mode in the microwave cavity and a single collective spin excitation (magnon) in a ferromagnetic yttrium iron garnet sphere. The nonreciprocity in transmission is observed to span nearly a 0.5-GHz frequency band, which outperforms by two orders of magnitude the previously achieved bandwidths. Our findings suggest a promising direction for robust coherent information processing in a broad range of systems in both the classical and the quantum regime.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Overview of recent results from the ST40 compact high-field spherical tokamak

ST40 is a compact, high-field ($B_{\mathrm{T0}}\unicode{x2A7D} 2.1\,\,\,\textrm{T}$) spherical tokamak (ST) with a mission to expand the physics and technology basis for the ST route to commercial fusion. The ST40 research programme covers confinement and stability; solenoid-free start-up; high-performance operating scenarios; and plasma exhaust. In 2022, ST40 obtained central deuterium ion temperatures of $9.6 \pm 0.4\ \textrm{keV}$, demonstrating for the first time that pilot plant relevant ion temperatures can be reached in a compact, high-field ST. Analysis of these high-ion temperature plasmas is presented, including a summary of confinement, transport and microstability characteristics, and energetic particle instabilities. Recent scenario development activities have focused on establishing diverted H-mode plasmas across a range of toroidal fields and plasma currents, along with scenarios with high non-inductive current fractions. In future operations, beginning in 2025, a 1 MW dual frequency (104/137 GHz) electron cyclotron (EC) system will be installed to enable the study of EC and electron Bernstein wave plasma start-up and current drive. Predictive modelling of the potential performance of these systems is presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Review of Radio Frequency Interference and Potential Impacts on the CMB-S4 Cosmic Microwave Background Survey

CMB-S4 will map the cosmic microwave background to unprecedented precision, while simultaneously surveying the millimeter-wave time-domain sky, in order to advance our understanding of cosmology and the universe. CMB-S4 will observe from two sites, the South Pole and the Atacama Desert of Chile. A combination of small- and large-aperture telescopes with hundreds of thousands of polarization-sensitive detectors will observe in several frequency bands from 20-300 GHz, surveying more than 50% of the sky to arcminute resolution with unprecedented sensitivity. CMB-54 seeks to make a dramatic leap in sensitivity while observing across a broad range of largely unprotected spectrum which is increasingly being utilized for terrestrial and satellite transmissions. Fundamental aspects of CMB instrument technology leave them vulnerable to radio frequency interference (RFI) across a wide range of frequencies, including frequencies outside of their observing bands. Ground-based CMB instruments achieve their extraordinary sensitivities by deploying large focal planes of superconducting bolometers to extremely dry, high-altitude sites, with large fractional bandwidths, wide fields of view, and years of integration time. Suitable observing sites have historically offered significant protection from RFI, both naturally through their extremely remote locations as well as through restrictions on local emissions. Since the coupling mechanisms are complex, "safe" levels or frequencies of emission that would not interfere with CMB measurements cannot always be determined through straightforward calculations. We discuss models of interference for various types of RFI relevant to CMB-54, mitigation strategies, and the potential impacts on survey sensitivity.

Cosmic Microwave Background↗
DOE OSTI2021

Identifying insects, clouds, and precipitation using vertically pointing polarimetric radar Doppler velocity spectra

Abstract. This study presents a method to identify and distinguish insects, clouds, and precipitation in 35 GHz (Ka-band) vertically pointing polarimetric radar Doppler velocity power spectra and then produce masks indicating the occurrence of hydrometeors (i.e., clouds or precipitation) and insects at each range gate. The polarimetric radar used in this study transmits a linear polarized wave and receives signals in collinear (CoPol) and cross-linear (XPol) polarized channels. The measured CoPol and XPol Doppler velocity spectra are used to calculate linear depolarization ratio (LDR) spectra. The insect–hydrometeor discrimination method uses CoPol and XPol spectral information in two separate algorithms with their spectral results merged and then filtered into single value products at each range gate. The first algorithm discriminates between insects and clouds in the CoPol Doppler velocity power spectra based on the spectra texture, or spectra roughness, which varies due to the scattering characteristics of insects vs. cloud particles. The second algorithm distinguishes insects from raindrops and ice particles by exploiting the larger Doppler velocity spectra LDR produced by asymmetric insects. Since XPol power return is always less than CoPol power return for the same target (i.e., insect or hydrometeor), fewer insects and hydrometeors are detected in the LDR algorithm than the CoPol algorithm, which drives the need for a CoPol based algorithm. After performing both CoPol and LDR detection algorithms, regions of insect and hydrometeor scattering from both algorithms are combined in the Doppler velocity spectra domain and then filtered to produce a binary hydrometeor mask indicating the occurrence of cloud, raindrops, or ice particles at each range gate. Forty-seven summertime days were processed with the insect–hydrometeor discrimination method using US Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) program Ka-band zenith pointing radar observations in northern Oklahoma, USA. For these 47 d, over 70 % of the hydrometeor mask column bottoms were within ±100 m of simultaneous ceilometer cloud base heights. All datasets and images are available to the public on the DOE ARM repository.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Measurements of the temperature and $E$-mode polarization of the cosmic microwave background from the full 500-square-degree SPTpol dataset

Using the full four-year SPTpol 500 deg 2 dataset in both the 95 and 150 GHz frequency bands, we present measurements of the temperature and E-mode polarization of the cosmic microwave background (CMB), as well as the E-mode polarization autopower spectrum (EE) and temperature-E-mode cross-power spectrum (TE) in the angular multipole range 50 < ℓ < 8000. We find the SPTpol dataset to be self-consistent, passing several internal consistency tests based on maps, frequency bands, bandpowers, and cosmological parameters. The full SPTpol dataset is well-fit by the ΛCDM model, for which we find H 0 = 70.48 ± 2.16 km s -1 Mpc -1 and Ω m = 0.271 ± 0.026, when using only the SPTpol data and a Planck-based prior on the optical depth to reionization. The ΛCDM parameter constraints are consistent across the 95 GHz-only, 150 GHz-only, TE-only, and EE-only data splits. Between the ℓ < 1000 and ℓ > 1000 data splits, the ΛCDM parameter constraints are borderline consistent at the ∼2σ level. This consistency improves when including a parameter A L , the degree of lensing of the CMB inferred from the smearing of acoustic peaks. When marginalized over A L , the ΛCDM parameter constraints from SPTpol are consistent with those from Planck. In conclusion, the power spectra presented here are the most sensitive measurements of the lensed CMB damping tail to date for roughly ℓ > 1700 in TE and ℓ > 2000 in EE.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Evaluation of Single-Cell Cavities Made of Forged Ingot Niobium at Jefferson Lab

Currently, fine grain niobium (Nb) (grain size ~ 50 um) and large grain Nb (grain size of a few cm) are being used for the fabrication of superconducting radio frequency (SRF) cavities. Medium grain forged ingot with grain size of a few hundred um may be beneficial for cost-effectiveness as well as providing better performance for future SRF-based accelerators. Forged ingot Nb with medium grain size is a novel production method to obtain Nb discs used for the fabrication of superconducting radio frequency cavities. We have fabricated two 1.5 GHz single cell cavities made from forged Nb ingot with a residual resistivity ratio of ~100. The cavities were chemically and mechanically polished and heat-treated in the temperature range of 650-1000 C before the rf test. One of the cavities reached an accelerating gradient of 34 MV/m with a quality factor Q > 1e10, while the second cavity was limited at 14 MV/m, likely due to a weld defect at the equator.

Dhakal, P.↗
DOE OSTI2020

Optical Design and Characterization of 40-GHz Detector and Module for the BICEP Array

Families of cosmic inflation models predict a primordial gravitational-wave background that imprints B-mode polarization pattern in the cosmic microwave background (CMB). High-sensitivity instruments with wide frequency coverage and well-controlled systematic errors are needed to constrain the faint B-mode amplitude. We have developed antenna-coupled transition edge sensor arrays for high-sensitivity polarized CMB observations over a wide range of millimeter-wave bands. BICEP array, the latest phase of the BICEP/Keck experiment series, is a multi-receiver experiment designed to search for inflationary B-mode polarization to a precision σ(r) between 0.002 and 0.004 after 3 full years of observations, depending on foreground complexity and the degree of lensing removal. We describe the electromagnetic design and measured performance of BICEP array’s low-frequency 40-GHz detector, their packaging in focal plane modules, and optical characterization including efficiency and beam matching between polarization pairs. We summarize the design and simulated optical performance, including an approach to improve the optical efficiency due to mismatch losses. Here, we report the measured beam maps for a new broadband corrugation design to minimize beam differential ellipticity between polarization pairs caused by interactions with the module housing frame, which helps minimize polarized beam mismatch that converts CMB temperature to polarization (T→P) anisotropy in CMB maps.

47 OTHER INSTRUMENTATION↗
DOE OSTI2026

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.]↗