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At least 487 records · Page 27

A pion-argon cross section measurement in the ProtoDUNE-SP experiment with cosmogenic muon

Neutrinos are tiny mysterious fundamental particles with small cross sections. Through neutrino physics, scientists across the world are trying to answer many intriguing questions about nature such as the dominance of matter over antimatter, CP violation in the lepton sector, number of supernovas in the early universe, etc. Detection of neutrinos requires massive particle detectors and intense neutrino beam owing to their small cross section. Deep Underground Neutrino Experiment (DUNE) is a next-generation neutrino experiment that is planned to start taking data beginning in 2026. DUNE will consist of 4 massive detectors, the first of which will be using single-phase liquid argon time projection chamber (LArTPC) technology. The ProtoDUNE-SP experiment is a prototype of the DUNE built at the CERN neutrino platform and uses the same detector technology that will be used in DUNE first module. The ProtoDUNE-SP experiment collected months of test beam and cosmic ray data beginning in September 2018. It was built to provide a testbed for the installation of detector parts for DUNE, showing long-term stability of the detector, understanding detector response for different test beam particles (including protons, pions, electrons, kaons, muons), and measurement of hadron-argon cross sections. When a particle passes through LArTPC electron-ion pairs are produced. To reconstruct the position and energy of a particle passing through the medium knowledge of ionization electron drift velocity is essential. The electron drift velocity is distorted by an excess positive charge built up in the detector, known as space charge. This study discusses a novel technique for measuring the ionization electron drift velocity using cosmic-ray muons. The technique uses tracks that travel the entire drift distance of the TPC for drift velocity determination. Secondly, the study discusses a method for converting the charge deposited into energy. The method is carried out in two step s. In th e first step detector response for energetic cosmic ray muons crossing the entire the TPC is used to make the charge deposition uniform throughout the TPC, and in the second step stopping cosmic-ray muons are used for determining the energy scale. Finally, the study discusses a pion-argon cross section measurement based on reweighting of Monte Carlo simulations using J. Calcutt's Geant4Reweight framework. Neutrinos cannot be directly detected; they are identified based on the interaction products. Pions are a common interaction product in a neutrino interaction. For precise modeling of neutrino event generators, it is essential to understand the pion-argon interaction. Pion-argon cross section measurement serves as an important input for neutrino interaction models. The results of the pion-argon total reaction cross section using the Geant4 reweighting technique are found to be in good agreement with Geant4 predictions. The many studies carried out in the ProtoDUNE-SP experi ment wil l be useful for current and future neutrino experiments using LArTPC technology including ICARUS, MicroBooNE, DUNE

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Development of a pulsed, variable-energy positron beam for atomic scale defect studies

Positron annihilation spectroscopy provides a sensitive means of non-destructive characterization of materials, capable of probing single atom vacancies in solids with 10 –7 sensitivity. Here, in this work, we detail the development of a magnetically guided, variable energy, pulsed positron beam designed to conduct depth-dependent defect studies in metals, semiconductors, and dielectrics, which will be the first of its kind in the United States. The design of the target stage provides capabilities for measurements during in situ annealing up to 800 °C and incorporates a new approach to minimize the background due to energetic backscattered positrons. The developed beam at Bowling Green State University provides a powerful tool for characterization of thin films, devices, and ion irradiated materials.

47 OTHER INSTRUMENTATION↗

Derivations of the Total Radiation Belt Electron Content

Abstract We present multiple derivations of the Total Radiation Belt Electron Content (TRBEC), an indicator of the global number of electrons that instantaneously occupy the radiation belts. Derived from electron flux measurements, the TRBEC reduces the spatial information into a scalar quantity that concisely describes global aspects of the system. This index provides a simple, global, and long‐term assessment of the radiation belts that enables systematic analysis. In this work, we examine the TRBEC using the adiabatic invariants of which has been used in previous articles as this coordinate system removes reversible adiabatic effects. We then introduce a new expression to compute the TRBEC using the non‐adiabatic coordinates of , relevant in the contexts of energetic electron precipitation, chorus, and hiss scattering where adiabatic invariant quantities are no longer conserved. From both expressions of the TRBEC we demonstrate that an erroneous factor of that appeared in previous works using the adiabatic derivation led to an overestimate of the reported electron populations. In addition, we quantify electron loss in the outer radiation belt via a case study using the Van Allen Probes data over a 20‐day period from March 2013 specifying particle populations both in terms of the aforementioned adiabatic and non‐adiabatic variables. The total number of electrons in the outer radiation belt reached upwards of electrons at the peak of the storm, a rest mass of roughly 10 g.

Astronomy & Astrophysics↗

A Vector Sensor-Based Acoustic Characterization System for Marine Renewable Energy

NoiseSpotter is a passive acoustic monitoring system that characterizes, classifies, and geo-locates anthropogenic and natural sounds in near real time. It was developed with the primary goal of supporting the evaluation of potential acoustic effects of offshore renewable energy projects. The system consists of a compact array of three acoustic vector sensors, which measures acoustic pressure and the three-dimensional particle velocity vector associated with the propagation of an acoustic wave, thereby inherently providing bearing information to an underwater source of sound. By utilizing an array of three vector sensors, the application of beamforming techniques can provide sound source localization, allowing for characterization of the acoustic signature of specific underwater acoustic sources. Here, performance characteristics of the system are presented, using data from controlled acoustic transmissions in a quiet environment and ambient noise measurements in an energetic tidal channel in the presence of non-acoustic flow noise. Data quality is demonstrated by the ability to reduce non-acoustic flow noise contamination, while system utility is shown by the ability to characterize and localize sources of sound in the underwater environment.

16 TIDAL AND WAVE POWER↗

Quantifying Thermal Output of Energetic Materials (LDRD Final Report)

We present the results of an LDRD project, funded by the Nuclear Deterrence IA, to develop capabilities for quantitative assessment of pyrotechnic thermal output. The thermal battery igniter is used as an exemplar system. Experimental methodologies for thermal output evaluation are demonstrated here, which can help designers and engineers better specify pyrotechnic components , provide thermal output guidelines for new formulations, and generate new metrics for assessing component performance and margin given a known failure condition. A heat-transfer analysis confirms that the dominant mode of energy transfer from the pyrotechnic output plume to the heat pellet is conduction via deposition of hot titanium particles. A simple lumped-parameter model of titanium particle heat transfer and a detailed multi-phase model of deposition heat transfer are discussed. Pyrotechnic function, as defined by "go/no-go" standoff testing of a heat pellet, is correlated with experimentally measured igniter plume temperature, titanium metal particle temperature, and energy deposition. Three high-speed thermal diagnostics were developed for this task. A three-color imaging pyrometer, acquiring 100k images per second on three color channels, is deployed for measurement of titanium particle temperatures. Complimentary measurements of the overall igniter plume emission ("color") temperature were conducted using a transmission-grating spectrograph in line-imaging mode. Heat flux and energy deposition to a cold wall at the heat-pellet location were estimated using an eroding thermocouple probe, with a frequency response of ~5 kHz. Ultimate "go/no-go" function in the igniter/heat-pellet system was correlated with quantitative thermal metrics, in particular surface energy deposition and plume color temperature. Titanium metal-particle and plume color temperatures both experience an upper bound approximated by the 3245-K boiling point of TiO 2 . Average metal-particle temperatures remained nearly constant for all standoff distances at T = 2850 K, ± 300 K, while plume color temperature and heat flux decay with standoff—suggesting that heat-pellet failure results from a drop in metal-particle flux and not particle temperature. At 50% likelihood of heat-pellet failure, peak time-resolved plume color temperatures drop well below TiO 2 boiling to ~2000 - 2200 K, near the TiO 2 melting point. Estimates of peak heat flux decline from up to 1 GW/m 2 for near-field standoffs to below 320 MW/m 2 at 50% failure likelihood.

36 MATERIALS SCIENCE↗

Enrichment by the first stars in a relic dwarf galaxy

Stars that contain trace amounts of elements heavier than helium (that is, ‘metallicity’) preserve the chemical fingerprints of the first stars. In the Milky Way, nearly all of the lowest-metallicity stars show an extreme over-abundance of carbon. The origin of this signature has remained a mystery owing to the lack of observational constraints on the environments in which it originates. Here, in this work, we present observations of a star in the >10-billion-year-old ultrafaint dwarf galaxy Pictor II, showing the lowest iron and calcium abundances outside the Milky Way (<1/43,000th solar and ~1/160,000th solar), with >3,000× relative carbon enhancement. The star’s exceptional paucity in iron and calcium make it clearly preserve enrichment from the first stars in a relic dwarf galaxy; Pictor II is one of the smallest, most chemically primordial systems known. This star supports the hypothesis that extreme carbon enhancement results from low-energy supernovae from the first stars, as the yields of energetic supernovae are harder to retain in small-scale environments. This signature of enrichment by the first stars may trace a regime inaccessible to current high-redshift observations, which can hardly detect the initial enrichment of the smallest galaxies.

chemical evolution↗

Tree-based solvers for adaptive mesh refinement code FLASH – III: a novel scheme for radiation pressure on dust and gas and radiative transfer from diffuse sources

Radiation is an important contributor to the energetics of the interstellar medium, yet its transport is difficult to solve numerically. We present a novel approach towards solving radiative transfer of diffuse sources via backwards ray tracing. Here, we focus on the radiative transfer of infrared radiation and the radiation pressure on dust. The new module, TREERAY/RADPRESSURE, is an extension to the novel radiative transfer method TREERAY implemented in the grid-based Magneto-Hydrodynamics code FLASH. In TREERAY/RADPRESSURE, every cell and every star particle is a source of infrared radiation. We also describe how gas, dust, and radiation are coupled via a chemical network. This allows us to compute the local dust temperature in thermal equilibrium, leading to a significantly improvement over the classical grey approximation. In several tests, we demonstrate that the scheme produces the correct radiative intensities as well as the correct momentum input by radiation pressure. Subsequently, we apply our new scheme to model massive star formation from a collapsing, turbulent core of 150 M ⊙ . We include the effects of both, ionizing and infrared radiation on the dynamics of the core. We find that the newborn massive star prevents fragmentation in its proximity due to radiative heating. Over time, dust and radiation temperature equalize, while the gas temperature can be either warmer due to shock heating or colder due to insufficient dust–gas coupling. Compared to gravity, the effects of radiation pressure are insignificant for the stellar mass on the simulated time-scale in this work.

(ISM:) HII regions↗

Optimized matching conditions for self-guided laser wakefield accelerators

We revisit the matching conditions for self-guided laser pulse propagation in plasma and refine their formulation to maximize the energy of electrons produced via laser wakefield acceleration. Bayesian optimization, combined with particle-in-cell simulations carried out in a quasi-three-dimensional geometry and a Lorentz-boosted frame, is employed. The optimization identifies the maximum electron energy that a self-guided laser wakefield accelerator, driven by a laser of a given energy, can produce, together with the corresponding acceleration distance. Our results further demonstrate that electrons with energies close to the maximum value can be obtained across a relatively wide range of input parameters and without the need for their precise tuning. This provides substantial flexibility for experimental implementation and significantly relaxes the operational constraints associated with self-guided laser wakefield accelerators.

43 PARTICLE ACCELERATORS↗

Reversible Interfacial Charge Transfer and Delayed Emission in InP/ZnSe/ZnS Quantum Dots with Hexadecanethiol

The results in this paper show that holes are rapidly and reversibly transferred from red-emitting InP/ZnSe/ZnS quantum dots (QDs) to adsorbed hexadecanethiol (HDT) forming an equilibrium between the thiols and the QD valence band. Photoexcitation results in populations of holes in the valence band and in slightly higher-energy shell-localized traps. Trap to valence band hole tunneling results in a photoluminescence risetime having time constants varying from 300 ps to 2 ns. The presence of adsorbed HDT eliminates the slower risetime component, indicating that hole transfer from the shell-localized traps that are closest to the particle surface efficiently competes with tunneling to the QD core. This shows that the interfacial charge transfer equilibrium is established in less than 2 ns. The population of the shell-localized traps corresponds to a reservoir of hole states that eventually tunnel to the core-localized valence band, resulting in delayed emission. The amount of delayed emission increases rapidly with ZnSe shell thickness and is slightly blue-shifted from the prompt photoluminescence. We propose an energetic model in which the HDT/valence band equilibrium is affected by the extent of valence band quantum confinement and an electric field produced by core–shell interfacial dipoles. Furthermore, this model explains the core size, shell thickness, and photoluminescence (PL) wavelength dependence of this equilibrium.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

First measurements of energetic protons in Mega Amp Spherical Tokamak Upgrade (MAST-U)

First proton production rates from the d(d,p)t reaction in the Mega Amp Spherical Tokamak Upgrade (MAST-U) are measured. The data were taken during the MAST-U experimental campaign with an upgraded version of the proton detector (PD) previously used in MAST. The new detector array consists of three collimated silicon surface barrier detectors with a depletion depth of 300 μm and a collimated 120 μm thick diamond detector, mounted on the MAST-U reciprocating probe arm. This array measures the energies of unconfined energetic 3 MeV protons and 1 MeV tritons mainly produced by beam-thermal DD reactions during neutral beam injection heating. Diamond detectors have the potential to be uniquely suited to detect charged fusion products as they promise to be much more radiation resistant and much less sensitive to temperature variations compared to silicon-based detectors. Using silicon and diamond-based detectors simultaneously allowed us to directly compare the performance of these two detector types. PD particle rates measured during different plasma scenarios are presented and compared to neutron rates measured using the neutron camera upgrade and TRANSP predictions.

Instruments & Instrumentation↗

Thermodynamics of Minerals Stable near Earth's Surface

Project “Thermodynamics of Minerals Stable Near the Earth’s Surface” uses specialized calorimetric techniques to obtain new thermochemical data for solid phases of interest in the Earth’s “critical zone”, the near surface regions of the planet most directly affecting and affected by human activity. Major activity was in three areas: manganese oxide materials, aluminum clusters which are precursors to aluminum oxyhydroxide precipitates, and zeolites. All these classes of minerals are potential carriers of heavy metals and radionuclides in the environment, both within their crystal structures and as adsorbed layers or colloids. Their thermodynamic stability, as well as the sequence of stability of competing phases, governs the aqueous solubility of contaminants (and nutrients) in soil, groundwater, and sediments. The thermodynamics of these phases is strongly affected by particle size and crystallinity, since they often occur as very fine particles which do not coarsen in the near-surface environment. Many of these materials exhibit extensive polymorphism, multicomponent solid solution, and variable hydration states. Thus, one must define and systematize important thermodynamic variables, since one cannot make measurements on each and every possible phase, particle size, and composition. A major finding of the work on manganese oxides was labile water-induced oxidation-reduction reactions. These will be studied further by a combination of thermodynamic and synchrotron-based spectroscopic methods, the latter in collaboration with Peggy O’Day at UC Merced. The adsorption of other species, including simple organics, on such redox-active surfaces will also be investigated by a combination of thermochemical and spectroscopic studies. Studies of the energetics of water adsorption on mineral surfaces will be expanded to emphasize the adsorption of CO2 and small organic molecules, relevant to soil, groundwater, and the subsurface environment. Gas adsorption calorimetry, immersion calorimetry, and solution calorimetry will be combined with appropriate analytical and spectroscopic techniques to obtain a comprehensive picture of the interactions and their energetics. The evolution of aqueous aluminum clusters to form aluminum oxyhydroxide precipitates will be studied in detail by a combination of calorimetric and structural methods applied to aqueous samples aged at room temperature. The energetics of new classes of clusters will be explored. The project addresses several common themes relevant to the broad mission of the Department of Energy. Thermochemical data for minerals stable near the Earth’s surface, though still incomplete, are essential for understanding both natural and anthropogenic processes that affect our very existence on this planet. Such data contribute to the fundamental underpinning for mitigation and management strategies for the extraction and use of energy. Fundamental thermodynamic and mechanistic understanding is required to model processes ranging from heavy metal pollution to nuclear waste disposal to climate change.

58 GEOSCIENCES↗

Search for Higgs Portal Scalars and Heavy Neutral Leptons Decaying in the MicroBooNE Detector

This thesis presents a search for Higgs Portal Scalars (HPS) and Heavy Neutral Leptons (HNL) decaying in the MicroBooNE liquid argon time projection chamber (LArTPC). The measurement was performed using data collected in-time with the Neutrino at the Main Injector (NuMI) beam with a total exposure corresponding to $7.01 \times 10^{20}$ protons on target. Mono-energetic HPS and HNL would be produced from kaons decaying at rest in the NuMI hadron absorber, before travelling ${\sim}100$~m to the MicroBooNE detector where they decay. A single selection and search strategy is used to target decays of HPS to $\mu\mu$ pairs and HNL to $\mu\pi$ pairs. The results are expressed as limits, at the $90\%$ confidence level, on the mixing angles that control the rates of production and decay for each new particle. For the HNL model, upper limits are set on the mixing parameter $\mumix$ in the range [$12.9 \times 10^{-8}$, $0.54 \times 10^{-8}$] for HNL with masses in the region $246$--$385$~MeV. % This represents an order of magnitude increase in sensitivity to the previous MicroBooNE HNL result. For the HPS model, limits on the scalar-Higgs mixing angle $\theta^2$ are set, excluding a region with a lower boundary between [$31.3 \times10^{-9}$, $1.09 \times 10^{-9}$] and an upper boundary between [$2.50 \times 10^{-5}$, $5.05 \times 10^{-9}$] for scalars with a mass of $212$--$275$ MeV. These results set the first constraints in this region of parameter space from a dedicated experimental search for HPS.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Constrained nuclear–electronic orbital method for periodic density functional theory: Application to H 2 chemisorption on Si(001) surfaces

The nuclear–electronic orbital (NEO) method provides a powerful computational framework for incorporating nuclear quantum effects (NQE) in electronic structure calculations beyond the Born–Oppenheimer approximation. By incorporating additional constraints to the position operator on quantum particles like protons, the NEO method enables calculation of effective potential that accounts for NQE. Here, in this work, we present a new constrained NEO (cNEO) formulation for density functional theory (cNEO-DFT) calculations in the context of extended periodic systems. Using the nudged elastic band method, we discuss an application of the cNEO-DFT approach to studying the adsorption of a hydrogen molecule on the Si(001) surfaces. The calculation shows how NQE impacts the reaction energetics. The proton density changes are computed along the reaction pathways. This work demonstrates the capability of the new cNEO-DFT method to study a wide range of chemical processes, such as surface reactions where the quantum nature of light atoms like protons is non-negligible.

Chemical processes↗

Search for Higgs Portal Scalars and Heavy Neutral Leptons Decaying in the MicroBooNE Detector

This thesis presents a search for Higgs Portal Scalars (HPS) and Heavy Neutral Leptons (HNL) decaying in the MicroBooNE liquid argon time projection chamber (LArTPC). The measurement was performed using data collected in-time with the Neutrino at the Main Injector (NuMI) beam with a total exposure corresponding to 7.01x10^20 protons on target. Mono-energetic HPS and HNL would be produced from kaons decaying at rest in the NuMI hadron absorber, before travelling ~100 m to the MicroBooNE detector where they decay. A single selection and search strategy is used to target decays of HPS to muon-muon pairs and HNL to muon-pion pairs. The results are expressed as limits, at the 90% confidence level, on the mixing angles that control the rates of production and decay for each new particle. For the HNL model, upper limits are set on the mixing parameter |U\mu4|^2 in the range [12.9 x 10^-8, 0.54 x 10^-8] for HNL with masses in the region 246 - 385 MeV. For the HPS model, limits on the scalar-Higgs mixing angle \theta^2 are set, excluding a region with a lower boundary between [31.3 x 10^-9, 1.09 x 10^-9] and an upper boundary between [2.50 x 10^-5, 5.05 x 10^-9] for scalars with a mass of 212-275 MeV. These results set the first constraints in this region of parameter space from a dedicated experimental search for HPS.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Exploring pressure-dependent inelastic deformation and failure in bonded granular composites: An energetic materials perspective

In polymer-filled granular composites, damage may develop in mechanical loading prior to material failure. Damage mechanisms such as microcracking or plastic deformation in the binder phase can substantially alter the material’s mesostructure. For energetic materials, such as solid propellants and plastic bonded explosives, these mesostructural changes can have far reaching effects including degraded mechanical properties, potentially increased sensitivity to further insults, and changes in expected performance. Unfortunately, predicting damage is nontrivial due to the complex nature of these composites and the entangled interactions between inelastic mechanisms. In this work, we assess the current literature of experimental knowledge, focusing on the pressure-dependent shear response, and propose a simple simulation framework of bonded particles to study four limiting-case material formulations at both meso- and macro-scales. Further, to construct the four cases, we systematically vary the relative interfacial strength between the polymer binder and granular filler phase and also vary the polymer’s glass transition temperature relative to operating temperature which determines how much the binder can plastically deform. These simulations identify key trends in global mechanical response, such as the emergence of strain hardening or softening regimes with increasing pressure which qualitatively resemble experimental results. By quantifying the activation of different inelastic mechanisms, such as bonds breaking and plastically straining, we identify when each mechanism becomes relevant and provide insight into potential origins for changes in mechanical responses. The locations of broken bonds are also used to define larger, mesoscopic cracks to test various metrics of damage. We primarily focus on triaxial compression, but also test the opposite case of triaxial extension to highlight the impact of Lode angle on mechanical behavior.

36 MATERIALS SCIENCE↗

On the importance of excited state species in low pressure capacitively coupled plasma argon discharges

In the past three decades, first principles-based fully kinetic particle-in-cell Monte Carlo collision (PIC/MCC) simulations have been proven to be an important tool for the understanding of the physics of low pressure capacitive discharges. However, there is a long-standing issue that the plasma density determined by PIC/MCC simulations shows quantitative deviations from experimental measurements, even in argon discharges, indicating that certain physics may be missing in previous modeling of the low pressure radio frequency (rf) driven capacitive discharges. In this work, we report that the energetic electron-induced secondary electron emission (SEE) and excited state atoms play an important role in low pressure rf capacitive argon plasma discharges. The ion-induced secondary electrons are accelerated by the high sheath field to strike the opposite electrode and produce a considerable number of secondary electrons that lead to additional ionizing impacts and further increase of the plasma density. Importantly, the presence of excited state species even further enhances the plasma density via excited state neutral and resonant state photon-induced SEE on the electrode surface. The PIC/MCC simulation results show good agreement with the recent experimental measurements in the low pressure range (1–10 Pa) that is commonly used for etching in the semiconductor industry. At the highest pressure (20 Pa) and driving voltage amplitudes 250 and 350 V explored here, the plasma densities from PIC/MCC simulations considering excited state neutrals and resonant photon-induced SEE are quantitatively higher than observed in the experiments, requiring further investigation on high pressure discharges.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Development of Density Functional Tight-Binding Parameters Using Relative Energy Fitting and Particle Swarm Optimization

We provide a strategy to optimize density functional tight-binding (DFTB) parameterization for the calculation of the structures and properties of organic molecules consisting of hydrogen, carbon, nitrogen, and oxygen. We utilize an objective function based on similarity measurements and the Particle Swarm Optimization (PSO) method to find an optimal set of parameters. This objective function considers not only the common DFTB descriptors of binding energies and atomic forces but also incorporates relative energies of isomers into the fitting procedure for more chemistry-driven results. The quality in the description of the binding energies and atomic forces is measured based on the Ballester similarity index and relative energies through a similarity index induced by the Levenshtein edit distance to quantify the correct energetic order of isomers. Training and testing datasets were created to include all relevant chemical functional groups. Finally, the accuracy of this strategy is assessed, and its range of applicability is discussed by comparison against our previous parameterization. The improved performance of the new DFTB parameterization is validated with respect to the density functional theory large datasets QM-9 and ANI-1, where excellent agreement is found between the structures and properties available in these datasets, and the ones obtained with DFTB.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Transient work function gating: A new photoemission regime

We present the theoretical basis for a new photoemission regime, transient work function gating (TWFG), which temporally and energetically gates photoemission and produces near-threshold photoelectrons with thermally limited emittance, percent-level quantum efficiency, and control over temporal coherence. The technique consists of actively gating the work function of a generalized photocathode using a non-ionizing long-wavelength optical field to produce an adiabatic modulation of the carrier density at their surface. We examine TWFG as a means to circumvent the long-standing trade-off between low emittance and high quantum efficiency, untethered to particle source or photocathode specifics. TWFG promises new opportunities in photoemission physics for next generation electron and accelerator-based x-ray photon sources.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗