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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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At least 577 records · Page 32
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DOE OSTI2021

The Nature of Jets in Double-peaked Emission-line AGN in the KISSR Sample

Double-peaked emission-line AGN (DPAGN) have been regarded as binary black hole candidates. We present here results from parsec-scale radio observations with the Very Long Baseline Array (VLBA) of five DPAGN belonging to the KISSR sample of emission-line galaxies. This work concludes our pilot study of nine type 2 Seyfert and LINER DPAGN from the KISSR sample. In the nine sources, dual compact cores are only detected in the “offset AGN,” KISSR 102. However, the overall incidence of jets in the eight sources that were detected with the VLBA is ≥ 60%. We find a difference in the “missing flux density” going from the Very Large Array to VLBA scales between Seyferts and LINERs, with LINERs showing less missing flux density on parsec-scales. Using the emission-line modeling code, MAPPINGS III, we find that the emission lines are likely to be influenced by jets in 5/9 sources. Furthermore, jet-medium interaction is the likely cause of the emission-line splitting observed in the SDSS spectra of these sources. Jets in radio-quiet AGN are therefore energetically capable of influencing their parsec- and kpcscale environments, which makes them agents of “radio AGN feedback” (similar to radio-loud AGN).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Very-high-energy Emission from Pulsars

Abstract Air-Cherenkov telescopes have detected pulsations at energies above 50 GeV from a growing number of Fermi pulsars. These include the Crab, Vela, PSR B1706−44, and Geminga, with the first two having pulsed detections above 1 TeV. In some cases, there appears to be very-high-energy (VHE) emission that is an extension of the Fermi spectra to high energies, while in other cases, additional higher-energy spectral components that require a separate emission mechanism may be present. We present results of broadband spectral modeling using global magnetospheric fields and multiple emission mechanisms that include synchro-curvature (SC) and inverse Compton scattered (ICS) radiation from accelerated particles (primaries) and synchrotron self-Compton (SSC) emission from lower-energy pairs. Our models predict three distinct VHE components: SC from primaries whose high-energy tail can extend to 100 GeV, SSC from pairs that can extend to several TeV, and ICS from primary particles accelerated in the current sheet that scatter pair synchrotron radiation, which appears beyond 10 TeV. Our models suggest that H.E.S.S.-II and MAGIC have detected the high-energy tail of the primary SC component that produces the Fermi spectrum in Vela, Geminga, and PSR B1706−44. We argue that the ICS component peaking above 10 TeV from Vela has been seen by H.E.S.S. Detection of this emission component from the Crab and other pulsars is possible with the High Altitude Water Cherenkov Observatory and Cherenkov Telescope Array, and will directly measure the maximum particle energy in pulsars.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

The Physical Properties of Low-redshift FeLoBAL Quasars. II. The Rest-frame Optical Emission Line Properties

We report the results of an analysis of the Hβ emission line region of a sample of 30 low-redshift (z < 1) iron low-ionization broad absorption line quasars (FeLoBALQs). Eleven of these objects are newly classified as FeLoBALQs. A matched sample of 132 unabsorbed quasars was analyzed in parallel. The emission lines showed the well-known anticorrelation between the [O III ] and Fe II emission. Using a summary statistic called E1 to quantify this anticorrelation, we found that while the distribution of E1 for the unabsorbed quasars has a single peak, the FeLoBALQs have a bimodal shape in this parameter. Previous studies have shown that the line emission properties of BAL and non-BALQs are consistent; therefore, the difference in the Hβ region emission between FeLoBALQs and unabsorbed quasars is a new result. The two populations of FeLoBALQs are characterized by low and high bolometric luminosities and Eddington ratios. Some previous studies have suggested that BALQs are high accretion rate objects and therefore the discovery of the low accretion rate branch of FeLoBAL quasars was unexpected. We also found that the Hβ FWHM is systematically broader among the FeLoBALQs, implying a higher inclination viewing angle or a dearth of low velocity line emitting gas.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Emission Lines of Fe xiv, Fe xv, and Fe xvi in the Extreme Ultraviolet Region 40–100 Å

We report on emission spectra of iron in the extreme ultraviolet recorded at an electron density of ~10 11 cm -3 on the Lawrence Livermore electron beam ion trap facility. We present a summary of the observed emission lines, including wavelengths and emission intensities, and present spectra of pure Fe xiv through Fe xvi emission derived from our measurements in the 40–100 Å wavelength range. We show that spectral models, especially the current version of CHIANTI v10.0, describe the M-shell emission from these three charge states of iron reasonably well, and we are able to verify several transitions in CHIANTI for the first time.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Particle-in-cell Simulations of Mildly Relativistic Outflows in Kilonova Emissions

Abstract The electromagnetic emission from neutron star mergers is comprised of multiple components. Synchrotron emission from the disk-powered jet and thermal emission from the merger ejecta (powered by a variety of sources) are among the most studied sources. The low masses and high velocities of the merger ejecta quickly develop conditions where emission from collisionless shocks becomes critical and synchrotron emission from the merger ejecta constitutes a third component to the observed signal. The aim of this project is to examine shock development, magnetic field generation, and particle acceleration in the case of mildly relativistic shocks, which are expected when the tidal ejecta of neutron star mergers drive a shock into the external medium. Using LANL’s vector particle-in-cell (VPIC) code, we have run simulations of such mildly relativistic, collisionless, weakly magnetized plasmas and computed the resultant magnetic fields and particle energy spectra. We show the effects of varying plasma conditions, as well as explore the validity of using different proton-to-electron mass ratios in VPIC. Our results have implications for observing late-time electromagnetic counterparts to gravitational wave detections of neutron star mergers.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Search for Continuous and Transient Neutrino Emission Associated with IceCube’s Highest-energy Tracks: An 11 yr Analysis

IceCube alert events are neutrinos with a moderate-to-high probability of having astrophysical origin. In this study, we analyze 11 yr of IceCube data and investigate 122 alert events and a selection of high-energy tracks detected between 2009 and the end of 2021. This high-energy event selection (alert events + high-energy tracks) has an average probability of ≥0.5 of being of astrophysical origin. We search for additional continuous and transient neutrino emission within the high-energy events' error regions. We find no evidence for significant continuous neutrino emission from any of the alert event directions. The only locally significant neutrino emission is the transient emission associated with the blazar TXS 0506+056, with a local significance of 3σ, which confirms previous IceCube studies. When correcting for 122 test positions, the global p-value is 0.156 and compatible with the background hypothesis. We constrain the total continuous flux emitted from all 122 test positions at 100 TeV to be below 1.2 × 10 –15 (TeV cm 2 s) –1 at 90% confidence assuming an E –2 spectrum. This corresponds to 4.5% of IceCube's astrophysical diffuse flux. Overall, we find no indication that alert events in general are linked to lower-energetic continuous or transient neutrino emission.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Multiwavelength Investigation of γ-Ray Source MGRO J1908+06 Emission Using Fermi-LAT, VERITAS and HAWC

This paper investigates the origin of the γ-ray emission from MGRO J1908+06 in the GeV–TeV energy band. By analyzing the data collected by the Fermi Large Area Telescope, the Very Energetic Radiation Imaging Telescope Array System, and High Altitude Water Cherenkov, with the addition of spectral data previously reported by LHAASO, a multiwavelength study of the morphological and spectral features of MGRO J1908+06 provides insight into the origin of the γ-ray emission. The mechanism behind the bright TeV emission is studied by constraining the magnetic field strength, the source age, and the distance through detailed broadband modeling. Both spectral shape and energy-dependent morphology support the scenario that inverse Compton emission of an evolved pulsar wind nebula associated with PSR J1907+0602 is responsible for the MGRO J1908+06 γ-ray emission with a best-fit true age of T = 22 ± 9 kyr and a magnetic field of B = 5.4 ± 0.8 μG, assuming the distance to the pulsar d PSR = 3.2 kpc.

Gamma-ray astronomy↗
DOE OSTI2025

DESI Spectroscopy of HETDEX Emission-line Candidates. I. Line Discrimination Validation

The Hobby–Eberly Dark Energy Experiment (HETDEX) is an untargeted spectroscopic galaxy survey that uses Lyα-emitting galaxies (LAEs) as tracers of 1.9 < z < 3.5 large-scale structure. Most detections consist of a single emission line, whose identity is inferred via a Bayesian analysis of ancillary data. To determine the accuracy of these line identifications, HETDEX detections were observed with the Dark Energy Spectroscopic Instrument (DESI). In two DESI pointings, high-confidence spectroscopic redshifts are obtained for 1157 sources, including 982 LAEs. The DESI spectra are used to evaluate the accuracy of the HETDEX object classifications and tune the methodology to achieve the HETDEX science requirement of ≲2% contamination of the LAE sample by low-redshift emission-line galaxies, while still assigning 96% of the true Lyα emission sample with the correct spectroscopic redshift. We compare emission-line measurements between the two experiments assuming a simple Gaussian line fitting model. Fitted values for the central wavelength of the emission line, the measured line flux, and line widths are consistent between the surveys within uncertainties. Derived spectroscopic redshifts, from the two classification pipelines, when both agree as an LAE classification, are consistent to within $\langle$Δz/(1 + z)$\rangle$ = 6.9 × 10 −5 with an rms scatter of 3.3 × 10 −4 . Data are available at https://data.desi.lbl.gov/desi/public/dr1/vac/dr1/hetdex.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Search for High-energy Neutrino Emission from Galactic X-Ray Binaries with IceCube

We present the first comprehensive search for high-energy neutrino emission from high- and low-mass X-ray binaries conducted by IceCube. Galactic X-ray binaries are long-standing candidates for the source of Galactic hadronic cosmic rays and neutrinos. The compact object in these systems can be the site of cosmic-ray acceleration, and neutrinos can be produced by interactions of cosmic rays with radiation or gas, in the jet of a microquasar, in the stellar wind, or in the atmosphere of the companion star. We study X-ray binaries using 7.5 yr of IceCube data with three separate analyses. In the first, we search for periodic neutrino emission from 55 binaries in the Northern Sky with known orbital periods. In the second, the X-ray light curves of 102 binaries across the entire sky are used as templates to search for time-dependent neutrino emission. Finally, we search for time-integrated emission of neutrinos for a list of 4 notable binaries identified as microquasars. In the absence of a significant excess, we place upper limits on the neutrino flux for each hypothesis and compare our results with theoretical predictions for several binaries. In addition, we evaluate the sensitivity of the next generation neutrino telescope at the South Pole, IceCube-Gen2, and demonstrate its power to identify potential neutrino emission from these binary sources in the Galaxy.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Connection between Emission and Absorption Outflows through the Study of Quasars with Extremely High Velocity Outflows

A recently discovered class of outflows, extremely high velocity outflows (EHVOs), may be key to understanding feedback processes, as it is likely the most powerful in terms of mass energy. These EHVOs have been observed at redshifts 1.052 < z em < 7.641, but the potential connection with outflows in emission has not been studied. We find that EHVOs, albeit their small numbers at the moment, appear to show distinct C IV and He II properties. In particular, EHVOs are more predominant in quasars with large blueshifts of the C IV emission line, suggesting a connection between emission and absorption outflowing signatures for these extreme outflows. We also find incipient trends with the maximum velocity of the outflows, which is similar to what has been previously found in BALQSOs but now extending previous studies to speeds up to ~0.2c. We find that the bolometric luminosities, Eddington ratios, and black hole masses of our sample are overall very similar to the general quasar population upon considering their C IV emission properties. This is close to the case for He II EW, as we observe a tentative upper limit to the He II strength for a quasar to host an EHVO. This study shows that extreme outflows such as EHVOs appear in quasars that are clearly a distinct class from the overall BALQSO population and solidify the relation between outflows observed in emission and absorption.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Detection of the Orbital Modulation of Fe Kα Fluorescence Emission in Centaurus X-3 Using the High-resolution Spectrometer Resolve on board XRISM

Abstract The Fe K α fluorescence line emission in X-ray spectra is a powerful diagnostic tool for various astrophysical objects to reveal the distribution of cold matter around photoionizing sources. The advent of the X-ray microcalorimeter on board the XRISM satellite will bring new constraints on the emission line. We present one of the first such results for the high-mass X-ray binary Centaurus X-3, which is composed of an O-type star and a neutron star (NS). We conducted a 155 ks observation covering an entire binary orbit. A weak Fe K α line was detected in all orbital phases at an equivalent width (EW) of 10–20 eV. We found for the first time that its radial velocity (RV) is sinusoidally modulated by the orbital phase. The RV amplitude is 248 ± 13 km s −1 , which is significantly smaller than the value (391 km s −1 ) expected if the emission is from the NS surface, but is consistent if the emission takes place at the O star surface. We discuss several possibilities of the line production site, including the NS surface, O star surface, O star wind, and accretion stream from the O star to the NS. We ran radiative transfer calculation for some of them assuming spherically symmetric density and velocity profiles and an isotropic distribution of X-ray emission from the NS. None of them explains the observed EW and velocity dispersion dependence on the orbital phase, suggesting that more elaborated modeling is needed. In other words, the present observational results have the capability to constrain deviations from these assumptions.

High energy astrophysics↗
DOE OSTI2022

Opinion: Coordinated development of emission inventories for climate forcers and air pollutants

Emissions into the atmosphere of fine particulate matter, its precursors, and precursors to tropospheric ozone impact not only human health and ecosystems, but also the climate by altering Earth's radiative balance. Accurately quantifying these impacts across local to global scales historically and in future scenarios requires emission inventories that are accurate, transparent, complete, comparable, and consistent. In an effort to better quantify the emissions and impacts of these pollutants, also called short-lived climate forcers (SLCFs), the Intergovernmental Panel on Climate Change (IPCC) is developing a new SLCF emissions methodology report. This report would supplement existing IPCC reporting guidance on greenhouse gas (GHG) emission inventories, which are currently used by inventory compilers to fulfill national reporting requirements under the United Nations Framework Convention on Climate Change (UNFCCC) and new requirements of the Enhanced Transparency Framework (ETF) under the Paris Agreement starting in 2024. We review the relevant issues, including how air pollutant and GHG inventory activities have historically been structured, as well as potential benefits, challenges, and recommendations for coordinating GHG and air pollutant inventory efforts. We argue that, while there are potential benefits to increasing coordination between air pollutant and GHG inventory development efforts, we also caution that there are differences in appropriate methodologies and applications that must jointly be considered.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Increased importance of aerosol–cloud interactions for surface PM 2.5 pollution relative to aerosol–radiation interactions in China with the anthropogenic emission reductions

Surface fine particulate matter (PM 2.5 ) pollution can be enhanced by feedback processes induced by aerosol–radiation interactions (ARIs) and aerosol–cloud interactions (ACIs). Many previous studies have reported enhanced PM 2.5 concentrations induced by ARIs and ACIs for episodic events in China. However, few studies have examined the changes in the ARI- and ACI-induced PM 2.5 enhancements over a long period, though the anthropogenic emissions have changed substantially in the last decade. In this study, we quantify the ARI- and ACI-induced PM 2.5 changes for 2013–2021 under different meteorology and emission scenarios using the Weather Research and Forecasting model with Chemistry (WRF-Chem), and we investigate the driving factors behind the changes. Our results show that, in January 2013, when China suffered from the worst PM 2.5 pollution, the PM 2.5 enhancement induced by ARIs in eastern China (5.59 µg m −3 ) was larger than that induced by ACIs (3.96 µg m −3 ). However, the ACI-induced PM 2.5 enhancement showed a significantly smaller decrease ratio (51 %) than the ARI-induced enhancement (75 %) for 2013–2021, making ACIs more important for enhancing PM 2.5 concentrations in January 2021. Our analyses suggest that the anthropogenic emission reductions played a key role in this shift. Owing to only anthropogenic emission reductions, the ACI-induced PM 2.5 enhancement decreased by 43 % in January, which was lower than the decrease ratio of the ARI-induced enhancement (57 %). The relative change in ARI- and ACI-induced PM 2.5 enhancement in July was similar to the pattern observed in January, caused by anthropogenic emission reductions. The primary reason for this phenomenon is that the decrease in ambient PM 2.5 for 2013–2021 caused a disproportionately small decrease in the liquid water path (LWP) and an increase in the cloud effective radius (Re) under the condition of high PM 2.5 concentrations. Therefore, the surface solar radiation attenuation (and, hence, the boundary layer height reduction) caused by ACIs decreased slower than that caused by ARIs. Moreover, the lower decrease ratio of the ACI-induced PM 2.5 enhancement was dominated by the lower decrease ratio of ACI-induced secondary PM 2.5 component enhancement, which was additionally caused by the smaller decrease ratio of the air temperature reduction and the relative humidity (RH) increase. Our findings indicate that, with the decrease in ambient PM 2.5 , the ACI-induced PM 2.5 enhancement inevitably becomes more important. This needs to be considered in the formulation of control policies to meet the national PM 2.5 air quality standard.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Development of a forced advection sampling technique (FAST) for quantification of methane emissions from orphaned wells

Abstract. Orphaned wells, meaning unplugged and non-producing wells lacking responsible owners, pose a significant and undersampled environmental challenge due to their vast number and unknown associated emissions. We propose, develop and test an alternative method for estimating emissions from orphaned wells using a forced advection sampling technique (FAST) that can overcome many of the limitations in current methods (cost, accuracy, safety). In contrast to existing ambient Gaussian plume methods, our approach uses a fan-generated flow to force advection between the emission source and a point methane (CH4) sensor. The fan flow field is characterized using a colocated sonic anemometer to measure the 3D wind profile generated by the fan. Using time-series measurements of CH4 concentration and wind, a simple estimate of the CH4 emission rate of the source can be inferred. The method was calibrated using outdoor controlled-release experiments and then tested on four orphaned wells in Lufkin, TX, and Osage County, OK. Our results suggest that the FAST method can provide a low-cost, portable, fast and safe alternative to existing methods with reasonable estimates of orphaned well emissions over a range of leak rates below 40 g h−1 and within certain geometric and atmospheric constraints.

Dubey, Mohit L↗
DOE OSTI2024

Numerical coupling of aerosol emissions, dry removal, and turbulent mixing in the E3SM Atmosphere Model version 1 (EAMv1) – Part 1: Dust budget analyses and the impacts of a revised coupling scheme

Abstract. An earlier study evaluating dust life cycle in the Energy Exascale Earth System Model (E3SM) Atmosphere Model version 1 (EAMv1) has revealed that the simulated global mean dust lifetime is substantially shorter when higher vertical resolution is used, primarily due to significant strengthening of dust dry removal in source regions. This paper demonstrates that the sequential splitting of aerosol emissions, dry removal, and turbulent mixing in the model's time integration loop, especially the calculation of dry removal after surface emissions and before turbulent mixing, is the primary reason for the vertical resolution sensitivity reported in that earlier study. Based on this reasoning, we propose a revised numerical process coupling scheme that requires the least amount of code changes, in which the surface emissions are applied before turbulent mixing instead of before dry removal. The revised scheme allows newly emitted particles to be transported aloft by turbulence before being removed from the atmosphere, and hence better resembles the dust life cycle in the real world. Sensitivity experiments show that the revised process coupling substantially weakens dry removal and strengthens vertical mixing in dust source regions. It also strengthens the large-scale transport from source to non-source regions, strengthens dry removal outside the source regions, and strengthens wet removal and activation globally. In transient simulations of the years 2000–2009 conducted using 1∘ horizontal grid spacing, 72 vertical layers, and unchanged tuning parameters of emission strength, the revised process coupling leads to a 40 % increase in the global total dust burden and an increase of dust lifetime from 1.8 to 2.5 d in terms of 10-year averages. Weakened dry removal and increased mixing ratios are also seen for other aerosol species that have substantial surface emissions, although the changes in mixing ratio are considerably smaller for the submicron species than for dust and sea salt. Numerical experiments confirm that the revised coupling scheme significantly reduces the strong and non-physical sensitivities of model results to vertical resolution in the original EAMv1. This provides a motivation for adopting the revised scheme in EAM as well as for further improvements on the simple revision presented in this paper.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Summertime methane and carbon dioxide emission rates and associated variables from a national-scale survey of 146 reservoirs in the United States, 2016-2023

Reservoirs are globally important sources of greenhouse gases, but the magnitude of their emissions is highly uncertain. Here we present data for 146 reservoirs from two surveys of reservoir methane and carbon dioxide emissions, one at the regional scale in the midwestern United States and one at the national scale in the conterminous United States, plus data from one reservoir in Washington and another in Puerto Rico. At all reservoirs, ebullitive and diffusive emissions and basic physiochemistry were measured at 15-70 locations during one 22 to 64-hour period during the summers of 2016-2023, with four reservoirs revisited a second time. Concomitant water chemistry measurements were also made at an index site. The dataset is comprised of two geospatial files and seven .csv files containing greenhouse gas emissions, water chemistry, morphology, and other relevant data. These data comprise the largest multi-reservoir emissions dataset ever assembled using consistent measurement methods.

Beaulieu, Jake [University of Notre Dame, IN]↗
DOE OSTI2022

Seamlessly Fuel Flexible Heat Pump with Optimal Model-based Control Strategies to Reduce Peak Demand, Utility Cost and CO2 Emission

This research develops a novel hybrid fuel heat pump system for space heating of residential and small commercial buildings with built-in optimization and control. Whereas conventional dual fuel systems either run on gas or electricity at any given moment, the proposed seamlessly fuel flexible heat pump (SFFHP) simultaneously consumes gas and electricity and continuously optimizes the proportion of each. The building air flows across the heat pump condenser first and then flows across the furnace coil, and this reduces the heat pump temperature lift. The SFFHP delivers energy savings by allowing each subsystem (gas furnace and electric heat pump) to operate where it performs best to improve energy efficiency, minimize energy cost, and minimize carbon footprint. The capacities of the electric heat pump and gas furnace are continuously adjusted based on ambient conditions, utility price signals, and marginal grid emission signals. An optimal model predictive control strategy was developed with the goal of minimizing utility cost and minimizing CO2 emission. Two case studies were conducted to simulate the performance of SFFHP during the heating season in Chicago and Los Angeles, respectively. Compared with a conventional electric heat pump, SFFHP yields 33% utility cost reduction and 49% CO2 emission reduction in Chicago. Similarly, it achieves 23% utility cost reduction and 17% CO2 emission reduction in Los Angeles. Case studies demonstrate that SFFHP can deliver significant reductions in peak demand, utility cost, and CO2 emission. Due to the hybrid fuel nature of this novel equipment, user comfort will always be maintained. The fuel flexibility makes it an attractive option for demand response programs.

Li, Zhenning↗
DOE OSTI2023

Theoretical Analysis of Resonant Tunneling Enhanced Field Emission

In this paper, we develop an exact analytical quantum theory for field emission from surfaces with a nearby quantum well, by solving the one-dimensional time-independent Schrödinger equation. The quantum well, which may be introduced by ions, atoms, nanoparticles, etc., is simplified as a square potential well with depth H, width d, and distance to the surface L. The theory is used to analyze the effects of the quantum well (d, H, and L), the cathode properties (work function W and Fermi energy E F ), and dc field F. It is found that the quantum well can lead to resonant tunneling enhanced field emission up to several orders of magnitude larger than that from bare cathode surfaces. In the meantime, the electron-emission-energy spectrum is significantly narrowed. The strong enhancement region is bounded by the conditions eFL + H ≥ W + C and eFL ≤ W, with e being the elementary charge (positive) and C a constant dependent on dc field F. It is also found that the linear shift of resonance peaks in the electron-emission-energy spectrum with dc field F follows ε p =ε p⁢0 –e⁢FL, with ε p⁢0 being approximately the eigenenergies for electrons confined in a square potential well without a dc field. Finally, the theory provides insights for the design of high-efficiency field emitters, which can produce a high current and highly collimated electron beams.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗