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At least 163 records · Page 9

Integrated FHR technology development: Tritium management, materials testing, salt chemistry control, thermal hydraulics and neutronics, associated benchmarking and commercial basis

This report summarizes the results of a 3-year Integrated Research Project (IRP) sponsored by the U.S. Department of Energy to address major technical challenges in the development of the Fluoride-salt-cooled High-temperature Reactor (FHR). The IRP universities included the Massachusetts Institute of Technology (MIT), the University of California at Berkeley (UCB), the University of Wisconsin (UW), and the University of New Mexico (UNM). The FHR is a new reactor concept less than 20 years old that combines (1) a clean fluoride salt coolant, (2) the graphite-matrix coated-particle fuel originally developed for High- Temperature Gas-Cooled Reactors and (3) passive decay heat removal systems from sodium fast reactors. The base-line design is a pebble-bed FHR that delivers heat between 600 to 700°C with a 7 Li 2 BeF 4 (flibe) salt coolant to the power cycle or industrial users. The Executive Summary describes what was accomplished and summarizes major conclusions. The main report contains stand-alone sections in each major area of work. Highlights are summarized below. Tritium. The coolant salt produces tritium necessitating understanding and control of tritium. Experimental work included measuring hydrogen uptake on carbon, tritium uptake during irradiation of graphite in 700°C salt and the permeability of tritium through metals with and without coatings. An FHR systems model was developed to predict tritium behavior and enable design of tritium control systems. The leading candidate for tritium removal from the flibe salt is carbon bed outside the reactor core. Thermal hydraulics and Neutronics. A 10-meter high FHR integral effects test facility, using Dowtherm A®, has been built and used to simulate the integral response of a representative FHR to improve understanding of FHR thermal hydraulics and validate thermal hydraulics codes used for the FHR. Neutronic analysis included code-to-code benchmarking, multiphysics modeling, uncertainty analysis for nuclear data uncertainties and shielding analysis. Twisted-tube heat exchangers were examined that may provide significant cost reductions because of their improved heat-transfer performance with liquid salts. The impacts on safety and design caused by uncertainties in physical properties of the salt were assessed with recommendations on where added physical property measurements are needed. Work began on understanding radiative heat transfer that becomes important in salt systems at higher temperatures. Materials. Static corrosion tests were conducted on graphite and materials in 700°C salt -- both in the UW laboratory and in the MIT reactor. In addition to static corrosion testing, a circulating salt corrosion loop was built and is operating. Methods to measure salt properties including redox were developed. The presence of carbon increases corrosion. With good redox control, the evidence indicates stainless steel can be used as a material of construction. Benchmarking. An additional series of workshops where held to enable benchmarking and comparison of results between different investigators. Commercialization. The FHR delivers higher average-temperature (~650°C) heat to the power cycle or industry than other reactors. This enables power cycles with lower-cost heat storage for variable electricity to the grid while the reactor operates at base-load -- providing a major competitive advantage by maximizing revenue from electricity sales. In October, 2016, a new startup company named Kairos Power was formed, and opened its first office in Jack London Square, Oakland, California, in January 2017. Kairos Power exists largely due to the work that was accomplished by this IRP and the previous DOE-funded FHR IRP that performed research on FHR technology from 2012 to 2015. In September, 2018, as this IRP is concluding, Kairos Power was staffed at 60 full time employees, working to develop technology derived from this IRP. Many of these employees worked with the IRP before joining Kairos Power 1 (https://kairospower.com). Other students and researchers from this IRP have joined other startup companies, including the Terrapower Molten Chloride Fast Reactor and the Terrestrial Energy development efforts.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Integral Measurement of the 237 Np($n$, γ) 238 Np Cross Section with Fast Neutrons

Accurate knowledge of the 237 Np($n$; γ) 238 Np cross section at fast neutron energies is important for applied nuclear science. The presently available experimental data has large disagreements in the fast neutron region. A measurement of the 237 Np($n$; γ) 238 Np cross section was performed using a well characterized fast neutron source and the results was compared with previous measurements and current nuclear data evaluations. This will provide an integral measurement that can be used as a benchmark for current evaluations. Multiple samples of 237 Np were irradiated in the Godiva-IV critical assembly. Following the irradiation, the samples placed in a γ-ray counting setup and the γ-rays emitted from the decay of 238 Np were measured over a time period of approximately 7 days. Multiple γ-ray decay branches of 238 Np were observed. The observed activity of 238 Np was used to calculate the amount of 238 Np produced during the irradiation via the 237 Np($n$; γ) 238 Np and an integral cross section of 359(10) mb was measured. The 238 Np half-life has been measured with a result of 50.34(7) hours. An integral measurement of the 237 Np($n$; γ) 238 Np cross section has been measured. This result has been compared to the calculated integral cross section using the ENDF/BVIII.0 and JENDL-4.0 evaluated cross sections and found to be in good agreement with ENDF/BVIII.0 value of 367 mb. The JENDL-4.0 evaluation yields a value of 312 mb, which is significantly lower than the measured cross section.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DEEP HE ii AND C iv SPECTROSCOPY OF A GIANT LYα NEBULA: DENSE COMPACT GAS CLUMPS IN THE CIRCUMGALACTIC MEDIUM OF A z ∼ 2 QUASAR

The recent discovery by Cantalupo et al. of the largest (∼500 kpc) luminous (L ≃ 1.43 × 10{sup 45} erg s{sup −1}) Lyα nebula associated with the quasar UM287 (z = 2.279) poses a great challenge to our current understanding of the astrophysics of the halos hosting massive z ∼ 2 galaxies. Either an enormous reservoir of cool gas is required M ≃ 10{sup 12} M{sub ⊙}, exceeding the expected baryonic mass available, or one must invoke extreme gas clumping factors not present in high-resolution cosmological simulations. However, observations of Lyα emission alone cannot distinguish between these two scenarios. We have obtained the deepest ever spectroscopic integrations in the He ii λ1640 and C iv λ1549 emission lines with the goal of detecting extended line emission, but detect neither line to a 3σ limiting SB ≃ 10{sup −18} erg s{sup −1} cm{sup −2} arcsec{sup −2}. We construct simple models of the expected emission spectrum in the highly probable scenario that the nebula is powered by photoionization from the central hyper-luminous quasar. The non-detection of He ii implies that the nebular emission arises from a mass M{sub c} ≲ 6.4 × 10{sup 10} M{sub ⊙} of cool gas on ∼200 kpc scales, distributed in a population of remarkably dense (n{sub H} ≳ 3 cm{sup −3}) and compact (R ≲ 20 pc) clouds, which would clearly be unresolved by current cosmological simulations. Given the large gas motions suggested by the Lyα line (v ≃ 500 km s{sup −1}), it is unclear how these clouds survive without being disrupted by hydrodynamic instabilities. Our work serves as a benchmark for future deep integrations with current and planned wide-field IFU spectrographs such as MUSE, KCWI, and KMOS. Our observations and models suggest that a ≃10 hr exposure would likely detect ∼10 rest-frame UV/optical emission lines, opening up the possibility of conducting detailed photoionization modeling to infer the physical state of gas in the circumgalactic medium.

79 ASTRONOMY AND ASTROPHYSICS↗

Overview of the 2014 Edition of the International Handbook of Evaluated Reactor Physics Benchmark Experiments (IRPhEP Handbook)

The International Reactor Physics Experiment Evaluation Project (IRPhEP) is a widely recognized world class program. The work of the IRPhEP is documented in the International Handbook of Evaluated Reactor Physics Benchmark Experiments (IRPhEP Handbook). Integral data from the IRPhEP Handbook is used by reactor safety and design, nuclear data, criticality safety, and analytical methods development specialists, worldwide, to perform necessary validations of their calculational techniques. The IRPhEP Handbook is among the most frequently quoted reference in the nuclear industry and is expected to be a valuable resource for future decades.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Uranium integral fission product yields for a spectrally-shaped 14.1 MeV neutron source at the National Ignition Facility

This paper describes the experimental results for an energy tuning assembly created to modify the National Ignition Facility deuterium–tritium fusion neutron source into a notional thermonuclear and prompt fission neutron spectrum, which has applications in integral measurements, nuclear data benchmarks, and radiation effects on microelectronics. The Monte Carlo neutron transport utilized MCNP5 to estimate the ETA-modified fluence using the ENDF-B/VIII.0 and IRDFF-II continuous energy nuclear data libraries, and SCALE Sampler was used to estimate the systematic nuclear data covariance using ENDF-B/VII.1 and IRDFF-II in a 252-group structure. The experiment fielded eight activation foils and a highly enriched uranium sample. This provided fifteen reaction channels that were used in a forward-fit comparison to the modeled results and to unfold the neutron spectrum using STAYSL. Gamma-ray spectrometry was performed on the activation and highly enriched uranium foils, and the reduced Χ 2 between the modeled and experimental values was 1.21. The results from the STAYSL unfold, reduced Χ 2 = 1.62, indicated that the modeled neutron spectrum was achieved and the systematic nuclear data uncertainty associated with the neutron transport and activation product cross sections was representative of the experiment. Integral cumulative fission product yield data were collected for 37 mass chains with a combination of gamma-ray spectrometry and radiochemical analysis. Fission product analysis was generally in agreement with two models using a semi-empirical fit and the General Observables of Fission code, with the exception of mass chains 88, 109, 111, 112, 113, 129, 139, 142, 144, 151, and 156.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

RELAP5-3D validation studies based on the High Temperature Test facility

In the spring and summer of 2019, experiments were conducted at the High Temperature Test Facility (HTTF) that form the basis of an upcoming high-temperature gas-cooled reactor (HTGR) thermal hydraulics (T/H) benchmark. HTTF is an integral effects test facility for HTGR T/H modeling validation. This paper presents RELAP5-3D models of two of those experiments: PG-27, a pressurized conduction cooldown (PCC); and PG-29, a depressurized conduction cooldown (DCC). These models used the RELAP5-3D model of HTTF originally developed by Paul Bayless as a starting point. The sensitivity analysis and uncertainty quantification code, RAVEN was used to perform calibration studies for the steady-state portion of PG-27. Here we developed four PG-27 calibrations based on steady-state conditions. These calibrations all used an effective thermal conductivity equal to 36 % of the measured thermal conductivity, but they differed with respect to the frictional pressure drops and radial conduction models. These models all captured the trends in steady-state temperature distributions and transient temperature behavior well. All four calibrations show room for improvement in predicting the transient temperature rise. The smallest error in temperature rise during the transient was a 21 % underprediction, and the largest was a 48 % underprediction. The errors in transient temperature rise are largely a result of a mismatch in power density between the RELAP5-3D model and the experiment due to the location of active heater rods along the boundary between heat structures in the model. The best of these calibrations was applied to PG-29 to model the DCC. Once again, temperatures during the transient were underpredicted but trends in temperature were captured. The RELAP5-3D model captured trends in the data but could not reproduce measured temperatures exactly. This result is not attributed to deficiencies in the experimental data or to RELAP5–3D itself. Rather, this result likely arises due to the some of the assumptions and decisions made when the RELAP5-3D model was first developed, prior to the execution of HTTF experiments. An agreement in prediction of temperature trends but challenges reproducing HTTF temperatures within measurement uncertainty is consistent with previous analyses of HTTF in the literature. Future RELAP5-3D validation activities centered around HTTF may be able to provide greater insight into the code’s capabilities for HTGR modeling with a more finely nodalized model.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Synthesis, optical imaging, and absorption spectroscopy data for 179072 metal oxides

Abstract Optical absorption spectroscopy is an important materials characterization for applications such as solar energy generation. This data descriptor describes the to date (Dec 2018) largest publicly available curated materials science dataset for near infrared to near UV (UV-Vis) light absorbance, composition and processing properties of metal oxides. By supplying the complete synthesis and processing history of each of the 179072 samples from 99965 unique compositions we believe the dataset will enable the community to develop predictive models for materials, such as prediction of optical properties based on composition and processing, and ultimately serve as a benchmark dataset for continued integration of machine learning in materials science. The dataset is also a resource for identifying materials composition and synthesis to attain specific optical properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The ATLAS experiment software on ARM

With an increased dataset obtained during the Run 3 of the LHC at CERN and the even larger expected increase of the dataset by more than one order of magnitude for the HL-LHC, the ATLAS experiment is reaching the limits of the current data processing model in terms of traditional CPU resources based on x86_64 architectures and an extensive program for software upgrades towards the HL-LHC has been set up. The ARM architecture is becoming a competitive and energy efficient alternative. Some surveys indicate its increased presence in HPCs and commercial clouds, and some WLCG sites have expressed their interest. Chip makers are also developing their next generation solutions on ARM architectures, sometimes combining ARM and GPU processors in the same chip. Consequently it is important that the ATLAS software embraces the change and is able to successfully exploit this architecture. We report on the successful porting to ARM of the Athena software framework, which is used by ATLAS for both online and offline computing operations. Furthermore we report on the successful validation of simulation workflows running on ARM resources. For this we have set up an ATLAS Grid site using ARM compatible middleware and containers on Amazon Web Services (AWS) ARM resources. The ARM version of Athena is fully integrated in the regular software build system and distributed in the same way as other software releases. In addition, the workflows have been integrated into the HEPscore benchmark suite which is the planned WLCG wide replacement of the HepSpec06 benchmark used for Grid site pledges. In the overall porting process we have used resources on AWS, Google Cloud Platform (GCP) and CERN. A performance comparison of different architectures and resources will be discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Coordinate parameterisation and spectral method optimisation for Beltrami field solver in stellarator geometry

The numerical solution of the stepped pressure equilibrium (Hudson et al 2012 Phys. Plasmas 19 112502) requires a fast and robust solver to obtain the Beltrami field in three-dimensional geometry such as stellarators. The spectral method implemented in the stepped pressure equilibrium code (SPEC) is efficient when the domain is a hollow torus, but ill-conditioning of the discretised linear equations occurs in the (solid) toroid due to the artificially singular coordinate parameterisation near the axis. Here, we propose an improved choice for the reference axis to prevent coordinates surfaces from overlapping. Then, we examine the parity and asymptotics of the magnetic vector potential near the axis and suggest the use of recombined and rescaled Zernike radial basis functions. The maximum relative error in the magnetic field of the Wendelstein 7-X geometry is shown to reach 10 –9 at high resolution in a series of convergence tests and benchmarks against the boundary integral equation solver for Taylor states. The new method is also reported to significantly improve the accuracy of multi-volume SPEC calculations. A comparison between free-boundary SPEC and the analytical Dommaschk potential is presented with higher-than-usual Fourier resolution. It is illustrated that we are able to resolve low amplitude current sheets when an interface is placed where there is no flux surface in the analytic solution. This was previously concealed because of insufficient numerical resolution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

IER 480: TEX-Pu Benchmark (PU-MET-THERM-004) to Test Polyethylene and Lucite Thermal Scattering Laws [Slides]

This presentation finds that PMT-004 has four new benchmark cases highly sensitive to PE TSL (2 cases) and PMMA TSL (2 Cases). PE cases were well predicted using MCNP6.2 and ENDF/B-VIII.0. PMMA cases overpredicted by approximately 0.6-0.7% in k eff at 20°C. Accepted into 2023 version of the ICSBEP Handbook. Temperature had a large impact on reactivity of the critical configuration. Implications for validation work for thermal cases- need to adjust TSL data to correct temperature as it can have hundreds of pcm effects for a few °C. Future thermal experiments should try and measure reactivity at multiple temperatures to aid in data testing and benchmark adjustment.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Summary of GFL Inverter Capability and Performance: Malawi [Slides]

This presentation provides a comprehensive comparison of inverter-based resource (IBR) technical requirements across multiple international grid codes - including IEEE 2800, ESO, EirGrid, and Malawi's evolving regulatory framework - to support capacity building for electricity-sector institutions in Malawi. It highlights key performance expectations for grid-following (GFL) inverters across critical domains such as primary and fast frequency response, ramping behavior, frequency and voltage ride-through capabilities, reactive power and voltage control, ROCOF withstand, phase jump tolerance, system strength considerations, protection schemes, and dynamic modeling requirements. Emphasizing a "Do no harm, do something, do more" philosophy, the document synthesizes best practices and operational benchmarks to guide the integration and stability of inverter-based resources within Malawi's power system. The presentation forms part of the SABESS Center of Excellence initiative supported by the Global Energy Alliance for People and the Planet.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Beyond Energy Efficiency: A clustering approach to embed demand flexibility into building energy benchmarking

The intermittency of carbon-free renewables and the demand changes associated with the widespread push for electrifying the transportation and building sectors provides an opportunity for buildings to go beyond energy efficiency and push towards providing demand flexibility to the electricity grid. The duality of energy efficiency and demand flexibility is necessary for success in a sustainable and reliable energy transition. Current building energy benchmarking models are limited in their ability to integrate concepts of demand flexibility and/or utilize granular smart meter data. Thus, current benchmarking methods are focused annual energy usage and fail to incorporate how the time of use of energy consumption impacts emissions in a quickly changing energy grid. Without a more comprehensive view of energy usage and associated real-time emissions, current benchmarking methods are unlikely to realize the full decarbonization potential of buildings. New emerging data streams provide an opportunity to develop a new generation of benchmarking energy models that embed dimensions of energy efficiency, grid interactivity, and demand flexibility into their analysis. In this paper, we propose a four-step method for embedding grid interactivity and demand flexibility into building benchmarking models that utilizes emerging building and time-series electricity data streams. We first engineer features to produce a mix-type dataset that encompasses many attributes of grid-interactive and efficient buildings, and then we apply K-medoids using Gower's Distance to produce peer-group clusters. We apply the method to a case study of 306 primary and secondary schools in southern California, USA. The results show that the method effectively clusters buildings by attributes of demand flexibility and energy efficiency. The clustering results reveal patterns in inefficient building operations and demand inflexibility at the building peer group level. In conclusion, the interpretation of clusters can serve as an integrated energy efficiency and demand flexibility benchmarking model and inform performance-specific policy targeting for buildings that go beyond traditional efficiency measures.

24 POWER TRANSMISSION AND DISTRIBUTION↗

U.S. Solar Photovoltaic System and Energy Storage Cost Benchmark: Q1 2021 [Slides]

Our benchmarking method includes bottom-up accounting for all necessary system and projectdevelopment costs incurred when installing residential, commercial, and utility-scale systems, and it models the Q1 2021 costs for such systems, excluding any previous supply agreements or contracts. In general, we attempt to model the typical installation techniques and business operations from an installed-cost perspective, and our benchmarks are national averages. The residential PV-only benchmark and the commercial rooftop PV-only benchmark average costs by inverter type (string inverters, string inverters with direct current [DC] optimizers, and microinverters), weighted by inverter market share. The residential PV-only benchmark is further averaged across small installer and national integrator business models, weighted by market share. All benchmarks include variations—accounting for the differences in size, equipment, and operational use (particularly for storage)—that are currently available in the marketplace. All benchmarks assume nonunionized construction labor; residential and commercial PV systems predominantly use nonunionized labor, and the type of labor required for utility-scale PV systems depends heavily on the development process. All benchmarks assume the use of monofacial monocrystalline silicon PV modules. Benchmarks using cadmium telluride or bifacial modules could result in significantly different results. The data in this annual benchmark report inform the formulation of and track progress toward the U.S. Department of Energy (DOE) Solar Energy Technologies Office’s Government Performance and Reporting Act cost targets.

14 SOLAR ENERGY↗

Integrated Multi Scale Data Analytics and Machine Learning for the Grid; Benchmarking Algorithms and Data Quality Analysis

Machine Learning and Data Analytics are terms which are utilized now ubiquitously throughout grid analytics forums, as a potential solution to the growing big data challenges for the distribution grid. As sensors become inexpensive and common, and communication networks grow, the analytics themselves must adapt and enable consumers and providers to visualize and utilize the data provided effectively. Machine learning is one of the techniques proposed in order to manage this data deluge. This report is a subset of the work in this activity, funded through the DOE Grid Modernization Initiative, to summarize the benchmarking and review of data quality impact on the algorithm sets being developed within each use case area.

42 ENGINEERING↗

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↗

Optimal Realization of Yang–Baxter Gate on Quantum Computers

Quantum computers provide a promising method to study the dynamics of many-body systems beyond classical simulation. On the other hand, the analytical methods developed and results obtained from the integrable systems provide deep insights on the many-body system. Quantum simulation of the integrable system not only provides a valid benchmark for quantum computers but is also the first step in studying integrable-breaking systems. The building block for the simulation of an integrable system is the Yang–Baxter gate. It is vital to know how to optimally realize the Yang–Baxter gates on quantum computers. Based on the geometric picture of the Yang–Baxter gates, the optimal realizations of two types of Yang–Baxter gates with a minimal number of controlled NOT (CNOT) or gates are presented. It is also shown how to systematically realize the Yang–Baxter gates via the pulse control. The different realizations on IBM quantum computers are tested and compared. It is found that the pulse realizations of the Yang–Baxter gates always have a higher gate fidelity compared to the optimal CNOT or realizations. On the basis of the above optimal realizations, the simulation of the Yang–Baxter equation on quantum computers is demonstrated. Finally, these results provide a guideline and standard for further experimental studies based on the Yang–Baxter gate.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗