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

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

Diurnal patterns of wheat spectral reflectances and their importance in the assessment of canopy parameters from remotely sensed observations

Spectral reflectances of Produra wheat were measured at 13 different times of the day at Phoenix, Arizona, during April 1979 using a nadir-oriented hand-held 4-band radiometer which had bandpass characteristics similar to those on LANDSAT satellites. Different Sun altitude and azimuth angles caused significant diurnal changes in radiant return in both visible and near-IR regions of the spectrum and in several vegetation indices derived from them. The magnitude of these changes were related to different canopy architecture, percent cover and green leaf area conditions. Spectral measurements taken at each time period were well correlated with green leaf area index but the nature of the relationship changed significantly with time of day. Thus, a significant bias in the estimation of the green leaf area index from remotely sensed spectral data could occur if sun angles are not properly accounted for.

Pinter, P. J.↗
NASA NTRS2014

Field Results from Three Campaigns to Validate the Performance of the Miniaturized Laser Heterodyne Radiometer (Mini‐LHR) for Measuring Carbon Dioxide and Methane in the Atmospheric Column

In a collaboration between NASA GSFC and GWU, a low-cost, surface instrument is being developed that can continuously monitor key carbon cycle gases in the atmospheric column: carbon dioxide (CO2) and methane (CH4). The instrument is based on a miniaturized, laser heterodyne radiometer (LHR) using near infrared (NIR) telecom lasers. Despite relatively weak absorption line strengths in this spectral region, spectrallyresolved atmospheric column absorptions for these two molecules fall in the range of 60-80% and thus sensitive and precise measurements of column concentrations are possible. In the last year, the instrument was deployed for field measurements at Park Falls, Wisconsin; Castle Airport near Atwater, California; and at the NOAA Mauna Loa Observatory in Hawaii. For each subsequent campaign, improvement in the figures of merit for the instrument has been observed. In the latest work the absorbance noise is approaching 0.002 optical density (OD) noise on a 1.8 OD signal. An overview of the measurement campaigns and the data retrieval algorithm for the calculation of column concentrations will be presented. For light transmission through the atmosphere, it is necessary to account for variation of pressure, temperature, composition, and refractive index through the atmosphere that are all functions of latitude, longitude, time of day, altitude, etc. For temperature, pressure, and humidity profiles with altitude we use the Modern-Era Retrospective Analysis for Research and Applications (MERRA) data. Spectral simulation is accomplished by integrating short-path segments along the trajectory using the SpecSyn spectral simulation suite developed at GW. Column concentrations are extracted by minimizing residuals between observed and modeled spectrum using the Nelder-Mead simplex algorithm. We will also present an assessment of uncertainty in the reported concentrations from assumptions made in the meteorological data, LHR instrument and tracker noise, and radio frequency bandwidth and describe additional future goals in instrument development and deployment target

meteorological data↗
DOE OSTI2017

Analysis of Neutron Spectrum and Control Rod Worth Measurements in Several ZPPR-15 Loadings

This paper discusses the analysis of neutron spectrum and control rod reactivity worth measurements with deterministic and Monte Carlo methods. Deterministic results are obtained with 3D reactor models generated with the BuildZPRModel tools developed at ANL. The Monte Carlo simulations are performed with MCNP6 and are based on 3D models that include all geometric details ('as built' models). This study also shows the application of the cross section processing options recently implemented in BuildZPRModel that are based on the leakage and TWODANT method to take better into account the coupling effects among the different reactor zones.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

SU(3) Gauge Symmetry: An Experimental Review of Diffractive Physics in e+p, p+p, p+ A, and A+A Collision Systems

This review focuses on diffractive physics, which involves the long-range interactions of strong nuclear force at high energies described by SU(3) gauge symmetry. It is expected that diffractive processes account for nearly 40% of the total cross-section at LHC energies. These processes consist of soft-scale physics where perturbation theory cannot be applied. Although highly successful and often described as a perfect theory, quantum chromodynamics relies heavily on perturbation theory, a model best suited for hard-scale physics. The study of pomerons could help bridge the soft and hard processes and provide a complete description of the theory of the strong interaction across the full momentum spectrum. Here, we will discuss some of the features of diffractive physics, experimental results from SPS, HERA, and the LHC, and where the field could potentially lead. With the recent publication of the odderon discovery in 2021 by the D0 and TOTEM collaborations and the new horizon of physics that lies ahead with the upcoming Electron-Ion Collider at Brookhaven National Laboratory, interest is seemingly piquing in high energy diffractive physics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2017

IceCube Constraints on the Fermi Bubbles

We analyze the IceCube four-year neutrino data in search of a signal from the Fermi bubbles. No signal is found from the bubbles or from their dense shell, even when taking into account the softer background. This imposes a conservative ξ {sub i} < 8% upper limit on the cosmic-ray ion (CRI) acceleration efficiency, and an η ≡ ξ {sub e} / ξ {sub i} ≳ 0.006 lower limit on the electron-to-ion ratio of acceleration efficiencies (at the 2 σ confidence level). For typical ξ {sub i} , a signal should surface once the number of IceCube neutrinos increases by ∼an order of magnitude, unless there is a <PeV cutoff on the CRI spectrum.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Growth of nano hexagon-like flake arrays cerium carbonate created with PAH as the substrate

Petals-like Ce{sub 2}(CO{sub 3}){sub 3} on Ce{sub 2}(CO{sub 3}){sub 3} nano hexagon-like flake arrays have been precipitatingly fabricated using PAH substrates. By changing the way of feeding, PAH concentration and aging time, petals-like Ce{sub 2}(CO{sub 3}){sub 3} was created best when adding PAH into the Ce(NO{sub 3}){sub 3} solution, joined (NH{sub 4}){sub 2}CO{sub 3} solution along with mixing, PAH concentration is 0.9 g/L, aging time is 4 h. A growth mechanism was proposed to account for the growth of the petals-like Ce{sub 2}(CO{sub 3}){sub 3} with PAH as the substrate. Poly allylamine hydrochloride (PAH) is as template agent which forms π-allyl complex with Ce{sup 3+} and controls the morphology of Ce{sub 2}(CO{sub 3}){sub 3} particle. PAH and Ce{sup 3+} form π-allyl complex, and then induce the formation of Ce{sub 2}(CO{sub 3}){sub 3} crystal nucleus. And infrared spectrum analysis verified. XRD show that after adding PAH which is adsorbed on the crystal plane, the growth of Ce{sub 2}(CO{sub 3}){sub 3} crystal is inhibited on (2 4 2), the growth is promoted on (2 0 2) which is differentiated into the new (1 5 1), (2 2 2) is unchanged, Ce{sub 2}(CO{sub 3}){sub 3} crystal is accumulated petals shape by hexagon-like flake. UV absorption spectra show that CeO{sub 2} as prepared precursor Ce{sub 2}(CO{sub 3}){sub 3} after calcinations in air at high temperatures, the petal-like CeO{sub 2} has strong UV absorption and reflection effects, and absorption interval changed significantly by the move to UVA from UVB. - Graphical abstract: Each Ce-atom connects three Cl-atoms and three allyls in three dimensional spaces. To take the plane as a reference plane which is arrayed with three Ce-atom as equilateral triangle. The triangular each vertex is Ce-atom, the triangular center place is Cl-atom, the equilateral triangle which is mutually perpendicular with Ce-triangle surface and the inclined angle is 60° is made up with three Cl-atoms. - Highlights: • Petals-like Ce{sub 2}(CO{sub 3}){sub 3} were synthesized with PAH. • PAH and Ce{sup 3+} form π-allyl complex. • The growth crystal is inhibited on (2 4 2) and promoted on (2 0 2). • CeO{sub 2} absorption interval changed by the move to UVA from UVB.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Infrared surface phonon nanospectroscopy of an interacting dielectric-particle–dielectric-substrate dimer using fast electrons

Refinements in energy monochromation and aberration correction in state-of-the-art scanning transmission electron microscopes has opened access to the far infrared regime for spectroscopic characterization at the nanoscale. At these low energies, the dielectric environment, such as a dielectric slab adjacent to the target specimen, may no longer play a passive role in the spectrum. Instead, the environment may itself host resonances that mix with those of the target and complicate interpretation of its spectral responses. This article explores a theoretical description of the coupling between the collective vibrational surface modes of a dielectric particle and dielectric slab of varying thickness for the purpose of elucidating the interacting phononic excitations in dielectric materials typical of inelastic electron scattering measurements in the infrared. Dynamical coordinates and a governing Hamiltonian are rigorously defined in the quasistatic limit to account for phonon mode mixing and forcing by an aloof electron probe, which travels along a grazing trajectory, parallel to the dielectric slab. As the spectral window of interrogation by fast electron probes has been extended down to thermal energies with unprecedented meV energy resolution, theoretical models like that presented herein are crucial for accurate interpretation of experimental data.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Spectra of Double Acceptors in Layers of Barriers and Quantum Wells of HgTe/CdHgTe Heterostructures

The states of double acceptors in HgTe/СdHgTe heterostructures containing quantum wells are theoretically investigated taking into account the substantial difference in the values of the permittivities of the barrier and quantum-well layers. The effect of such a difference and the charge induced at the heterointerfaces arising from it are described with the image-charge potential. Calculation shows a significant change in the binding energy of the acceptor centers—mercury vacancies due to the induced charge; the ionization energies of mercury vacancies are in good agreement with the position of the spectral features in the photoluminescence spectrum of the HgTe/CdHgTe heterostructures containing quantum wells.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

A time-dependent momentum-resolved scattering approach to core-level spectroscopies

While new light sources allow for unprecedented resolution in experiments with X-rays, a theoretical understanding of the scattering cross-section is lacking. In the particular case of strongly correlated electron systems, numerical techniques are quite limited, since conventional approaches rely on calculating a response function (Kramers-Heisenberg formula) that is obtained from a perturbative analysis of scattering processes in the frequency domain. This requires a knowledge of a full set of eigenstates in order to account for all intermediate processes away from equilibrium, limiting the applicability to small tractable systems. In this work, we present an alternative paradigm, recasting the problem in the time domain and explicitly solving the time-dependent Schrödinger equation without the limitations of perturbation theory: a faithful simulation of the scattering processes taking place in actual experiments, including photons and core electrons. We show how this approach can yield the full time and momentum resolved Resonant Inelastic X-Ray Scattering (RIXS) spectrum of strongly interacting many-body systems. We demonstrate the formalism with an application to Mott insulating Hubbard chains using the time-dependent density matrix renormalization group method, which does not require a priory knowledge of the eigenstates and can solve very large systems with dozens of orbitals. This approach can readily be applied to systems out of equilibrium without modification and generalized to other spectroscopies.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

MIXING THE SOLAR WIND PROTON AND ELECTRON SCALES: EFFECTS OF ELECTRON TEMPERATURE ANISOTROPY ON THE OBLIQUE PROTON FIREHOSE INSTABILITY

The double adiabatic expansion of the nearly collisionless solar wind plasma creates conditions for the firehose instability to develop and efficiently prevent the further increase of the plasma temperature in the direction parallel to the interplanetary magnetic field. The conditions imposed by the firehose instability have been extensively studied using idealized approaches that ignore the mutual effects of electrons and protons. Recently, more realistic approaches have been proposed that take into account the interplay between electrons and protons, unveiling new regimes of the parallel oscillatory modes. However, for oblique wave propagation the instability develops distinct branches that grow much faster and may therefore be more efficient than the parallel firehose instability in constraining the temperature anisotropy of the plasma particles. This paper reports for the first time on the effects of electron plasma properties on the oblique proton firehose (PFH) instability and provides a comprehensive vision of the entire unstable wave-vector spectrum, unifying the proton and the smaller electron scales. The plasma β and temperature anisotropy regimes considered here are specific for the solar wind and magnetospheric conditions, and enable the electrons and protons to interact via the excited electromagnetic fluctuations. For the selected parameters, simultaneous electron and PFH instabilities can be observed with a dispersion spectrum of the electron firehose (EFH) extending toward the proton scales. Growth rates of the PFH instability are markedly boosted by the anisotropic electrons, especially in the oblique direction where the EFH growth rates are orders of magnitude higher.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

BOOSTING LY α AND He ii λ 1640 LINE FLUXES FROM POPULATION III GALAXIES: STOCHASTIC IMF SAMPLING AND DEPARTURES FROM CASE-B

We revisit calculations of nebular hydrogen Ly α and He ii λ 1640 line strengths for Population III (Pop III) galaxies, undergoing continuous, and bursts of, star formation. We focus on initial mass functions (IMFs) motivated by recent theoretical studies, which generally span a lower range of stellar masses than earlier works. We also account for case-B departures and the stochastic sampling of the IMF. In agreement with previous work, we find that departures from case-B can enhance the Ly α flux by a factor of a few, but we argue that this enhancement is driven mainly by collisional excitation and ionization, and not due to photoionization from the n = 2 state of atomic hydrogen. The increased sensitivity of the Ly α flux to the high-energy end of the galaxy spectrum makes it more subject to stochastic sampling of the IMF. The latter introduces a dispersion in the predicted nebular line fluxes around the deterministic value by as much as a factor of ∼4. In contrast, the stochastic sampling of the IMF has less impact on the emerging Lyman Werner photon flux. When case-B departures and stochasticity effects are combined, nebular line emission from Pop III galaxies can be up to one order of magnitude brighter than predicted by “standard” calculations that do not include these effects. This enhances the prospects for detection with future facilities such as the James Webb Space Telescope and large, ground-based telescopes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Comparisons Between Resolved Star Formation Rate and Gas Tracers in the Strongly Lensed Galaxy SDSS J0901+1814 at Cosmic Noon

We report new radio observations of SDSS J090122.37+181432.3, a strongly lensed star-forming galaxy at $z=2.26$. We image 1.4 GHz (L-band) and 3 GHz (S-band) continuum using the VLA and 1.2 mm (band 6) continuum with ALMA, in addition to the CO(7-6) and CI(${\rm ^3P_2\rightarrow ^3\!P_1}$) lines, all at $\lesssim1.^{\prime\prime}7$ resolution. Based on the VLA integrated flux densities, we decompose the radio spectrum into its free-free (FF) and non-thermal components. The infrared-radio correlation (IRRC) parameter $q_{\rm TIR}=2.65_{-0.31}^{+0.24}$ is consistent with expectations for star forming galaxies. We obtain radio continuum-derived SFRs that are free of dust extinction, finding $\rm {620}_{-220}^{+280}\,M_\odot\,yr^{-1}$, $\rm {230}_{-160}^{+570}\,M_\odot\,yr^{-1}$, and $\rm {280}_{-120}^{+460}\,M_\odot\,yr^{-1}$ from the FF emission, non-thermal emission, and when accounting for both emission processes, respectively, in agreement with previous results. We estimate the gas mass from the CI(${\rm ^3P_2\rightarrow ^3\!P_1}$) line as $M_{\rm gas}=(1.2\pm0.2)\times10^{11}\,M_\odot$, which is consistent with prior CO(1-0)-derived gas masses. Using our new IR and radio continuum data to map the SFR, we assess the dependence of the Schmidt-Kennicutt relation on choices of SFR and gas tracer for $\sim{\rm kpc}$ scales. The different SFR tracers yield different slopes, with the IR being the steepest, potentially due to highly obscured star formation in J0901. The radio continuum maps have the lowest slopes and overall fidelity for mapping the SFR, despite producing consistent total SFRs. We also find that the Schmidt-Kennicutt relation slope is flattest when using CO(7-6) or CI(${\rm ^3P_2\rightarrow ^3\!P_1}$) to trace gas mass, suggesting that those transitions are not suitable for tracing the bulk molecular gas in galaxies like J0901.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1992

Spherical harmonic analysis of steady photospheric flows. II

The use of the spherical harmonic functions to analyze the nearly steady flows in the solar photosphere is extended to situations in which B(0) the latitude at disk center, is nonzero and spurious velocities are present. The procedures for extracting the rotation profile and meridional circulation are altered to account for the seasonal tilt of the sun's rotation axis toward and away from the observer. A more robust and accurate method for separating the limb shift and meridional circulation signals is described. The analysis procedures include the ability to mask out areas containing spurious velocities (velocity-like signals that do not represent true flow velocities in the photosphere). The procedures are shown to work well in extracting the various flow components from realistic artificial data with a broad, continuous spectrum for the supergranulation. The presence of this supergranulation signal introduces errors of a few m/s in the measurements of the rotation profile, meridional circulation, and limb shift from a single Doppler image.

Hathaway, David H.↗
NASA NTRS2016

Mixing the Solar Wind Proton and Electron Scales: Effects of Electron Temperature Anisotropy on the Oblique Proton Firehose Instability

The double adiabatic expansion of the nearly collisionless solar wind plasma creates conditions for the firehose instability to develop and efficiently prevent the further increase of the plasma temperature in the direction parallel to the interplanetary magnetic field. The conditions imposed by the firehose instability have been extensively studied using idealized approaches that ignore the mutual effects of electrons and protons. Recently, more realistic approaches have been proposed that take into account the interplay between electrons and protons, unveiling new regimes of the parallel oscillatory modes. However, for oblique wave propagation the instability develops distinct branches that grow much faster and may therefore be more efficient than the parallel firehose instability in constraining the temperature anisotropy of the plasma particles. This paper reports for the first time on the effects of electron plasma properties on the oblique proton firehose (PFH) instability and provides a comprehensive vision of the entire unstable wave-vector spectrum, unifying the proton and the smaller electron scales. The plasma β and temperature anisotropy regimes considered here are specific for the solar wind and magnetospheric conditions, and enable the electrons and protons to interact via the excited electromagnetic fluctuations. For the selected parameters, simultaneous electron and PFH instabilities can be observed with a dispersion spectrum of the electron firehose (EFH) extending toward the proton scales. Growth rates of the PFH instability are markedly boosted by the anisotropic electrons, especially in the oblique direction where the EFH growth rates are orders of magnitude higher.

plasmas↗
DOE OSTI2015

Neutrino masses and cosmology with Lyman-alpha forest power spectrum

We present constraints on neutrino masses, the primordial fluctuation spectrum from inflation, and other parameters of the ΛCDM model, using the one-dimensional Lyα-forest power spectrum measured by [1] from the Baryon Oscillation Spectroscopic Survey (BOSS) of the Sloan Digital Sky Survey (SDSS-III), complemented by Planck 2015 cosmic microwave background (CMB) data and other cosmological probes. This paper improves on the previous analysis by [2] by using a more powerful set of calibrating hydrodynamical simulations that reduces uncertainties associated with resolution and box size, by adopting a more flexible set of nuisance parameters for describing the evolution of the intergalactic medium, by including additional freedom to account for systematic uncertainties, and by using Planck 2015 constraints in place of Planck 2013. Fitting Lyα data alone leads to cosmological parameters in excellent agreement with the values derived independently from CMB data, except for a weak tension on the scalar index n{sub s}. Combining BOSS Lyα with Planck CMB constrains the sum of neutrino masses to ∑ m{sub ν} < 0.12 eV (95% C.L.) including all identified systematic uncertainties, tighter than our previous limit (0.15 eV) and more robust. Adding Lyα data to CMB data reduces the uncertainties on the optical depth to reionization τ, through the correlation of τ with σ{sub 8}. Similarly, correlations between cosmological parameters help in constraining the tensor-to-scalar ratio of primordial fluctuations r. The tension on n{sub s} can be accommodated by allowing for a running dn{sub s}/d ln k. Allowing running as a free parameter in the fits does not change the limit on ∑ m{sub ν}. We discuss possible interpretations of these results in the context of slow-roll inflation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Stellar population models based on the SDSS-IV MaStar library of stellar spectra – I. Intermediate-age/old models

ABSTRACT We use the first release of the SDSS/MaStar stellar library comprising ∼9000, high S/N spectra, to calculate integrated spectra of stellar population models. The models extend over the wavelength range 0.36–1.03 µm and share the same spectral resolution ($R\sim 1800$) and flux calibration as the SDSS-IV/MaNGA galaxy data. The parameter space covered by the stellar spectra collected thus far allows the calculation of models with ages and chemical composition in the range $\rm {\mathit{ t}\gt 200 \,Myr, -2 \lt = [Z/H] \lt = + 0.35}$, which will be extended as MaStar proceeds. Notably, the models include spectra for dwarf main-sequence stars close to the core H-burning limit, as well as spectra for cold, metal-rich giants. Both stellar types are crucial for modelling λ > 0.7 µm absorption spectra. Moreover, a better parameter coverage at low metallicity allows the calculation of models as young as 500 Myr and the full account of the blue horizontal branch phase of old populations. We present models adopting two independent sets of stellar parameters (Teff, log g, [Z/H]). In a novel approach, their reliability is tested ‘on the fly’ using the stellar population models themselves. We perform tests with Milky Way and Magellanic Clouds globular clusters, finding that the new models recover their ages and metallicities remarkably well, with systematics as low as a few per cent for homogeneous calibration sets. We also fit a MaNGA galaxy spectrum, finding residuals of the order of a few per cent comparable to the state-of-art models, but now over a wider wavelength range.

Maraston, C.↗
NASA NTRS1985

Polycyclic aromatic hydrocarbons and the unidentified infrared emission bands - Auto exhaust along the Milky Way

The unidentified infrared emission features (UIR bands) are attributed to a collection of partially hydrogenated, positively charged polycyclic aromatic hydrocarbons (PAHs). This assignment is based on a spectroscopic analysis of the UIR bands. Comparison of the observed interstellar 6.2 and 7.7-micron bands with the laboratory measured Raman spectrum of a collection of carbon-based particulates (auto exhaust) shows a very good agreement, supporting this identification. The infrared emission is due to relaxation from highly vibrationally and electronically excited states. The excitation is probably caused by UV photon absorption. The infrared fluorescence of one particular, highly vibrationally excited PAH (chrysene) is modeled. In this analysis the species is treated as a molecule rather than bulk material and the non-thermodynamic equilibrium nature of the emission is fully taken into account. From a comparison of the observed ratio of the 3.3 to 11.3-micron UIR bands with the model calculations, the average number of carbon atoms per molecule is estimated to be about 20. The abundance of interstellar PAHs is calculated to be about 2 x 10 to the -7th with respect to hydrogen.

Allamandola, L. J.↗
DOE OSTI2016

fuel cycle cost analysis of Th/U MOX fuel in a block-type HTR - 18619

With a rapid development of nuclear energy in these years, the supply of nuclear fuel is becoming more and more important. Thorium regains attention because of its abundant reserves and excellent physical properties. As a next generation reactor, the high temperature reactor (HTR) is a promising choice for thorium utilization because of its deeper burnup, harder spectrum and better inherent safety. Therefore, a 600 MWth 108-column modular high temperature reactor (MHR) core model with 20%UO{sub 2}-80%ThO{sub 2}; MOX fuel is adapted. A traditional two-step calculation scheme, lattice calculation then core calculation, is used to get the neutronic performance of equilibrium cycle including uranium enrichment and mass of fuel. Using these data, the fuel cycle cost of HTR can be calculated by the levelized lifetime cost method. In order to take into account the variation of unit price, a well-established, standard statistical analysis technique is used by Monte Carlo simulation, (thus, the probability distribution of fuel cycle cost can be obtained. Furthermore, sensitivity calculations are made to analyze the impact on the fuel cycle cost of variations in the unit prices for each fuel cycle component. The result shows that the most influential parameters are unit price of natural uranium, enrichment and discount rate. Finally a comparison of fuel cycle cost between 100%UO{sub 2} and 20%UO{sub 2}-80%ThO{sub 2} MOX fuel is made. The latter is 11% cheaper than the former. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗