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At least 307 records · Page 17

Atomic Oxygen Erosion Yield Prediction for Spacecraft Polymers in Low Earth Orbit

The ability to predict the atomic oxygen erosion yield of polymers based on their chemistry and physical properties has been only partially successful because of a lack of reliable low Earth orbit (LEO) erosion yield data. Unfortunately, many of the early experiments did not utilize dehydrated mass loss measurements for erosion yield determination, and the resulting mass loss due to atomic oxygen exposure may have been compromised because samples were often not in consistent states of dehydration during the pre-flight and post-flight mass measurements. This is a particular problem for short duration mission exposures or low erosion yield materials. However, as a result of the retrieval of the Polymer Erosion and Contamination Experiment (PEACE) flown as part of the Materials International Space Station Experiment 2 (MISSE 2), the erosion yields of 38 polymers and pyrolytic graphite were accurately measured. The experiment was exposed to the LEO environment for 3.95 years from August 16, 2001 to July 30, 2005 and was successfully retrieved during a space walk on July 30, 2005 during Discovery s STS-114 Return to Flight mission. The 40 different materials tested (including Kapton H fluence witness samples) were selected specifically to represent a variety of polymers used in space as well as a wide variety of polymer chemical structures. The MISSE 2 PEACE Polymers experiment used carefully dehydrated mass measurements, as well as accurate density measurements to obtain accurate erosion yield data for high-fluence (8.43 1021 atoms/sq cm). The resulting data was used to develop an erosion yield predictive tool with a correlation coefficient of 0.895 and uncertainty of +/-6.3 10(exp -25)cu cm/atom. The predictive tool utilizes the chemical structures and physical properties of polymers to predict in-space atomic oxygen erosion yields. A predictive tool concept (September 2009 version) is presented which represents an improvement over an earlier (December 2008) version.

Banks, Bruce A.↗

The Electron Thermal Conductivity of Pu and Zr Substituted $\mathcal{γ}$-U

Uranium alloys are attractive recycled nuclear fuels because of their high thermal conductivity (𝑘) and fissile density. Limited experimental studies of the 𝑘 of U-Pu-Zr alloys in the range of 15 to 20 wt% Pu and 6 to 15 wt% Zr indicate that increasing the content of either Zr or Pu tends to lower 𝑘. However, which element has the greater effect on 𝑘, and the associated mechanisms, remains unclear. Here, in this study, the electron thermal conductivity (𝑘 𝑒 ) of U-Pu-Zr compositions are calculated using density functional theory. The electronic structure is evaluated to understand the effects of plutonium (Pu) and zirconium (Zr) substitution on the 𝑘 𝑒 of 𝛾-U. Alloys of up to 37.5 at. % Pu and 37.5 at. % Zr are examined. Two methods are applied to calculate 𝑘 𝑒 ; we find that the accuracy of each method depends on the electronic and mass similarities between the solute and solvent atoms. Specifically, when the solute atom is similar in electronic structure and mass, the more accurate method is that which employs the electron relaxation time of 𝛾-U, while if the elements are dissimilar, a mixed method that mixes several parameters associated with JNW_S⁢3033426825100132 from each element in the alloy is best. The introduction of all alloying elements decreases 𝑘 𝑒 ; however, in binary compounds, Pu and Zr have different effects. Pu flattens the electronic bands but compensates for this deleterious effect by increasing electron density near the Fermi level. Zr flattens the electronic bands more severely without adding electron density near the Fermi level. Therefore, Zr decreases 𝑘 𝑒 more than Pu in binary compounds. In ternary compounds, the difference between Pu and Zr is minimal due to the phononic change from the large mass change of Zr substitution, even at 12.5 at. %. Thus, we predict that higher loadings of Pu, and potentially other actinides, can be added to U-Pu-Zr compositions for faster recycling of spent fuel without sacrificing 𝑘. We also note that these 𝑘 𝑒 calculation methods can be applied to non-fuel alloys that require 𝑘 𝑒 predictions, such as cladding, heat exchanger, and structural materials.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

The Electron Thermal Conductivity of Pu and Zr Substituted Gamma-Uranium

Uranium alloys are attractive recycled nuclear fuels because of their high thermal conductivity (k) and fissile density; however, the effects of alloying elements on k remain unclear. Here, the electron thermal conductivity (k_e) of U-Pu-Zr compositions are calculated using density functional theory. The electronic structure is evaluated to understand the effects of plutonium (Pu) and zirconium (Zr) substitution on the k_e of ?-U. Alloys of up to 37.5 at. % Pu and 37.5 at. % Zr are examined. Two methods are applied to calculate k_e; we find that the accuracy of each method depends on the electronic and mass similarities between the solute and solvent atoms. Specifically, when the solute atom is similar in electronic structure and mass, the method that applies the electron relaxation time of ?-U is best, while if the elements are dissimilar, a mixed method that mixes several parameters associated with k_e from each element in the alloy is best. The introduction of all alloying elements decreases k_e; however, in binary compounds, Pu and Zr have different effects. Pu generally flattens the electronic bands but compensates for this deleterious effect by increasing electron density near the Fermi level. Zr flattens the electronic bands more severely without adding electron density near the Fermi level. Therefore, Zr decreases the k_e more than Pu in binary compounds. In ternary compounds, the difference between Pu and Zr is minimal due to the phononic change from the large mass change of Zr substitution, even at 12.5 at. %. Thus, we predict that higher loadings of Pu, and potentially other actinides, can be added to U-Pu-Zr compositions for faster recycling of spent fuel with without sacrificing k. We also note that these k_e calculation methods can be applied to non-fuel alloys that require k_e predictions, such as cladding, heat exchanger, and structural materials.

36 MATERIALS SCIENCE↗

Comparison of High-Performance Fiber Materials Properties in Simulated and Actual Space Environments

A variety of high-performance fibers, including Kevlar, Nomex, Vectran, and Spectra, have been tested for durability in the space environment, mostly the low Earth orbital environment. These materials have been tested in yarn, tether/cable, and fabric forms. Some material samples were tested in a simulated space environment, such as the Atomic Oxygen Beam Facility and solar simulators in the laboratory. Other samples were flown on the International Space Station as part of the Materials on International Space Station Experiment. Mass loss due to atomic oxygen erosion and optical property changes due to ultraviolet radiation degradation are given. Tensile test results are also presented, including where moisture loss in a vacuum had an impact on tensile strength.

Finckenor, M. M.↗

Arc jet diagnostics tests

Two objectives were addressed during a 10 week 1988 NASA/ASEE summer faculty fellowship at the Johnson Space Center Atmospheric Reentry Materials Structures Evaluation Facility (ARMSEF). These objectives were the evaluation of mass spectrometry for the measurement of atomic and molecular species in an arc jet environment, and the determination of atomic recombination coefficients for reaction cured glass (RCG) coated high temperature surface insulation (HRSI) materials subjected to simulated reentry conditions. Evaluation of mass spectrometry for the measurement of atomic and molecular species provided some of the first measurements of point compositions in arc jet tunnel environments. A major objective of this project centered around the sampling residence time. A three staged vacuum sampling system pulled the molecules and atoms from the arc jet to a quadrupole ionization mass spectrometer in 400 milliseconds. Conditions investigated included a composition survey across the nozzle exit at 3 cm z-distance from the nozzle exit for 3 different currents. Also, a point composition survey was taken around a shock created by the presence of a blunt body.

Willey, Ronald J.↗

Converging towards atomic and nuclear pressures (Final Report)

his report details the development of transformational tools and techniques, allowing the accurate characterization of matter at the most extreme conditions yet studied in the high energy density (HED) domain. Before this work, most experiments quantitatively mapping the nature of matter in the HED realm were performed using planar geometry, which allows for the isolation and measurement of variables in a single thermodynamic state. Such measurements include equation of state variables, optical conductivity, heat transport and more. However, due to a variety of plasma processes, such experiments are limited to below ~10 TPa (100 Mbar) pressures. To achieve higher pressures, convergent experiments are needed. Historically, convergent experiments have not been used for benchmark data because they are integral measurements. That is each part of a convergent target undergoes a time dependent wide range of states, making it difficult to accurately isolate any particular quantity for a given thermodynamic state. This effort developed innovative convergent HED platforms and techniques enabling the exploration of matter from atomic to nuclear scale pressures. This effort also performed pioneering experiments that yielded the first rigorous benchmark data at these extreme conditions. This funding award began with the overarching goal to understand the behavior of matter at extreme (atomic-to-nuclear scale) pressures. The motivation for these goals lie in the fact that every time scientists explore matter beyond the threshold of an atomic unit, there is a fundamental shift in science. The atomic unit for energy, mass, charge, length, and time have each been explored, and each time such a threshold was crossed, a new sequence of discoveries was made resulting in significant awards such as the Nobel Prize. The only unexplored atomic unit is pressure, and this effort set the course for exploring matter at and beyond such pressures. That most of the recently discovered extrasolar planets and stars, as well as matter in the late implosion stages of inertial fusion targets, have deep internal pressures at and beyond atomic pressures amplifies the importance of this effort. Much of the initial work in developing techniques to create these atomic-to-nuclear pressures already existed within the HED community, predominantly at large scale laser facilities such as the National Ignition Facility (NIF) and the Omega60 laser the University of Rochester and although these experiments were routinely performed the ability to extract information about the underlying physical states and processes remained elusive due to the complexity of the experiments, extreme scales in both time and space, and the integrated nature of all the measurements. This work built a rigorous framework so such measurements can routinely be made. This was done in part through the introduction of Bayesian inference techniques into the field of HED science. These techniques allow for the self-consistent extraction of the relevant variables and their explicit and implicit correlations, so as to make use of integrated experimental data to constrain physical models and provide accurate uncertainty bounds for the data. The techniques developed here are fully transparent and proved immediately useful providing quantitative rigorous benchmarks for physical states and processes at some of the most extreme conditions yet explored on Earth. This funding is directly or partly responsible for 7 publications in major peer-reviewed scientific journals, a doctoral thesis, 3 invited talks at major conferences, and the training of a post-doc, 2 graduate students, and 1 undergraduate student. Beyond the effort supported by this award launched the introduction of Bayesian inference into the HED physics community and helped push the usage if modern data-science techniques within the physics community at large.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

X‑ray Coherent Diffractive Imaging of Large Helium Nanodroplets Doped with Small Molecules

We report the first X-ray coherent diffractive imaging experiment on molecule-doped helium nanodroplets. It complements previous work, where we reported single-shot X-ray coherent diffractive imaging studies of Xe dopant clusters formed in 4He and 3He droplets. These noble gas clusters were used to visualize the impact of rotational excitation of the droplets on the spatial distribution of atomic dopants within the droplets, and to study the differences and connections between quantum and classical droplet rotational motion. Here, we expand our studies to the molecular dopants CF4, CHF3, CH3CN, and SF6, imaged with 1.5 keV photons. We find multiple Bragg spots in the diffraction patterns of molecule-doped droplets with radii of approximately 600 nm, which provide evidence that molecules form elongated clusters with preferential alignment along the angular momentum axis of the 4He droplets, in agreement with our previous results on the aggregation of Xe clusters on quantum vortices. Real-space reconstructions of molecular dopant cluster density profiles are obtained for droplets with smaller radii of approximately 300 nm. The diffuse images suggest the formation of low-density, potentially porous, molecular clusters upon aggregation at T = 0.4 K in 4He droplets. In the normal fluid 3He droplets, molecules aggregate into loose clusters on the droplets' equator, similar to previous observations for Xe atoms. Time-of-flight mass spectra reveal that the doped helium nanodroplet moieties fragment extensively into constituent atomic ions, producing only a small fraction of molecular fragment ions. The findings are discussed in the context of previously proposed schemes to use He droplets as potential tamper materials for ultrafast X-ray imaging experiments.

Feinberg, AlexandraJ↗

Coupling between bulk thermal defects and surface segregation dynamics

Surface segregation is a phenomenon that depends on the delicate interplay between thermodynamic driving forces and kinetic obstacles, for which elevated temperature is often needed to enhance the atom mobility and reach equilibrium. Using the classic system of Cu 3 Au ( 100 ) under nonisothermal conditions, in this study, we show an adatom process underlying transient surface segregation dynamics through the temperature-change-driven creation and annihilation of thermal vacancies in the bulk and the resulting bulk-surface mass exchanges. This is demonstrated by monitoring the surface composition evolution of Cu 3 Au ( 100 ) with temperature changes between 250 and 500 ° C , showing that the increase in temperature decreases monotonically the surface Au concentration as a result of the transfer of more Cu than Au from the bulk to the surface to form Cu-rich clusters of adatoms. Such a bulk thermal defect effect is expected to be universal in inducing the disparity in the bulk-surface mass exchanges of dissimilar atoms in multicomponent materials because of the inherent differences in the vacancy formation energies of the constituent atoms.

36 MATERIALS SCIENCE↗

A New Coordinated NanoSIMS, Transmission Electron Microscopy and Atom Probe Tomography Approach For the Characterization of Primitive Astromaterials

Presolar grains are remnants of evolved stellar systems preserved within primitive extraterrestrial materials. They are important for studying physical and chemical processing, and formation mechanisms occurring within the interstellar medium, Solar Nebula and their parent stellar environments [1]. Our recent work has shown coordinated nano-scale Secondary Ion Mass Spectrometry (NanoSIMS) and Atom Probe Tomography (APT) can show isotopic and chemical signatures at major to trace levels, morphological signatures, and regional contextual relationships [2,3]. Previous studies have shown Transmission Electron Microscopy (TEM) of Focus Ion Beam (FIB) TEM lamella, can provide localized contextual relationships, crystallographic information and chemical information [1]. Coordinating NanoSIMS, TEM, and APT could gain access to almost all contextual, structural and geochemical signatures within each presolar grain. However, this has proved challenging owing to the preparation requirements for TEM and APT. For example, studying specimen prepared as APT needles in TEM removes the local context, the higher degree of surface exposure can alter the chemistry of beam sensitive materials, and the shank angle of the needle can impact the quality of TEM diffraction images. We designed a new FIB method which takes a 100 nm thick FIB-TEM lamella and sandwiches it between two indium slices (5 μm x ~300 nm x 3 μm). The indium is melted onto the lamella surface using the electron beam (Fig 1). This process adds bulk to the lamella, making it more amenable to APT needle formation (Fig 2). Consequently, samples can be prepared per the optimal requirements for each technique improving data quality, acquisition stability, and access to the signatures and relationships summarised earlier. This technique can be used for measuring multiple phases across a TEM lamella and targeting an individual phase. For example, a presolar grain identified in NanoSIMS could be targeted, studied in TEM and then indium sandwiched with its precise location in the TEM lamella marked using a Pt button for preparation of an APT needle and atomic scale acquisition. [1] A. M. Davis (2014) Meteorites and cosmochemical processes, 1. [2] Nevill N. et al. (2023) LPSC, 54, #1707. [3] Nevill N. et al. (2023) LPSC, 54, #1714.

NanoSIMS↗

Launch Vehicle Performance for Bipropellant Propulsion Using Atomic Propellants With Oxygen

Atomic propellants for bipropellant launch vehicles using atomic boron, carbon, and hydrogen were analyzed. The gross liftoff weights (GLOW) and dry masses of the vehicles were estimated, and the 'best' design points for atomic propellants were identified. Engine performance was estimated for a wide range of oxidizer to fuel (O/F) ratios, atom loadings in the solid hydrogen particles, and amounts of helium carrier fluid. Rocket vehicle GLOW was minimized by operating at an O/F ratio of 1.0 to 3.0 for the atomic boron and carbon cases. For the atomic hydrogen cases, a minimum GLOW occurred when using the fuel as a monopropellant (O/F = 0.0). The atomic vehicle dry masses are also presented, and these data exhibit minimum values at the same or similar O/F ratios as those for the vehicle GLOW. A technology assessment of atomic propellants has shown that atomic boron and carbon rocket analyses are considered to be much more near term options than the atomic hydrogen rockets. The technology for storing atomic boron and carbon has shown significant progress, while atomic hydrogen is not able to be stored at the high densities needed for effective propulsion. The GLOW and dry mass data can be used to estimate the cost of future vehicles and their atomic propellant production facilities. The lower the propellant's mass, the lower the overall investment for the specially manufactured atomic propellants.

Palaszewski, Bryan↗

Enhancing the sensitivity of the LUX-ZEPLIN (LZ) dark matter experiment to low energy signals

Two-phase xenon detectors, such as that at the core of the forthcoming LZ dark matter experiment, use photomultiplier tubes to sense the primary (S1) and secondary (S2) scintillation signals resulting from particle interactions in their liquid xenon target. This paper describes a simulation study exploring two techniques to lower the energy threshold of LZ to gain sensitivity to low-mass dark matter and astrophysical neutrinos, which will be applicable to other liquid xenon detectors. The energy threshold is determined by the number of detected S1 photons; typically, these must be recorded in three or more photomultiplier channels to avoid dark count coincidences that mimic real signals. To lower this threshold: a) we take advantage of the double photoelectron emission effect, whereby a single vacuum ultraviolet photon has a $\sim20\%$ probability of ejecting two photoelectrons from a photomultiplier tube photocathode; and b) we drop the requirement of an S1 signal altogether, and use only the ionization signal, which can be detected more efficiently. For both techniques we develop signal and background models for the nominal exposure, and explore accompanying systematic effects, including the dependence on the free electron lifetime in the liquid xenon. When incorporating double photoelectron signals, we predict a factor of $\sim 4$ sensitivity improvement to the dark matter-nucleon scattering cross-section at $2.5$ GeV/c$^2$, and a factor of $\sim1.6$ increase in the solar $^8$B neutrino detection rate. Dropping the S1 requirement may allow sensitivity gains of two orders of magnitude in both cases. Finally, we apply these techniques to even lower masses by taking into account the atomic Migdal effect; this could lower the dark matter particle mass threshold to $80$ MeV/c$^2$.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Enhancing the sensitivity of the LUX-ZEPLIN (LZ) dark matter experiment to low energy signals

Two-phase xenon detectors, such as that at the core of the forthcoming LZ dark matter experiment, use photomultiplier tubes to sense the primary (S1) and secondary (S2) scintillation signals resulting from particle interactions in their liquid xenon target. This paper describes a simulation study exploring two techniques to lower the energy threshold of LZ to gain sensitivity to low-mass dark matter and astrophysical neutrinos, which will be applicable to other liquid xenon detectors. The energy threshold is determined by the number of detected S1 photons; typically, these must be recorded in three or more photomultiplier channels to avoid dark count coincidences that mimic real signals. To lower this threshold: a) we take advantage of the double photoelectron emission effect, whereby a single vacuum ultraviolet photon has a $\sim20\%$ probability of ejecting two photoelectrons from a photomultiplier tube photocathode; and b) we drop the requirement of an S1 signal altogether, and use only the ionization signal, which can be detected more efficiently. For both techniques we develop signal and background models for the nominal exposure, and explore accompanying systematic effects, including the dependence on the free electron lifetime in the liquid xenon. When incorporating double photoelectron signals, we predict a factor of $\sim 4$ sensitivity improvement to the dark matter-nucleon scattering cross-section at $2.5$ GeV/c$^2$, and a factor of $\sim1.6$ increase in the solar $^8$B neutrino detection rate. Dropping the S1 requirement may allow sensitivity gains of two orders of magnitude in both cases. Finally, we apply these techniques to even lower masses by taking into account the atomic Migdal effect; this could lower the dark matter particle mass threshold to $80$ MeV/c$^2$.

Akerib, DS↗

Low Earth Orbit Environmental Effects on Space Tether Materials

Atomic oxygen (AO) and ultraviolet (UV) radiation erode and embrittle most polymeric materials. This research was designed to test several different materials and coatings under consideration for their application to space tethers, for resistance to these effects. The samples were vacuum dehydrated, weighed and then exposed to various levels of AO or UV radiation at the NASA Marshall Space Flight Center. They were then re-weighed to determine mass loss due to atomic oxygen erosion, inspected for damage and tensile tested to determine strength loss. The experiments determined that the Photosil coating process, while affording some protection, damaged the tether materials worse than the AO exposure. TOR-LM also failed to fully protect the materials, especially from UV radiation. The POSS and nickel coatings did provide some protection to the tethers, which survived the entire test regime. M5 was tested, uncoated, and survived AO exposure, though its brittleness prevented any tensile testing.

Finckernor, Miria M.↗

Density wave triggered star formation in grand design spirals

In normal spiral galaxies the arms are the main sites for star formation. This is the cause of their optical contrast compared with the rest of the disc. The spiral structure can be observed as a higher concentration of H2 regions, neutral gas (both atomic and molecular via CO), dust and stars than in the interarm disc. It seens generally accepted that, at least in grand design spirals, there are density waves in the discs. However, several questions are not clear yet and still under discussion. An important question could be termed the triggering dilemma (by analogy with the 'winding dilemma' raised in the forties): Is the enhanced star formation in the spiral arms triggered by the passage of a system of density waves or is it simply due to the presence of a higher column density of gas there? In the present work, we use triggering in the same sense as the moderate to strong triggering defined by Elmegreen (1992), that is to say that star formation in the arms occurs at a rate faster than that in the interarm zone, relative to the available placental gas. Our group has designed several tests to elucidate whether or not star formation is triggered in the arms with respect to the interarm region and we summarize one of them, that of the ratio of the star formation efficiency in the arms divided by that of the interarm zone at the same galactocentric distance which we may call the relative massive star formation efficiency, where the efficiency is defined using the ratio of the mass of stars (evaluated via the H alpha flux) to the mass of neutral gas, atomic plus molecular (which must be measured with the adequate angular resolution). If the relative efficiency is of order unity, the star formation is proportional to the mass of gas, if some kind of induced star formation is present, the relative efficiency should be considerably larger than unity.

Cepa, J.↗

Atomic nitrogen measurements in the upper thermosphere

The open source neutral mass spectrometer on board the Atmosphere Explorer satellites measures, besides other neutral constituents, atomic nitrogen densities in the upper thermosphere. Atomic nitrogen combines with atomic oxygen on the walls of the mass spectrometer ion source to form NO. From the measured NO concentration atomic nitrogen is deduced. Studies of the diurnal variation show that the maximum atomic nitrogen densities occur near 1600 local solar time (LST) and minimum densities near 0400 LST. The diurnal amplitude at 300 km is about a factor of 8, which is lower than predicted in present models. Atomic nitrogen also exhibits a pronounced seasonal variation with an amplitude similar to that of the diurnal variation; summer values are considerably higher than winter ones.

Mauersberger, K.↗

Atomic oxygen beam source for erosion simulation

A device for production of low-energy (5-10 eV) neutral atomic beams for surface modification studies, which recreates the flux of atomic oxygen in LEO, is described. The beam is produced by acceleration of plasma ions onto a negatively biased plate of high-Z metal; the ions are neutralized and reflected by the surface, retaining a large fraction of their incident kinetic energy, forming a beam of atoms. The device is based on a magnetically confined (3-4 kG) coaxial plasma source and the atom energy can be varied by adjusting the bias voltage. The source provides a neutral flux of roughly 5 x 10 to the 16th/sq cm/s at a distance of 10 cm and a fluence of roughly 10 to the 21st/sq cm in five hours. The source has been characterized with plasma diagnostics and by measuring the energy of an atomic argon beam using a mass spectrometer. Samples of carbon film, carbon-based paint, Kapton, Mylar, and Teflon exposed to atomic O beams show erosion quite similar to those observed in orbit on the Space Shuttle.

Cuthbertson, J. W.↗

The Next Breakthroughs in Neutrino Physics (LDRD Final Report)

The neutrino is an important fundamental particle, one of the building blocks of the universe. Abetter understanding of the neutrino will answer questions regarding the origin of mass, the matter and anti-matter asymmetry of the universe, and the nature of dark matter. The nation's research community has recognized that the answers to these and other questions are within reach and has assigned neutrino experiments the highest priority for both nuclear and particle physics programs. We are investigating three aspects of neutrino experimentation: detection techniques, target materials, and data analysis. Our efforts targeted multiple applications including experiments to measure neutrinoless double-beta-decay, neutrino-oscillation and neutrino mass. Our research objectives include (1) developing approaches that make detectors scalable to larger sizes and insensitive to background signals; (2) increasing the signal strength and reducing noise from targets; and (3) efficiently distinguishing background noise from signals during analysis. In this LDRD we have advanced all of these areas. We have demonstrated the scale up of a metal organic framework that can adsorb xenon directly from the air that will allow for large neutrino detectors made from xenon. We have studied the use of Cherenkov radiation to reduce the signal backgrounds. We demonstrated the cracking of hydrogen to make atomic tritium for neutrino mass measurements, and lastly we demonstrated the benefits of machine learning techniques to improve signal to noise during analysis

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗