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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Measuring the Mean Free Path of H i Ionizing Photons at 3.2 ≤ z ≤ 4.6 with DESI Y1 Quasars

The mean free path of ionizing photons in the intergalactic medium (IGM; λ $^{912}_{mpf}$ ) is a crucial quantity in modeling the ionization state of the IGM and the extragalactic ultraviolet background, and it is widely used in hydrodynamical simulations of galaxies and reionization. We construct the largest quasar spectrum data set to date—12,595 signal-to-noise ratio > 3 spectra—using the Y1 observations of the Dark Energy Spectroscopic Instrument, to make the most precise model-independent measurement of the mean free path at 3.2 ≤ z ≤ 4.6. By stacking the spectra in 17 redshift bins and modeling the Lyman-continuum profile, we get a redshift evolution λ $^{912}_{mpf}$ ∝ ( 1 + z ) − 4.27 at 2 ≤ z ≤ 5, which is much shallower than the previous estimate, λ $^{912}_{mpf}$ ∝ ( 1 + z ) − 5.4 . We then explore the sources of systematic bias, including the choice of the intrinsic quasar continuum, the consideration of Lyman-series opacity and Lyman-limit opacity evolution, and the definition of λ $^{912}_{mpf}$ . Combining our results with estimates of λ $^{912}_{mpf}$ at higher redshifts, we conclude at high confidence that the evolution in λ $^{912}_{mpf}$ steepens at z ≈ 5. We interpret this inflection as the transition from the end of H i reionization to a fully ionized plasma that characterizes the IGM of the past ∼10 billion yr.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Phonon Mean Free Path Spectroscopy: Theory and Experiments

Chapter 6 reviews the current status of resolving the phonon mean free path distribution in real materials from both the computational and experimental perspectives, which is essential for engineering materials at the nanoscale to achieve desirable thermal transport properties.

Hua, Chengyun↗
DOE OSTI2022

The short ionizing photon mean free path at z = 6 in Cosmic Dawn III, a new fully coupled radiation-hydrodynamical simulation of the Epoch of Reionization

ABSTRACT Recent determinations of the mean free path of ionizing photons (mfp) in the intergalactic medium (IGM) at z = 6 are lower than many theoretical predictions. In order to gain insight, we investigate the evolution of the mfp in our new massive fully coupled radiation-hydrodynamics cosmological simulation of reionization: Cosmic Dawn III (CoDa III). CoDa III’s scale ($\rm 94^3 \, cMpc^3$) and resolution ($\rm 8192^3$ grid) make it particularly suitable to study the IGM during reionization. The simulation was performed with ramses-cudaton on Summit, and used 13 1072 processors coupled to 24 576 GPUs, making it the largest reionization simulation, and largest ever ramses simulation. A superior agreement with global constraints on reionization is obtained in CoDa III over Cosmic Dawn II (CoDa II), especially for the evolution of the neutral hydrogen fraction and the cosmic photoionization rate, thanks to an improved calibration, later end of reionization (z = 5.6), and higher spatial resolution. Analysing the mfp, we find that CoDa III reproduces the most recent observations very well, from z = 6 to z = 4.6. We show that the distribution of the mfp in CoDa III is bimodal, with short (neutral) and long (ionized) mfp modes, due to the patchiness of reionization and the coexistence of neutral versus ionized regions during reionization. The neutral mode peaks at sub-kpc to kpc scales of mfp, while the ionized mode peak evolves from 0.1 Mpc h−1 at z = 7 to ∼10 Mpc h−1 at z = 5.2. Computing the mfp as the average of the ionized mode provides the best match to the recent observational determinations. The distribution reduces to a single neutral (ionized) mode at z > 13 (z < 5).

Lewis, Joseph S. W. (ORCID:0000000179178474)↗
DOE OSTI2023

Thickness-Dependent Thermal Conductivity and Phonon Mean Free Path Distribution in Single-Crystalline Barium Titanate

Nanosized perovskite ferroelectrics are widely employed in several electromechanical, photonics, and thermoelectric applications. Scaling of ferroelectric materials entails a severe reduction in the lattice (phonon) thermal conductivity, particularly at sub-100 nm length scales. Such thermal conductivity reduction can be accurately predicted using the information of phonon mean free path (MFP) distribution. The current understanding of phonon MFP distribution in perovskite ferroelectrics is still inconclusive despite the critical thermal management implications. Here, high-quality single-crystalline barium titanate (BTO) thin films, a representative perovskite ferroelectric material, are grown at several thicknesses. Using experimental thermal conductivity measurements and first-principles based modeling (including four-phonon scattering), the phonon MFP distribution is determined in BTO. The simulation results agree with the measured thickness-dependent thermal conductivity. The results show that the phonons with sub-100 nm MFP dominate the thermal transport in BTO, and phonons with MFP exceeding 10 nm contribute ≈35% to the total thermal conductivity, in significant contrast to previously published experimental results. The experimentally validated phonon MFP distribution is consistent with the theoretical predictions of other complex crystals with strong anharmonicity. This work paves the way for thermal management in nanostructured and ferroelectric-domain-engineered systems for oxide perovskite-based functional materials.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Forecasting constraints on the mean free path of ionizing photons at z ≥ 5.4 from the Lyman-α forest flux autocorrelation function

ABSTRACT Fluctuations in Lyman-α (Ly α) forest transmission towards high-z quasars are partially sourced from spatial fluctuations in the ultraviolet background, the level of which are set by the mean free path of ionizing photons (λmfp). The autocorrelation function of Ly α forest flux characterizes the strength and scale of transmission fluctuations and, as we show, is thus sensitive to λmfp. Recent measurements at z ∼ 6 suggest a rapid evolution of λmfp at z > 5.0 which would leave a signature in the evolution of the autocorrelation function. For this forecast, we model mock Ly α forest data with properties similar to the XQR-30 extended data set at 5.4 ≤ z ≤ 6.0. At each z, we investigate 100 mock data sets and an ideal case where mock data matches model values of the autocorrelation function. For ideal data with λmfp = 9.0 cMpc at z = 6.0, we recover $\lambda _{\text{mfp}}=12^{+6}_{-3}$ cMpc. This precision is comparable to direct measurements of λmfp from the stacking of quasar spectra beyond the Lyman limit. Hypothetical high-resolution data leads to a $\sim 40~{{\ \rm per\ cent}}$ reduction in the error bars over all z. The distribution of mock values of the autocorrelation function in this work is highly non-Gaussian for high-z, which should caution work with other statistics of the high-z Ly α forest against making this assumption. We use a rigorous statistical method to pass an inference test, however future work on non-Gaussian methods will enable higher precision measurements.

Astronomy & Astrophysics↗
DOE OSTI2020

Electron inelastic mean free path in water

Liquid phase transmission electron microscopy (LPTEM) is rapidly developing as a powerful tool for probing processes in liquid environments with close to atomic resolution. Knowledge of the water thickness is needed for reliable interpretation and modelling of analytical studies in LPTEM, and is particularly essential when using thin liquid layers, required for achieving the highest spatial resolutions. Furthermore, the log-ratio method in electron energy-loss spectroscopy (EELS) is often applied in TEM to quantify the sample thickness, which is measured relative to the inelastic mean free path ( λ IMFP ). However, λ IMFP itself is dependent on sample material, the electron energy, and the convergence and divergence angles of the microscope electronoptics. Here, we present a detailed quantitative analysis of the λ IMFP of water as functions of the EELS collection angle ( β ) at 120 keV and 300 keV in a novel nanochannel liquid cell. We observe good agreement with earlier studies conducted on ice, but find that the most widely used theoretical models significantly underestimate λ IMFP of water. We determine an adjusted average energy-loss term E m, water , and characteristic scattering angle θ E, water that improve the accuracy. The results provide a comprehensive knowledge of the λ IMFP of water (or ice) for reliable interpretation and quantification of observations in LPTEM and cryo-TEM studies.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2020

Measurement of the Low-Energy Electron Inelastic Mean Free Path in Monolayer Graphene

Measuring the electron-transport properties of substrate-supported nanomaterials with the traditional two-point comparison method is difficult at electron energies below 50 eV, where core-level signals are too feeble to be detected against the strong secondary-electron background. Herein, a data-driven spectral analysis technique is used to study the low-energy electron-transport properties of substrate-supported target nanomaterials, while eliminating the influence of the substrate signal. Applying this technique, the electron-transport properties of the effective attenuation length and the inelastic mean free path (IMFP) can be determined with extremely high efficiency over the entire measured energy range of 6–600 eV. Further, these results show excellent agreement with other experimental and theoretical results. In this work, significant differences are observed between monolayer graphene and the bulk graphite IMFP, which illustrates the importance of the nanometer effect in the electron-transport properties of the material. Furthermore, this technique is readily applicable to any ultrathin material that can be transferred onto a polycrystalline gold substrate.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Spin response and neutrino mean free path in neutron matter

The longitudinal and transverse density- and spin-density response functions in pure neutron matter (PNM) are derived over a wide range of densities within the time dependent local spin density approximation. The underlying density functional was derived from an Auxiliary Field Diffusion Monte Carlo computation of the equation of state of unpolarized and fully spin polarized PNM. In order to assess the dependence of the results on the specific underlying nucleon–nucleon Hamiltonian, we used both the phenomenological Argonne AV8' + UIX force, and local chiral forces up to next-to-next-to-leading-order (N 2 LO). Finally, the resulting response function has then been applied to the study of the neutrino mean free path in PNM.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Pulsed Sphere Time of Flight Neutron Spectrum Measurements: Blank Run and 1.8 Mean-Free-Path thick Polyethylene Moderating Sphere

From the late 1960s to 1985, Lawrence Livermore National Laboratory (LLNL) undertook a series of ‘pulsed sphere’ experiments for 32 materials involving 148 different experiments using 75 different spheres to measure the neutron leakage spectra for different materials from 14-MeV neutrons generated by 3 H(d, n) 4 He reactions induced by an incident D+ beam from the Insulated Core Transformer (ICT) accelerator at LLNL. This deuteron beam was focused to impinge on tritium loaded onto a titanium substrate within a low mass target assembly placed within the center of a spherical shell constructed from the material of interest. The neutron time of flight was measured at a detector outside a collimator. The program was intended to be comprehensive with numerous targets of various thicknesses spanning the periodic table from H to 239 Pu. Five different neutron detectors were utilized to avoid possible systematic errors due to differences in detector responses. Further, these measurements were designed with the aim that the simple geometry of the measurements could be easily simulated to validate Monte Carlo transport codes and nuclear data libraries. As a result, these benchmarks have been extensively used in the validation of ENDL, ENDF and other libraries. Two experiments selected as benchmark cases in this evaluation are: 1) target assembly without material sphere (blank run), and 2) target assembly with a hollow polyethylene sphere, 1.8 mean free path (mfp) or 16.56 cm thick.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

A coded aperture with sub-mean-free-path thickness for implosion geometry imaging on ICF and IFE experiments

Inertial confinement fusion and inertial fusion energy experiments diagnose the geometry of the fusion region through imaging of the neutrons released through fusion reactions. Pinhole arrays typically used for such imaging require thick substrates to obtain high contrast along with a small pinhole diameter to obtain high resolution capability, resulting in pinholes that have large aspect ratios. This leads to expensive pinhole arrays that have small solid angles and are difficult to align. Here, we propose a coded aperture with scatter and partial attenuation (CASPA) for fusion neutron imaging that relaxes the thick substrate requirement for good image contrast. These coded apertures are expected to scale to larger solid angles and are easier to align without sacrificing imaging resolution or throughput. We use Monte Carlo simulations (Geant4) to explore a coded aperture design to measure neutron implosion asymmetries on fusion experiments at the National Ignition Facility (NIF) and discuss the viability of this technique, matching the current nominal resolution of 10 µm. The results show that a 10 mm thick tungsten CASPA can image NIF implosions with neutron yields above 10 14 with quality comparable to unprocessed data from a current NIF neutron imaging aperture. Furthermore, this CASPA substrate is 20 times thinner than the current aperture arrays for fusion neutron imaging and less than one mean free-path of 14.1 MeV neutrons through the substrate. Since the resolution, solid angle, and throughput are decoupled in coded aperture imaging, the resolution and solid angle achievable with future designs will be limited primarily by manufacturing capability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Molecular-gas-dynamics simulations of turbulent Couette flow over a mean-free-path-scale permeable substrate

Here we report flow statistics and visualizations from molecular-gas-dynamics simulations using the direct simulation Monte Carlo (DSMC) method for turbulent Couette flow in a minimal domain where the lower wall is replaced by an idealized permeable fibrous substrate representative of thermal-protection-system materials for which the Knudsen number is O(10 -1 ). Comparisons are made with smooth-wall DSMC simulations and smooth-wall direct numerical simulations (DNS) of the Navier-Stokes equations for the same conditions. Roughness, permeability, and noncontinuum effects are assessed. In the range of Reynolds numbers considered herein, the scalings of the skin friction on the permeable substrate and of the mean flow within the substrate suggest that they are dominated by viscous effects. While the regenerative cycle characteristic of smooth-wall turbulence remains intact for all cases considered, we observe that the near-wall velocity fluctuations are modulated by the permeable substrate with a wavelength equal to the pore spacing. Additionally, the flow within the substrate shows significant rarefaction effects, resulting in an apparent permeability that is 13% larger than the intrinsic permeability. In contrast, the smooth-wall DSMC and DNS simulations exhibit remarkably good agreement for the statistics examined, despite the Knudsen number based on the viscous length scale being as large as O(10 -1 ). This latter result is at variance with classical estimates for the breakdown of the continuum assumption and calls for further investigations into the interaction of noncontinuum effects and turbulence.

42 ENGINEERING↗
DOE OSTI2023

Uncertainty quantification for neutrino opacities in core-collapse supernovae and neutron star mergers

We perform an extensive study of the correlations between the neutrino-nucleon inverse mean free paths (IMFPs) and the underlying equation of states (EoSs). Strong interaction uncertainties in the neutrino mean free path are investigated in different density regimes. The nucleon effective mass, the nucleon chemical potentials, and the residual interactions in the medium play an important role in determining neutrino-nucleon interactions in a density-dependent manner. Here we study how the above quantities are constrained by an EoS consistent with (i) nuclear mass measurements, (ii) proton-proton scattering phase shifts, and (iii) neutron star observations. We then study the uncertainties of both the charged current and the neutral current neutrino-nucleon inverse mean free paths due to the variation of these quantities, using the Hartree-Fock+random phase approximation method. Finally, we calculate the Pearson correlation coefficients between (i) the EoS-based quantities and the EoS-based quantities; (ii) the EoS-based quantities and the IMFPs; (iii) the IMFPs and the IMFPs. We find a strong impact of residual interactions on neutrino opacity in the spin and spin-isospin channels, which are not well constrained by current nuclear modelings.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Thermodynamics and transport in molten chloride salts and their mixtures

Relationship between thermophysical properties and phonon mean free path. Heat capacity, viscosity, and thermal conductivity in ionic liquids decrease as mean free path decreases and dynamics become less “solid-like” and collect motion diminishes.

Cockrell, C. [Nuclear Futures Institute, Bangor Un↗
DOE OSTI2024

Spatially Dependent Seismic Wavefield Scattering from an Underground Chemical Explosion: Analysis of the Source Physics Experiment Dry Alluvium Geology Large- N Array

Explosion sources have been observed to generate significant shear‐wave energy despite their isotropic nature. To investigate this phenomenon, we conduct an analysis of the seismic data collected as part of the Source Physics Experiment (SPE): Dry Alluvium Geology (DAG) and investigate the generation of shear‐wave energy via scattering. The data were produced by three underground chemical explosions and consist of three‐component seismograms, which were recorded by the DAG Large‐N array. Synthetic tests suggest that for the DAG experiments, small‐scale stochastic heterogeneities, defined as features with correlation lengths of 10–100s of meters, are more effective than large‐scale geologic structure (scales >1–10 km) at reproducing the scattering of explosion generated wavefields observed at DAG. We analyze the seismic data for spatially variable ratios between transversely and radially polarized seismic energy, and then estimate the mean free path of P and S waves. All analyses are conducted within a frequency band of 5–50 Hz. The ratio of transversely to radially polarized energy is the highest in the east and west portion of the Large‐N array. In addition, the magnitude of the estimated S‐wave mean free path is shorter in the eastern portion of the Large‐N array. This variation indicates that the eastern area of the DAG array is where more scattering is occurring, suggesting azimuthal dependence of P‐to‐P and P‐to‐S scattering. Furthermore, this azimuthal dependence of P‐to‐S scattering can have implications for explosion discrimination based on spectral ratios of seismic wave types, because the general assumption is that explosions do not generate shear‐wave energy. Synthetic tests modeling only larger‐scale geologic structure had lower transversely polarized energy (only four stations showing a transversely to radially polarized energy ratio greater than 1) and fewer stations (<10) displaying shorter (<300 m) mean free paths than what was observed in the DAG data results.

Darrh, Andréa Nicole↗
DOE OSTI2024

A collision-based hybrid method for the BGK equation

In this article, we apply the collision-based hybrid method introduced by Hauck and McClarren to the Boltzmann equation with the BGK operator and a hyperbolic scaling. An implicit treatment of the source term is used to handle stiffness associated with the BGK operator. Although it helps the numerical scheme become stable with a large time step size, it is still not obvious to achieve the desired order of accuracy due to the relationship between the size of the spatial cell and the mean free path. Without asymptotic preserving property, a very restricted grid size is required to resolve the mean free path, which is not practical. Our approaches are based on the noncollision-collision decomposition of the BGK equation. We introduce the arbitrary order of nodal discontinuous Galerkin (DG) discretization in space with a semi-implicit time-stepping method; we employ the backward Euler time integration for the uncollided equation and the 2nd order predictor-corrector scheme for the collided equation, i.e., both source terms in uncollided and collided equations are treated implicitly and only streaming term in the collided equation is solved explicitly. This improves the computational efficiency without the complexity of the numerical implementation. Numerical results are presented for various Knudsen numbers to present the effectiveness and accuracy of our hybrid method. Also, we compare the solutions of the hybrid and non-hybrid schemes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Magnon heat transport in a two-dimensional Mott insulator

Whether or not anomalies in the thermal conductivity in insulating cuprates can be attributed to antiferromagnetic order and magnons in a 2D Mott insulator remains an intriguing open question. To shed light on this issue, we investigate the thermal conductivity $\kappa$ and its relationship with the specific heat $c_v$ in the half-filled 2D single-band Hubbard model, using the numerically exact determinant quantum Monte Carlo algorithm and maximum entropy analytic continuation. At low temperatures where the charge degrees of freedom are gapped-out and $c_v$ exhibits a clear magnon peak, we observe that thermal conductivity $\kappa$ also tends to form a peak at similar temperatures. Reducing temperature further produces a sharp upturn in $\kappa$, associated with an increasing mean-free path. Here we identify this as the high-temperature side of the anomalous peak in insulating cuprates, where the mean-free path eventually is cut-off by other scattering effects, including phonons, disorder, and physical size. Different scattering effects in our model are identified and analyzed in the thermal diffusivity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Thickness-Dependent Cross-Plane Thermal Conductivity Measurements of Exfoliated Hexagonal Boron Nitride

Submicrometer-thick layers of hexagonal boron nitride (hBN) exhibit high in-plane thermal conductivity and useful optical properties, and serve as dielectric encapsulation layers with low electrostatic inhomogeneity for graphene devices. Despite the promising applications of hBN as a heat spreader, the thickness dependence of its cross-plane thermal conductivity is not known, and the cross-plane phonon mean free paths (MFPs) have not been measured. We measure the cross-plane thermal conductivity of hBN flakes exfoliated from bulk crystals. We find that submicrometer thick flakes exhibit thermal conductivities up to 8.1 ± 0.5 W m –1 K –1 at 295 K, which exceeds previously reported bulk values by more than 60%. Surprisingly, the average phonon mean free path is found to be several hundred nanometers at room temperature, a factor of 5 larger than previous predictions. When planar twist interfaces are introduced into the crystal by mechanically stacking multiple thin flakes, the cross-plane thermal conductivity of the stack is found to be a factor of 7 below that of individual flakes with similar total thickness, thus providing strong evidence that phonon scattering at twist boundaries limits the maximum phonon MFPs. These results have important implications for hBN integration in nanoelectronics and improve our understanding of thermal transport in twodimensional materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗