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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 163 records · Page 9

Physics of the thermal quench in MST tokamak plasmas (Final Technical Report)

This project at the University of Wisconsin-Madison targeted measurements in tokamak plasmas in the Madison Symmetric Torus (MST) to help elucidate the physics of the tokamak disruption. We intended to focus on the thermal quench, during which energy is lost from the plasma in a very short time. Understanding and ultimately mitigating the thermal quench are among the highest priority research thrusts for ITER, a large international fusion experiment presently under construction. The measurements in MST exploited an advanced set of diagnostics for internal measurements with high time resolution, targeting linear and nonlinear magnetohydrodynamic (MHD) activity as well as the electron temperature and density profiles. We also exploited other features of the MST device, including very flexible power supplies for the toroidal magnetic field and toroidal plasma current that are capable of producing almost arbitrary waveforms. While the work funded by this project was purely experimental, we continued and expanded an existing collaboration with UW-Madison experts in nonlinear MHD computational modeling of tokamak plasmas. That modeling incorporated realistic, experimentally measured parameters. The results of the modeling were anticipated to deepen considerably our understanding of the experimental measurements, and in turn, the experimental measurements were anticipated to help validate the modeling results. The science of transients such as disruptions is one of the highest priority research areas in the U.S. and international fusion programs. The work carried out in this project was targeted to help advance the science of tokamak disruptions which will in turn contribute to the success of ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Eco-Friendly High-Performance Carbon Building Material Development from Coal

The development of eco-friendly high-performance building materials based on coal-derived materials is greatly beneficial for promoting environmental sustainability and the coal industry. This project focused on advancing technology to create innovative and scalable construction materials from two domestic sources: (1) coal-derived pyrolyzed char (PC), and (2) solvent-extracted coal deposit, extracts, and residue (CDER). It aimed to simultaneously develop and produce two types of coal-derived building products: (1) char-based concrete bricks (CCB) for wall construction in buildings, and (2) carbon-based structural units (CSU) intended as alternatives to traditional wood, concrete, or steel framing structures. The project team has successfully developed methods for manufacturing CCB samples. Extensive experiments were conducted to assess various manufacturing techniques for these samples. This included measuring their physical properties such as thermal conductivity (ranging from 0.26 to 0.38 W/mK) and bulk density (ranging from 0.85 to 1.15 g/cm 3 ), along with their mechanical properties (e.g., compressive strength ranging from 14 to 16 MPa at 28 days) for samples with a PC composition of 70%. Quality assurance and quality control tests, focusing on density and compressive strength, were also performed on samples selected randomly from pilot-scale production, and cured for a long term (over three months). The average long-term compressive strength of two randomly selected CCB samples was measured as 15.1 MPa, which was higher than the required target strength of 14 MPa. This indicates that the manufactured CCB samples from the preliminary pilot scale production run have good quality control and long-term strength performance.

01 COAL, LIGNITE, AND PEAT↗

Feasibility Assessment of Using Electrical Impedance Tomography for Damage Localization in Graphite Microreactor Components

Microreactors have great potential to decrease capital costs and construction timelines, reducing the barriers to implementing advanced nuclear reactor technologies. However, the lower power output of these microreactors introduces economic challenges if the operation and maintenance costs cannot be reduced sufficiently. Many microreactor concepts use graphite materials for in-core moderator and structural purposes, which will require periodic inspection or, ideally, in situ structural health monitoring. This work describes an initial evaluation of the feasibility of leveraging graphite’s semiconducting properties to perform electrical impedance tomography (EIT) for defect localization. First, a study was performed to identify the best methods for bonding electrical contacts to minimize the effects of contact resistance that interfere with impedance measurements of the graphite. After determining the best bonding approach, electrodes were attached to multiple graphite components with varying geometries (e.g., simple block and more representative microreactor hexagonal block). In parallel, finite element analysis approaches were developed and implemented to analyze the impact of defects and contact resistances and to inform an iterative inverse model for reconstructing the conductivity distribution. The results of this study show that defect localization in graphite components is possible using EIT if a sufficient number of electrodes (to improve spatial resolution) can be bonded using a technique with very low contact resistance and those contact resistances remain stable during reactor operation. If the reactor core and vessel design do not allow electrodes to be bonded during reactor operation, then it may be possible to detach/reattach electrodes between reactor operation and outages if a suitable mechanical connection that offers repeatable contact resistance can be identified. Alternatively, future work could focus on identifying contacts that can survive the harsh reactor operating environment so that contacts do not need to be removed.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

High-Transmission Neutron Optical Devices Utilizing Micro-Machined Structures

Neutrons are a powerful probe in material science with unique penetrating abilities. A major challenge stems from the fact that neutron optical devices are limited to refractive indices on the order of n≈1±10−5. By exploiting advances in precision manufacturing, we designed and constructed micro-meter period triangular grating with a high-aspect ratio of 14.3. The manufacturing quality is demonstrated with white-light interferometric data and microscope imaging. Neutron-scattering experiment results are presented, showing agreement with refraction modelling. The capabilities of neutron Fresnel prisms and lenses based on this design are contrasted with existing neutron focusing techniques, and the path separation of a prism-based neutron interferometer is estimated.

Kapahi, Connor (ORCID:0000000160516859)↗

Transparent soil microcosms for live-cell imaging and non-destructive stable isotope probing of soil microorganisms

Microscale processes are critically important to soil ecology and biogeochemistry yet are difficult to study due to soil’s opacity and complexity. To advance the study of soil processes, we constructed transparent soil microcosms that enable the visualization of microbes via fluorescence microscopy and the non-destructive measurement of microbial activity and carbon uptake in situ via Raman microspectroscopy. We assessed the polymer Nafion and the crystal cryolite as optically transparent soil substrates. We demonstrated that both substrates enable the growth, maintenance, and visualization of microbial cells in three dimensions over time, and are compatible with stable isotope probing using Raman. We applied this system to ascertain that after a dry-down/rewetting cycle, bacteria on and near dead fungal hyphae were more metabolically active than those far from hyphae. These data underscore the impact fungi have facilitating bacterial survival in fluctuating conditions and how these microcosms can yield insights into microscale microbial activities.

59 BASIC BIOLOGICAL SCIENCES↗

Validation of HVAC Hardware-in-the-Loop Simulation for Advanced Control Strategies in Smart Homes: Preprint

Residences with smart thermostats can use advanced control strategies to manage their cooling/heating demand, but it is difficult to evaluate optimal control strategies for flexible heating, ventilation, and air conditioning (HVAC) systems in a traditional laboratory setting. The HVAC hardware-in-the-loop (HIL) system combines physical HVAC equipment and a physical thermostat with a simulated house to enable realistic operation of the hardware in any climate. This HIL platform allows researchers to evaluate advanced control strategies for homes with different construction or vintage types, as well as different climates and occupancy schedules. To demonstrate the capabilities of the HVAC HIL system, experimental results with a SEER 16, HSPF 9.5, 3 ton single-speed air source heat pump are validated against past field data collected from a heavily instrumented, unoccupied, retrofit house located in Sacramento, California. Three different cooling strategies are recreated in the HVAC HIL platform, including two different pre-cooling schedules that were designed to shift energy use away from the evening peak. The room temperatures, heat pump energy use, and run time show good agreement between the field data and HIL experimental results for three strategies.

cooling strategies↗

Report on Year-4 of Water NSTF Matrix Testing: Facility Maintenance and Accident Testing

Under support from the Department of Energy (DOE) and the Office of Advanced Reactor Technologies (ART), a large-scale test facility has been constructed at Argonne National Laboratory to generate NQA-1 qualified validation data for passive decay heat removal systems in advanced reactors. The Natural convection Shutdown heat removal Test Facility (NSTF) reflects key features of a ½ scale, water-based, Reactor Cavity Cooling System (RCCS) and is intended to study the behavior, bound performance, and ultimately guide design decisions for passive decay heat removal systems for advanced reactors. In addition to the experimental activities detailed in this report, a supportive computational modeling effort is on-going which has been demonstrated to significantly strengthen the experimental program while also improving accuracy of the computer models. Together these create a mutually beneficial relationship integral to meeting the overall program objective of examining the heat removal performance of the RCCS concept. This report serves as a summary of maintenance and experimental activities during the program’s fourth year of water-based operation. A planned six-month maintenance period began in August 2021, during which major inspections, repairs, cleaning, and installation of new instrumentation and data acquisition hardware were conducted. Most significantly, two heaters that faulted during Year-3 were repaired, allowing the facility to resume use of the full heated section area and full range of available electric power. The remainder of the year consisted of eight months of test operations, during which the facility logged 211 hours of active heating across one bake-out (following the maintenance period) and seven matrix tests; five classifieds as Accepted per NQA-1, one as Trending, and one as Failed. Testing began by performing two repeat cases to confirm expected facility response and behavior during both single- and two-phase flow conditions, ensuring no changes were introduced during the maintenance period that might have altered the thermal-hydraulic characteristics of the facility. In continuation of the power parametric series initiated in previous years, a high-power test case was then performed examining heat removal performance at a decay heat load equivalent to 2.4 MWt, full-scale, a level exceeding maximum design targets. Additional testing then introduced various blockage scenarios along the network piping, examining the effects of partial and complete blockages of the flow paths on the system behavior and heat removal performance. A study of static boiling tests directed at understanding the geysering two-phase instability was also conducted. The loop was filled only to the bottom of the tank outlet, creating an open loop configuration that prevents any natural circulation flow from occurring, and the heaters were powered on until the facility reached saturation conditions. Following, a series of quasi-steady-state conditions were introduced by adjusting the inventory level in the adiabatic chimney piping at decreasingly lower elevations above the heated region. A strong correlation of geysering characteristics and loop level was observed, with flow and temperature excursions decreasing in intensity, but increasing in frequency, as the fill were reduced to lower elevations along the chimney piping. Once the level fell very low in the chimney, at points near the top of the heated section, the system reached a stable state of continuous boiling without any occurrence of geysering eruptions. A final significant testing accomplishment this year was successful completion of an “accident scenario” test, whose operating conditions were based on a prototypic decay heat curve provided by Framatome and scaled for the NSTF. This test began by establishing steady-state, single-phase “normal operation” conditions, before simulating an accident trip where the availability of active cooling systems was lost. Loop temperatures gradually increased until reaching saturation and subsequent two-phase boiling flow. Over the course of an extended operational period along the defined decay heat curve, steam boil-off caused gradual but continued depletion of liquid inventory until reaching a critically low level causing flow stagnation and cessation of natural circulation heat removal. At this point, after nearly 72 hours of continuous operation, a cold refill was performed to replenish the system inventory and allow the facility to re-establish closed loop natural circulation flow and return to a safe operational state.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

FY23 Report on Water NSTF Testing at Two-Phase Conditions: Off-normal Scenarios

Under support from the Department of Energy (DOE) and the Office of Advanced Reactor Technologies (ART), a large-scale test facility has been constructed at Argonne National Laboratory to generate NQA-1 qualified validation data for passive decay heat removal systems in advanced reactors. The Natural convection Shutdown heat removal Test Facility (NSTF) reflects key features of a ½ scale, water-based, Reactor Cavity Cooling System (RCCS) and is intended to study the behavior, bound performance, and ultimately guide design decisions for passive decay heat removal systems for advanced reactors. In addition to the experimental activities detailed in this report, a supportive computational modeling effort is on-going which has been demonstrated to significantly strengthen the experimental program while also improving accuracy of the computer models. Together these create a mutually beneficial relationship integral to meeting the overall program objective of examining the heat removal performance of the RCCS concept. This report details the experimental activities and upgrades performed during the program’s fifth year of water-based operation. The theme of this year of testing was examining off-normal scenarios. In practice, that meant examining scenarios with blockages or other design basis conditions. From a maintenance and capability standpoint that meant assessing valving options for implementing blockages, assessing drain and refill capabilities, and ensuring in all cases that operators could safely, efficiently, and repeatably bring the facility to an off-normal condition and return it to the normal operating state. In one notable case, no solution existed, nor was a solution commercially available, that met the facility needs for implementing blockages within the two-phase region of the chimney. A valve and feedthrough were custom-designed for NSTF to operate submerged in saturated water while being safely actuated from outside the tank. The fifth year of testing included eight matrix tests consisting of 162 hours of active heating, 9,735 kWh of electrical heating, with seven tests classified as Accepted per NQA-1 and one as Trending. All matrix tests were performed at two-phase flow conditions. The power parametric series from previous years was extended to include another scenario with a decay load equivalent to 1.75 MWt, full scale, further resolving the system flow oscillation response as a function of input power. A depletion test was performed to extend previous work and examine the system’s approach to stagnation and geysering that were not previously observed. This test began at an initial inventory level of 50%, prototypic power of 2.1 MWt, and employed an accelerated drain of 0.75 gpm plus boiloff until stagnation conditions were achieved and multiple geysering events were recorded. Further exploring the geysering phenomenon was a separate effects test examining static boiling in the risers and chimney. This static boiling test was performed at 48 kWe, a higher power than testing in the previous year, and included enhancements to the drain system to remove inventory in a better-controlled and more reliable manner. Two tests were performed, at prototypic conditions of 1.4 MWt and 2.4 MWt, respectively, examining the system response to throttled conditions in the singlephase region of the piping. A ball valve immediately before he riser inlet header was increasingly throttled, progressing the system through a repeatable pattern of two-phase oscillations and stable regimes before ultimately inducing stagnation and geysering. Concluding the year, two tests were performed at baseline conditions of 70% initial inventory level and 2.1 MWt of prototypic decay heat to examine both repeatability and the response to throttling within the two-phase region, at the inventory tank inlet using the custom valve mentioned above. The first such test repeated transient operating conditions and revealed significant sensitivity t

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Off-Road Vehicle Decarbonization and Energy Systems Integration: R&D Gaps and Opportunities

This report summarizes findings from the Off-Road Decarbonization and Energy Systems Integration workshop, hosted by the National Renewable Energy Laboratory (NREL) from March 22-24, 2022. The workshop focused on the importance of collaboration among the off-road vehicle industry and government to address barriers and opportunities for decarbonization. The workshop aligns with priorities of the U.S. Department of Energy (DOE) Vehicle Technologies Office and Hydrogen and Fuel Cell Technologies Office to decarbonize transportation in the agriculture, mining, construction, and military industries. This decarbonization effort is also intended to support original equipment manufacturers, industry associations, technology developers, utilities, and consultants. The sections within this report correspond to the three topic areas covered in the 3-day workshop: a high-level perspective of needs and challenges, vehicle and equipment decarbonization strategies, and energy systems integration opportunities.

33 ADVANCED PROPULSION SYSTEMS↗

A New Platform for Twistronics: Perovskite Moiré Superlattices Beyond van der Waals

Moiré superlattices have reshaped condensed‐matter physics by enabling twist‐angle engineering of electronic and excitonic states, traditionally in van der Waals (vdW) systems. This Perspective focuses on perovskites as a transformative non‐van der Waals (non‐vdW) platform for twistronics. These materials are distinguished by ionic‐covalent bonding and soft octahedral lattices that support deep moiré potentials (≈100–200 meV), which in turn yield bright, room‐temperature excitons and tunable quantum phenomena. We organize recent advances into two core classes: (i) moiré superlattices constructed from 2D Ruddlesden‐Popper (RP) perovskites via spontaneous or guided twisted stacking; and (ii) moiré architectures in 3D perovskite lamellae, achieved through topotactic 2D RP‐to‐3D conversion and ligand‐induced self‐assembly. Key experimental observations in these systems include twist‐tunable moiré periods, suppressed exciton–exciton annihilation, flat band‐like transport, and ferroelectric vortex lattices in their oxide perovskite counterparts. Here, we outline key bottlenecks, including defects arising during phase conversion, stringent lattice‐matching requirements, and the absence of in situ twist metrology, and highlight opportunities in lattice‐mismatched heterostructures and multifunctional quantum‐optoelectronic devices. Collectively, these advances establish perovskite moiré systems as a critical bridge between fundamental moiré physics and room‐temperature technological applications.

2D Ruddlesden–Popper perovskites↗

Embedding Equity into Electric Vehicle Charging Station Design

Once a site location is selected for the installation of an electric vehicle (EV) charging station, the next step is to plan and design the specific station. Local and state governments can require and/ or incentivize accessible and safe design elements, so the station is constructed in an equitable manner.

ADVANCED PROPULSION SYSTEMS,ENERGY PLANNING, POLIC↗

Surrogate Constructed Scalable Circuits ADAPT-VQE in the Schwinger model

Inspired by recent advancements of simulating periodic systems on quantum computers, we develop a new approach, (SC)$^2$-ADAPT-VQE, to further advance the simulation of these systems. Our approach extends the scalable circuits ADAPT-VQE framework, which builds an ansatz from a pool of coordinate-invariant operators defined for arbitrarily large, though not arbitrarily small, volumes. Our method uses a classically tractable ``Surrogate Constructed'' method to remove irrelevant operators from the pool, reducing the minimum size for which the scalable circuits are defined. Bringing together the scalable circuits and the surrogate constructed approaches forms the core of the (SC)$^2$ methodology. Our approach allows for a wider set of classical computations, on small volumes, which can be used for a more robust extrapolation protocol. While developed in the context of lattice models, the surrogate construction portion is applicable to a wide variety of problems where information about the relative importance of operators in the pool is available. As an example, we use it to compute properties of the Schwinger model - quantum electrodynamics for a single, massive fermion in $1+1$ dimensions - and show that our method can be used to accurately extrapolate to the continuum limit.

Gustafson, Erik [RIACS, Mtn. View] (ORCID:00000001↗

High Velocity Joining of Multi-material Stacks Containing 3rd Generation Advanced High-Strength Stainless Steel and Aluminum Extrusion and Casting (Abstract)

Advanced lightweight materials, including multi-phase steels, aluminum extrusions and aluminum castings, have increasingly replaced mild steel to meet original equipment manufacturer (OEM) demand for increased fuel economy and crash-safety requirements. Third Generation (Gen 3) AHSS provides a superior combination of strength and ductility for crash energy management components in the vehicle body-in-white (BIW). Aluminum extrusions are widely used for bumper, door rocker panel, cradle and battery frame applications. Aluminum castings are increasingly being used in electric vehicles to provide part consolidation, weight saving and increased driving range. Rocker panels are, for example, an important component of the battery electric vehicle (BEV) body structure. The rocker panel serves several purposes, including structural support, crash resistance, protection for the vehicle's underbody and battery tray, and contributing to the overall aesthetics. In order to reduce weight, rocker panels are usually constructed using outer panels consisting of 3rd generation advanced high strength steels (AHSS) and an inner multicell aluminum extrusion structure for energy absorption which protects the batteries in a crash event. It is well known, however, that these material combinations provide significant challenges for joining and are susceptible to liquid metal embrittlement and loss of strength. The overall goal is to find a solution that addresses these challenges in order to produce multi-material vehicle components with reduced weight and minimal galvanic and recyclability issues. The approach being proposed here is to utilize a novel high velocity (HiVe) riveting and clinching technique recently demonstrated by Pacific Northwest National Laboratory (PNNL) to join (2T/3T) sheets of aluminum alloys and steel. This process will not only address the aforementioned challenges but also help significantly reduce the joining cycle time. This work will also demonstrate use of HiVe assemblies to be retrofitted to existing body-shop robots thus having minimal impact to existing body shop operations.

36 MATERIALS SCIENCE↗

The Dual-Axis Radiographic Hydrodynamic Test Facility Capability Expansion (DCX) Strategy

The Dual-Axis Radiographic Hydrodynamic Test (DARHT) facility is a vital and important part of the Nation’s nuclear security enterprise. With more than two decades of operations, DARHT has a storied history. Conceived in the 1970s, constructed in the 1990s, and operational since 2000, DARHT has advanced from open-air hydrodynamic experiments (hydros) to foam-confined hydros, to vessel-confined hydros, and in 2022, the 75th hydro was successfully completed. Radiography has advanced from a single-axis, single-pulse system to a dual-axis, multi-pulse capability to variable fields of view (VFV) on both accelerators. The culmination of these experiences, accomplishments, and advancements has brought us to a very important question: What do the next two decades at DARHT look like? The world is not the same place it was in the 1990s when construction at DARHT was in progress. Evolving threats, an expanding mission, and technology changes necessitate adaptation. To adapt, the aging facility, accelerators, vessels, and detector systems require improvements to ensure DARHT remains the Nation’s hydrodynamic data foundation for stockpile certification, safety, surety, and global security threats.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

The Dual-Axis Radiographic Hydrodynamic Test Facility Capability eXpansion (DCX) Strategy

The Dual-Axis Radiographic Hydrodynamic Test (DARHT) facility is a vital and important part of the Nation’s nuclear security enterprise. The Department of Energy/National Nuclear Security Administration (DOE/ NNSA) Stockpile Stewardship Management Plan (SSMP) identifies DARHT as a weapons mission critical facility along with the need to modernize DARHT to support weapons modernization efforts. With more than two decades of operations, DARHT has a storied history. Conceived in the 1970s, constructed in the 1990s, and operational since 2000, DARHT has advanced from open-air hydrodynamic experiments (hydros) to foam-confined hydros, to vessel-confined hydros, and in 2022, the 75 th hydro was successfully completed. Radiography has advanced from a single-axis, single-pulse system to a dual-axis, multi-pulse capability to variable fields of view (VFV) on both accelerators. The culmination of these experiences, accomplishments, and advancements has brought us to a very important question: What do the next two decades at DARHT look like? The world is not the same place it was in the 1990s when construction at DARHT was in progress. Evolving threats, an expanding mission, and technology changes necessitate adaptation. The 2018 Nuclear Posture Review (NPR) states that the nuclear weapons infrastructure has suffered the effects of age and underfunding with no margin for further delay in recapitalizing the physical infrastructure. To adapt, the aging facility, accelerators, vessels, and detector systems require improvements to ensure DARHT remains the Nation’s hydrodynamic data foundation for stockpile certification, safety, surety, and global security threats.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

Constraining Kick Signals Through Advanced Multi-Phase Data

<ul><li>Re-designed ambient experimental apparatus constructed and operational</li><li>Finalized design of elevated experiments w/ LSU</li><li>Shakedown reveals that current sensors do not respond to changes in gas content</li><li>Designing surrogate sensor(s) w/ LSU</li><li>Implemented a sequence anomaly detection algorithm to identify kicks</li></ul>

Carney, Janine↗

CRISPR Tools for Engineering Prokaryotic Systems: Recent Advances and New Applications

In the past decades, the broad selection of CRISPR-Cas systems has revolutionized biotechnology by enabling multimodal genetic manipulation in diverse organisms. Rooted in a molecular engineering perspective, we recapitulate the different CRISPR components and how they can be designed for specific genetic engineering applications. We first introduce the repertoire of Cas proteins and tethered effectors used to program new biological functions through gene editing and gene regulation. We review current guide RNA (gRNA) design strategies and computational tools and how CRISPR-based genetic circuits can be constructed through regulated gRNA expression. Then, we present recent advances in CRISPR-based biosensing, bioproduction, and biotherapeutics across in vitro and in vivo prokaryotic systems. Finally, we discuss forthcoming applications in prokaryotic CRISPR technology that will transform synthetic biology principles in the near future.

59 BASIC BIOLOGICAL SCIENCES↗

Radiative classical gravitational observables at $ \mathcal{O} $(G 3 ) from scattering amplitudes

We compute classical gravitational observables for the scattering of two spinless black holes in general relativity and N =8 supergravity in the formalism of Kosower, Maybee, and O’Connell (KMOC). We focus on the gravitational impulse with radiation reaction and the radiated momentum in black hole scattering at $ \mathcal{O} $(G 3 ) to all orders in the velocity. These classical observables require the construction and evaluation of certain loop-level quantities which are greatly simplified by harnessing recent advances from scattering amplitudes and collider physics. In particular, we make use of generalized unitarity to construct the relevant loop integrands, employ reverse unitarity, the method of regions, integration-by-parts (IBP), and (canonical) differential equations to simplify and evaluate all loop and phase-space integrals to obtain the classical gravitational observables of interest to two-loop order. The KMOC formalism naturally incorporates radiation effects which enables us to explore these classical quantities beyond the conservative two-body dynamics. From the impulse and the radiated momentum, we extract the scattering angle and the radiated energy. Finally, we discuss universality of the impulse in the high-energy limit and the relation to the eikonal phase.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗