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DOE OSTI2022

A Search for Sterile-Neutrino-Based Muon Neutrino Disappearance Using the MicroBooNe Deep Learning Analysis

We describe a search for νµ disappearance using the MicroBooNE Deep Learning analysis 1µ1p selection. Presently, the unexplained MiniBooNE and LSND anomalies could be explained by a sterile neutrino impacting neutrino oscillations. Our analysis searches for the allowed parameter space that could describe such a sterile neutrino. We determine the allowed and excluded region of a 3+1 sterile-based muon neutrino disappearance model in MicroBooNE at 90% confidence. Our allowed region includes both the null model, and current global best fit model. Context for the underlying Deep Learning analysis is provided and several validation studies surrounding both the disappearance search, and originating 1µ1p selection are performed to strengthen confidence in the result. In addition, a next-generation deep learning tool for cosmic-ray-muon event discrimination is proposed and evaluated, demonstrating a removal of 70% of the remaining event background when added to current methods, under the cut criteria used.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2018

The near-nucleus gas coma of comet 67P/Churyumov-Gerasimenko prior to the descent of the surface lander PHILAE

Context. The European Space Agency (ESA) Rosetta mission was the most comprehensive study of a comet ever performed. In particular, the Rosetta orbiter, which carried many instruments for monitoring the evolution of the dusty gas emitted by the cometary nucleus, returned an enormous volume of observational data collected from the close vicinity of the nucleus of comet 67P/Churyumov-Gerasimenko. Aims. Such data are expected to yield unique information on the physical processes of gas and dust emission, using current physical model fits to the data. We present such a model (the RZC model) and our procedure of adjustment of this model to the data. Methods. The RZC model consists of two components: (1) a numerical three-dimensional time-dependent code solving the Eulerian/Navier-Stokes equations governing the gas outflow, and a direct simulation Monte Carlo (DSMC) gaskinetic code with the same objective; and (2) an iterative procedure to adjust the assumed model parameters to best-fit the observational data at all times. Results. We demonstrate that our model is able to reproduce the overall features of the local neutral number density and composition measurements of Rosetta Orbiter Spectrometer for Ion and Neutral Analysis (ROSINA) Comet Pressure Sensor (COPS) and Double Focusing Mass Spectrometer (DFMS) instruments in the period August 1–November 30, 2014. The results of numerical simulations show that illumination conditions on the nucleus are the main driver for the gas activity of the comet. We present the distribution of surface inhomogeneity best-fitted to the ROSINA COPS and DFMS in situ measurements.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

sparse-msrf:A package for sparse modeling and estimation of fossil-fuel CO2 emission fields

The software is used to fit models of emission fields (e.g., fossil-fuel CO2 emissions) to sparse measurements of gaseous concentrations. Its primary aim is to provide an implementation and a demonstration for the algorithms and models developed in J. Ray, V. Yadav, A. M. Michalak, B. van Bloemen Waanders and S. A. McKenna, "A multiresolution spatial parameterization for the estimation of fossil-fuel carbon dioxide emissions via atmospheric inversions", accepted, Geoscientific Model Development, 2014. The software can be used to estimate emissions of non-reactive gases such as fossil-fuel CO2, methane etc. The software uses a proxy of the emission field being estimated (e.g., for fossil-fuel CO2, a population density map is a good proxy) to construct a wavelet model for the emission field. It then uses a shrinkage regression algorithm called Stagewise Orthogonal Matching Pursuit (StOMP) to fit the wavelet model to concentration measurements, using an atmospheric transport model to relate emission and concentration fields. Algorithmic novelties described in the paper above (1) ensure that the estimated emission fields are non-negative, (2) allow the use of guesses for emission fields to accelerate the estimation processes and (3) ensure that under/overestimates in the guesses do not skew the estimation.

None, JinaLee↗

DOE OSTI2014

sparse-msrf:A package for sparse modeling and estimation of fossil-fuel CO2 emission fields

Source record↗

DOE OSTI2016

AGES OF MASSIVE GALAXIES AT 0.5 > z > 2.0 FROM 3D-HST REST-FRAME OPTICAL SPECTROSCOPY

We present low-resolution near-infrared stacked spectra from the 3D–HST survey up to z = 2.0 and fit them with commonly used stellar population synthesis models: BC03, FSPS10 (Flexible Stellar Population Synthesis), and FSPS-C3K. The accuracy of the grism redshifts allows the unambiguous detection of many emission and absorption features and thus a first systematic exploration of the rest-frame optical spectra of galaxies up to z = 2. We select massive galaxies (log(M{sub ∗}/M{sub ⊙})>10.8), we divide them into quiescent and star-forming via a rest-frame color–color technique, and we median-stack the samples in three redshift bins between z = 0.5 and z = 2.0. We find that stellar population models fit the observations well at wavelengths below the 6500 Å rest frame, but show systematic residuals at redder wavelengths. The FSPS-C3K model generally provides the best fits (evaluated with χ {sup 2} {sub red} statistics) for quiescent galaxies, while BC03 performs the best for star-forming galaxies. The stellar ages of quiescent galaxies implied by the models, assuming solar metallicity, vary from 4 Gyr at z ∼ 0.75 to 1.5 Gyr at z ∼ 1.75, with an uncertainty of a factor of two caused by the unknown metallicity. On average, the stellar ages are half the age of the universe at these redshifts. We show that the inferred evolution of ages of quiescent galaxies is in agreement with fundamental plane measurements, assuming an 8 Gyr age for local galaxies. For star-forming galaxies, the inferred ages depend strongly on the stellar population model and the shape of the assumed star-formation history.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

3C 273 with NuSTAR: Unveiling the active galactic nucleus

We present results from a 244 ks NuSTAR observation of 3C 273 obtained during a cross-calibration campaign with the Chandra, INTEGRAL, Suzaku, Swift, and XMM-Newton observatories. We show that the spectrum, when fit with a power-law model using data from all observatories except INTEGRAL over the 1–78 keV band, leaves significant residuals in the NuSTAR data between 30 and 78 keV. The NuSTAR 3–78 keV spectrum is well described by an exponentially cutoff power law (Γ=1.646±0.006, E{sub cutoff}=202{sub −34}{sup +51} keV) with a weak reflection component from cold, dense material. There is also evidence for a weak (EW=23±11 eV) neutral iron line. We interpret these features as arising from coronal emission plus reflection off an accretion disk or distant material. Beyond 80 keV INTEGRAL data show clear excess flux relative to an extrapolation of the active galactic nucleus model fit to NuSTAR. This high-energy power law is consistent with the presence of a beamed jet, which begins to dominate over emission from the inner accretion flow at 30–40 keV. Modeling the jet locally (in the NuSTAR + INTEGRAL band) as a power law, we find that the coronal component is fit by Γ{sub AGN}=1.638±0.045, E{sub cutoff}=47±15 keV, and jet photon index by Γ{sub jet}=1.05±0.4. We also consider Fermi/LAT observations of 3C 273, and here the broadband spectrum of the jet can be described by a log-parabolic model, peaking at ∼2 MeV. Finally, we investigate the spectral variability in the NuSTAR band and find an inverse correlation between flux and Γ.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

Study of GRB light-curve decay indices in the afterglow phase

In this work, we study the distribution of temporal power-law decay indices, α, in the gamma-ray burst (GRB) afterglow phase, fitted for 176 GRBs (139 long GRBs, 12 short GRBs with extended emission, and 25 X-ray flashes) with known redshifts. These indices are compared with the temporal decay index, α {sub W}, derived with the light-curve fitting using the Willingale et al. model. This model fitting yields similar distributions of α {sub W} to the fitted α, but for individual bursts a difference can be significant. Analysis of (α, L {sub a}) distribution, where L {sub a} is the characteristic luminosity at the end of the plateau, reveals only a weak correlation of these quantities. However, we discovered a significant regular trend when studying GRB α values along the Dainotti et al. correlation between L {sub a} and the end time of the plateau emission in the rest frame, T{sub a}{sup ∗}, hereafter LT correlation. We note a systematic variation of the α parameter distribution with luminosity for any selected T{sub a}{sup ∗}. We analyze this systematics with respect to the fitted LT correlation line, expecting that the presented trend may allow us to constrain the GRB physical models. We also attempted to use the derived correlation of α(T{sub a}) versus L{sub a}(T{sub a}) to diminish the luminosity scatter related to the variations of α along the LT distribution, a step forward in the effort of standardizing GRBs. A proposed toy model accounting for this systematics applied to the analyzed GRB distribution results in a slight increase of the LT correlation coefficient.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Suppressing simulation bias in multi-modal data using transfer learning

Abstract Many problems in science and engineering require making predictions based on few observations. To build a robust predictive model, these sparse data may need to be augmented with simulated data, especially when the design space is multi-dimensional. Simulations, however, often suffer from an inherent bias. Estimation of this bias may be poorly constrained not only because of data sparsity, but also because traditional predictive models fit only one type of observed outputs, such as scalars or images, instead of all available output data modalities, which might have been acquired and simulated at great cost. To break this limitation and open up the path for multi-modal calibration, we propose to combine a novel, transfer learning technique for suppressing the bias with recent developments in deep learning, which allow building predictive models with multi-modal outputs. First, we train an initial neural network model on simulated data to learn important correlations between different output modalities and between simulation inputs and outputs. Then, the model is partially retrained, or transfer learned, to fit the experiments; a method that has never been implemented in this type of architecture. Using fewer than 10 inertial confinement fusion experiments for training, transfer learning systematically improves the simulation predictions while a simple output calibration, which we design as a baseline, makes the predictions worse. We also offer extensive cross-validation with real and carefully designed synthetic data. The method described in this paper can be applied to a wide range of problems that require transferring knowledge from simulations to the domain of experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Active learning using hybrid surrogate tool life modeling for machining process optimization

Here, this paper describes an active learning approach for part-to-part iterative machining process optimization using a hybrid surrogate tool life model. A probabilistic interpolating tool life model is developed by combining the empirical Taylor-type tool life equation and the model fit error. The probabilistic tool life model is then used to calculate the machining cost per part distribution. The optimal machining parameters are selected using an expected improvement in machining cost per part criterion. The method is validated numerically using experimental results; the results show a median convergence error of 2.2% after three tests over 400 simulations. The method is validated experimentally on two industrial applications for Ti-6Al-4V roughing resulting in a cost per part reduction greater than 23% after two tests. The described method is a robust solution for rapid convergence to optimal machining parameters in an industrial production environment.

Active learning↗

DOE OSTI2013

Quintessence versus phantom dark energy: the arbitrating power of current and future observations

We analyze the possibility to distinguish between quintessence and phantom scalar field models of dark energy using observations of luminosity distance moduli of SNe Ia, CMB anisotropies and polarization, matter density perturbations and baryon acoustic oscillations. Among the present observations only Planck data on CMB anisotropy and SDSS DR9 data on baryon acoustic oscillations may be able to decide between quintessence or phantom scalar field models, however for each model a set of best-fit parameters exists, which matches all data with similar goodness of fit. We compare the relative differences of best-fit model predictions with observational uncertainties for each type of data and we show that the accuracy of SNe Ia luminosity distance data is far from the one necessary to distinguish these types of dark energy models, while the CMB data (WMAP, ACT, SPT and especially Planck) are close to being able to reliably distinguish them. Also an improvement of the large-scale structure data (future releases of SDSS BOSS and e.g. Euclid or BigBOSS) will enable us to surely decide between quintessence and phantom dark energy.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Radon Kinetics in a Basement Space Measured with Different Devices

Although indoor monitoring of radon and benchmarking of radon measurement devices remain important research topics, few intercomparisons of active radon measurement devices have been performed under realistic conditions, let alone dynamic ones enabling comparison of their transient behavior. Five different radon monitors were therefore placed in a poorly ventilated basement space under three different conditions: 24 h under a steady, elevated radon level, 24 h with fans turned on to produce a radon washout transient, and 9 d with fans turned off for a radon buildup transient. Resulting radon concentrations varied between ~200 and ~2,000 Bq m -3 . Accuracy of the devices were evaluated using root-mean-square error, and ventilation data were fit to first order linear compartmental models. To more accurately model behaviors such as cyclic diurnal variations, the source term corresponding to entry of radon from soil into the basement was considered to be non-constant, as it is likely to vary drastically with both the indoor-outdoor pressure differential and soil concentration variations. Here, the improved radon washout model fit very well with the measurements. Despite a wide variety in list prices, all devices performed similarly during transients and at different radon concentrations.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2020

3D CFD Model Validation Using Benchmark Data of 1/16th Scaled VHTR Upper Plenum and Development of Wall Heat-Transfer Correlation For Laminar Flow

With support from the U.S. Department of Energy-Office of Nuclear Energy’s (DOE-NE’s) Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, an effort has been pursued to support high-temperature gas-cooled reactor (HTGR) technology development and its modeling and simulation needs. There is a particular need for advanced modeling and simulation tools to predict thermal-fluid behavior in the nuclear reactor primary system, especially in the core and the lower and upper plena, during safety-related transients. In this report, two main such activities are presented relevant to the HTGRs: (1) three-dimensional (3D) computational fluid dynamics (CFD) validation using benchmark data from the upper plenum of Texas A&M University’s 1/16th scaled very-high-temperature gas-cooled reactor (VHTR), and (2) development of wall heat-transfer correlation for laminar flow in a wall-heated pipe. The CFD tool validation exercises can be helpful to choose the models and CFD tools to simulate and design specific components of the HTRGs such as upper plenum where jet mixing is a complex phenomenon. In a loss of forced circulation event, the laminar flow can be observed during the development of natural circulation flow. This work includes the development and validation of heat transfer correlations for laminar flow using the Nek5000 CFD code due to limited available experimental data for laminar flow conditions to guide low-order models (1D). In this report, the flow characteristics of a single isothermal jet discharging into the upper plenum was investigated using the Nek5000 Large-Eddy Simulation (LES) CFD tool. Several numerical simulations were performed for various jet-discharged Reynolds numbers ranging from 3,413 to 12,819. A grid-independent study was performed. The numerical results of mean velocity, root-mean-square fluctuating velocity, and Reynolds stress were compared against the benchmark data. Good agreement was obtained between simulated and measured data for axial mean velocities, except near the upper plenum hemisphere. The maximum predicted errors for axial mean velocities at various normalized coolant channel diameter heights of 1, 5, and 10 are 1.56%, 1.88%, and 3.82%, respectively. In addition, the predicted root-mean-square fluctuating velocity and Reynolds stress are qualitatively in agreement with the experimental data. The Nek5000 code was used to develop wall-heat transfer correlation for laminar flow in a cylindrical tube. Several simulations were performed for various Reynolds flow and wall-heat fluxes. A new heat transfer correlation was developed using data from Nek5000 simulation results and regression functions in Matlab. The developed heat transfer correlation is valid for various Reynolds flows from 200 to 2000. The predicted R² value for model fit was 0.875, which ensures that 87.5% of the model data lies on the Nek5000 data. Moreover, a machine learning (ML) tool was used to train and test the Nek5000 data. A good fit of the ML-based model was observed with the test data.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2017

Oxidation and Condensation of Zinc Fume From Zn-CO 2 -CO-H 2 O Streams Relevant to Steelmaking Off-Gas Systems

Here the objective of this research was to study the condensation of zinc vapor to metallic zinc and zinc oxide solid under varying environments to investigate the feasibility of in-process separation of zinc from steelmaking off-gas dusts. Water vapor content, temperature, degree of cooling, gas composition, and initial zinc partial pressure were varied to simulate the possible conditions that can occur within steelmaking off-gas systems, limited to Zn-CO 2 -CO-H 2 O gas compositions. The temperature of deposition and the effect of rapidly quenching the gas were specifically studied. A homogeneous nucleation model for applicable experiments was applied to the analysis of the experimental data. It was determined that under the experimental conditions, oxidation of zinc vapor by H 2 O or CO 2 does not occur above 1108 K (835 °C) even for highly oxidizing streams (CO 2 /CO = 40/7). Rate expressions that correlate CO 2 and H 2 O oxidation rates to gas composition, partial pressure of water vapor, temperature, and zinc partial pressure were determined to be as follows: Rate $ \left(\frac{mol}{m^2s}\right) $ = 406 exp $ \left(\frac{-50.2 kJ/mol}{RT}\right) $ (pZnpCO 2 $-$ PCO/K eq CO 2 ) $\frac{mol}{m^2 x s}$ Rate $ \left(\frac{mol}{m^2s}\right) $ = 32.9 exp $ \left(\frac{-13.7 kJ/mol}{RT}\right) $ (pZnPH 2 O $-$ PH 2 /K eq H 2 O) $\frac{mol}{m^2 x s}$. It was proven that a rapid cooling rate (500 K/s) significantly increases the ratio of metallic zinc to zinc oxide as opposed to a slow cooling rate (250 K/s). SEM analysis found evidence of heterogeneous growth of ZnO as well as of homogeneous formation of metallic zinc. The homogeneous nucleation model fit well with experiments where only metallic zinc deposited. An expanded model with rates of oxidation by CO 2 and H 2 O as shown was combined with the homogenous nucleation model and then compared with experimental data. The calculated results based on the model gave a reasonable fit to the measured data. For the conditions used in this study, the rate equations for the oxidation of zinc by carbon dioxide and water vapor as well as the homogeneous nucleation model of metallic zinc were applicable for various temperatures, zinc partial pressures, CO 2 :CO ratios, and H 2 O partial pressures.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Local models for scatter estimation and descattering in polyenergetic X-ray tomography

We propose a new modeling approach for scatter estimation and descattering in polyenergetic X-ray computed tomography (CT) based on fitting models to local neighborhoods of a training set. X-ray CT is widely used in medical and industrial applications. X-ray scatter, if not accounted for during reconstruction, creates a loss of contrast in CT reconstructions and introduces severe artifacts including cupping, shading, and streaks. Even when these qualitative artifacts are not apparent, scatter can pose a major obstacle in obtaining quantitatively accurate reconstructions. Our approach to estimating scatter is, first, to generate a training set of 2D radiographs with and without scatter using particle transport simulation software. To estimate scatter for a new radiograph, we adaptively fit a scatter model to a small subset of the training data containing the radiographs most similar to it. We compared local and global (fit on full data sets) versions of several X-ray scatter models, including two from the recent literature, as well as a recent deep learning-based scatter model, in the context of descattering and quantitative density reconstruction of simulated, spherically symmetrical, single-material objects comprising shells of various densities. Our results show that, when applied locally, even simple models provide state-of-the-art descattering, reducing the error in density reconstruction due to scatter by more than half.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2014

Observations and modeling of the companions of short period binary millisecond pulsars: evidence for high-mass neutron stars

We present observations of fields containing eight recently discovered binary millisecond pulsars using the telescopes at MDM Observatory. Optical counterparts to four of these systems are detected, one of which, PSR J2214+3000, is a novel detection. Additionally, we present the fully phase-resolved B, V, and R light curves of the optical counterparts to two objects, PSR J1810+1744 and PSR J2215+5135 for which we employ model fitting using the eclipsing light curve (ELC) model of Orosz and Hauschildt to measure the unknown system parameters. For PSR J1810+1744, we find that the system parameters cannot be fit even assuming that 100% of the spin-down luminosity of the pulsar is irradiating the secondary, and so radial velocity measurements of this object will be required for the complete solution. However, PSR J2215+5135 exhibits light curves that are extremely well constrained using the ELC model and we find that the mass of the neutron star is constrained by these and the radio observations to be M {sub NS} > 1.75 M {sub ☉} at the 3σ level. We also find a discrepancy between the model temperature and the measured colors of this object, which we interpret as possible evidence for an additional high-temperature source such as a quiescent disk. Given this and the fact that PSR J2215+5135 contains a relatively high mass companion (M {sub c} > 0.1 M {sub ☉}), we propose that similar to the binary pulsar systems PSR J1023+0038 and IGR J18245–2452, the pulsar may transition between accretion- and rotation-powered modes.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2019

Reduction Kinetics of Perovskite Oxides for Selective Hydrogen Combustion in the Context of Olefin Production

Chemical looping represents a novel approach for generating light olefins in which thermal cracking or catalytic dehydrogenation is coupled with selective hydrogen combustion (SHC) by a metal oxide redox catalyst, which enables autothermal operation, increased per-pass conversion, and greater-than-equilibrium yields. Recent studies indicate that Na 2 WO 4 -promoted perovskite oxides are effective redox catalysts with high olefin selectivity. Herein, kinetic parameters, rates, and reaction models for the reduction of unpromoted and Na 2 WO 4 -promoted CaMnO 3 redox catalysts by H 2 , C 2 H 4 , and C 2 H 6 , is reported. Reduction rates of CaMnO 3 under ethylene and ethane are significantly lower than under H 2 . Additionally, model fitting of reduction kinetics show good agreement with reaction order–controlled models for CaMnO 3 reduction and predict greater oxygen site dependence and higher activation energy for CaMnO 3 reduction by C 2 H 4 as compared with H 2 . Avrami–Erofe'ev nucleation and growth models provide the best fit to the reduction of Na 2 WO 4 /CaMnO 3 in H 2 and in C 2 H 4 . After Na 2 WO 4 promotion, the reduction rate of CaMnO 3 is three orders of magnitude lower in ethylene in comparison to hydrogen, consistent with its superior selectivity to hydrogen combustion. The models developed can be applied toward reactor design and optimization in the context of enhanced olefin production via SHC under a cyclic redox scheme.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2017

Models of the Hydrodynamic Histories of Post-AGB Stars. I. Multiflow Shaping of OH 231.8+04.2

We present a detailed hydrodynamic model that matches the present structure of the well-observed preplanetary nebula (“pPN”) OH 231.8+04.2 (“OH231”). The purpose of the model is to present a physically justified and coherent picture of its evolutionary history from about 100 years from the start of the formation of its complex outer structures to the present. We have adopted a set of initial conditions that are heavily constrained by high-quality observations of its present structure and kinematics. The shaping of the nebula occurs while the densities of the flows are “light,” i.e., less than the surrounding AGB-wind environment. The simulations show that pairs of essentially coeval clumps and sprays of the same extent and density, but different outflow speeds, sculpted both the pair of thin axial flow “or spine” and the bulbs. The total ejected mass and momentum in the best-fit model are surprisingly large—3 M {sub ⊙} and 2.2 × 10{sup 41} gm cm s{sup −1}, respectively—however, these values are reduced by up to a factor of 10 in other models that fit the data almost as well. Our ultimate goal is to combine the present model results of masses, momenta, flow speeds, and flow geometries for OH231 with those of other models to be published in the future in order to find common attributes of their ejection histories.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Response of CR-39 nuclear track detectors to protons with non-normal incidence

This paper presents data from experiments with protons at non-normal incidence to CR-39 nuclear track detectors, analyzing the properties of detection efficiency, proton track diameter, track contrast, and track eccentricity. Understanding the CR-39 response to protons incident at an angle is important for designing charged particle detectors for inertial confinement fusion (ICF) applications. This study considers protons with incident energies less than 3 MeV. In this regime, an incident angle of 10° has no effect on CR-39 detection efficiency, and >85% detection efficiency is preserved up through 25° in the range of 1.0 MeV–2.1 MeV. For ICF applications, incident angles above 30° are deemed impractical for detector design due to significant drops in proton detection at all energies. We observe significant reductions in detection efficiency compared to theoretical predictions, particularly at low energies where proton tracks are etched away. The proton track diameter measured by the scan system is observed to decrease with higher incident angles. The track diameters are analyzed with two fitting models, and it is shown that the diameter–energy relation can be fit with the existing models at angles up to 30° . The optical contrast of the tracks tends to increase with the angle, meaning that the tracks are fainter, and a larger increase is observed for higher energies. Eccentricity, a measure of how elongated proton tracks are, increases with the incident angle and drops after the critical angle. The lowest energy tracks remain nearly circular even at higher angles.

47 OTHER INSTRUMENTATION↗