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NASA NTRS2007

Convergent Close-Coupling Approach to Electron-Atom Collisions

It was with great pleasure and honour to accept the invitation to make a presentation at the symposium celebrating the life-long work of Aaron Temkin and Richard Drachman. The work of Aaron Temkin was particularly influential on our own during the development of the CCC method for electron-atom collisions. There are a number of key problems that need to be dealt with when developing a general computational approach to such collisions. Traditionally, the electron energy range was subdivided into the low, intermediate, and high energies. At the low energies only a finite number of channels are open and variational or close-coupling techniques could be used to obtain accurate results. At high energies an infinite number of discrete channels and the target continuum are open, but perturbative techniques are able to yield accurate results. However, at the intermediate energies perturbative techniques fail and computational approaches need to be found for treating the infinite number of open channels. In addition, there are also problems associated with the identical nature of electrons and the difficulty of implementing the boundary conditions for ionization processes. The beauty of the Temkin-Poet model of electron-hydrogen scattering is that it simplifies the full computational problem by neglecting any non-zero orbital angular momenta in the partial-wave expansion, without loosing the complexity associated with the above-mentioned problems. The unique nature of the problem allowed for accurate solution leading to benchmark results which could then be used to test the much more general approaches to electron-atom collision problems. The immense value of the Temkin-Poet model is readily summarised by the fact that the initial papers of Temkin and Poet have been collectively cited around 250 times to date and are still being cited in present times. Many of the citations came from our own work during the course of the development of the CCC method, which we now describe.

Bray, Igor↗

NASA NTRS2003

A Dynamic Risk Model for Evaluation of Space Shuttle Abort Scenarios

The Space Shuttle is an advanced manned launch system with a respectable history of service and a demonstrated level of safety. Recent studies have shown that the Space Shuttle has a relatively low probability of having a failure that is instantaneously catastrophic during nominal flight as compared with many US and international launch systems. However, since the Space Shuttle is a manned. system, a number of mission abort contingencies exist to primarily ensure the safety of the crew during off-nominal situations and to attempt to maintain the integrity of the Orbiter. As the Space Shuttle ascends to orbit it transverses various intact abort regions evaluated and planned before the flight to ensure that the Space Shuttle Orbiter, along with its crew, may be returned intact either to the original launch site, a transoceanic landing site, or returned from a substandard orbit. An intact abort may be initiated due to a number of system failures but the highest likelihood and most challenging abort scenarios are initiated by a premature shutdown of a Space Shuttle Main Engine (SSME). The potential consequences of such a shutdown vary as a function of a number of mission parameters but all of them may be related to mission time for a specific mission profile. This paper focuses on the Dynamic Abort Risk Evaluation (DARE) model process, applications, and its capability to evaluate the risk of Loss Of Vehicle (LOV) due to the complex systems interactions that occur during Space Shuttle intact abort scenarios. In addition, the paper will examine which of the Space Shuttle subsystems are critical to ensuring a successful return of the Space Shuttle Orbiter and crew from such a situation.

Henderson, Edward M.↗

NASA NTRS2016

Expanding the Envelope of UAS Certification: What it Takes to Type Certify a UAS for Precision Agricultural Spraying

One of the key challenges to the development of a commercial Unmanned Air-craft System (UAS) market is the lack of explicit consideration of UAS in the current regulatory framework. Despite recent progress, additional steps are needed to enable broad UAS types and operational models. This paper discusses recent research that examines how a risk-based approach for safety might change the process and substance of airworthiness requirements for UAS. The project proposed risk-centric airworthiness requirements for a midsize un-manned rotorcraft used for agricultural spraying and also identified factors that may contribute to distinguishing safety risk among different UAS types and operational concepts. Lessons learned regarding how a risk-based approach can expand the envelope of UAS certification are discussed.

Maddalon, J. M.↗

NASA NTRS2019

Comparison of Electrical Output Format Options for the Analysis of Strain-Gage Balance Calibration Data

Fundamental characteristics of three gage output formats are discussed that may be used to both interpret and analyze wind tunnel strain-gage balance data. The first output format uses raw outputs, i.e., absolute voltage measurements, for the analysis. This choice requires an intercept term in the regression model of the outputs if the Iterative Method is chosen for the load prediction. Raw outputs can be used for the analysis of all known output characteristics as long as the Iterative Method is applied. However, raw outputs cannot be used to analyze data of a balance with bi-directional outputs if the Non-Iterative Method is chosen for the analysis. The second output format, i.e., difference type 1, uses the difference between raw outputs and the natural zeros of the balance gages for the analysis. In this case, the use of the intercept term becomes optional. Analysis results for difference type 1 will exactly match analysis results obtained by using raw outputs as long as identical math models are used for the regression analysis. In addition, difference type 1 may be used to analyze data of a balance with bi directional outputs if an analyst prefers to process data using the Non-Iterative Method. The third output format, i.e., difference type 2, uses the difference between raw outputs and the outputs of the zero load point of a load series for the data analysis. The application of this format is only recommended if the maximum magnitude of all tare loads of a given balance calibration data set is less than two percent of capacity. Data from the calibration of a force balance is used to illustrate the application of the three gage output formats.

Wind Tunnel Strain-Gage Balance↗

NASA NTRSDate not supplied

Evaluation of Aerosol Data Assimilation and Forecasts in the NASA GEOS Model during the ASIA-AQ Campaign

Fine particulate matter (PM2.5) poses significant risks to human health and the environment by penetrating the lungs and causing respiratory and cardiovascular diseases, making it crucial to understand its sources and behavior for effective air quality management. The Goddard Earth Observing System (GEOS) Forward Processing (FP) system model, operated by the Global Modeling and Assimilation Office (GMAO) at NASA's Goddard Space Flight Center, provides real-time weather and aerosol analyses and forecasts. In addition to meteorological data assimilation, the GEOS-FP system also assimilates aerosol using Moderate Resolution Imaging Spectroradiometer (MODIS) Aerosol Optical Depth (AOD) and Aerosol Robotic Network (AERONET) AOD data. In this study, the aerosol data assimilation and forecasts performance of the GEOS-FP model were evaluated for predicting PM2.5 in Korea using observations from the Airborne and Satellite Investigation of Asian Air Quality (ASIA-AQ) campaign. The ASIA-AQ campaign, an international collaborative field study initiative, aims to enhance understanding of local air quality issues and address common challenges in interpreting satellite data and air quality modeling. Conducted in South Korea from February 15 to March 13, 2024, during the high PM2.5 concentration winter season, this campaign provided extensive airborne and ground observations for intensive analysis of PM2.5 model simulations. We demonstrate how the assimilation runs and the forecasting performance of PM2.5 at 24-hour and 48-hour intervals vary. Additionally, we analyzed the differences and characteristics of PM2.5 composition in cases of long-range transport and local emissions. Using ASIA-AQ airborne data, we also examined the vertical profile of fine particulate matter. Through the intensive observations of this campaign, the GEOS model was assessed over South Korea using both in situ and airborne measurements to establish a baseline and identify priorities for future development.

Seunghee Lee↗

NASA NTRS2017

Future ATM Concepts Evaluation Tool (FACET) Interface Control Document

This Interface Control Document (ICD) documents the airspace adaptation and air traffic inputs of NASA's Future ATM Concepts and Evaluation Tool (FACET). Its intended audience is the project manager, project team, development team, and stakeholders interested in interfacing with the system. FACET equips Air Traffic Management (ATM) researchers and service providers with a way to explore, develop and evaluate advanced air transportation concepts before they are field-tested and eventually deployed. FACET is a flexible software tool that is capable of quickly generating and analyzing thousands of aircraft trajectories. It provides researchers with a simulation environment for preliminary testing of advanced ATM concepts. Using aircraft performance profiles, airspace models, weather data, and flight schedules, the tool models trajectories for the climb, cruise, and descent phases of flight for each type of aircraft. An advanced graphical interface displays traffic patterns in two and three dimensions, under various current and projected conditions for specific airspace regions or over the entire continental United States. The system is able to simulate a full day's dynamic national airspace system (NAS) operations, model system uncertainty, measure the impact of different decision-makers in the NAS, and provide analysis of the results in graphical form, including sector, airport, fix, and airway usage statistics. NASA researchers test and analyze the system-wide impact of new traffic flow management algorithms under anticipated air traffic growth projections on the nation's air traffic system. In addition to modeling the airspace system for NASA research, FACET has also successfully transitioned into a valuable tool for operational use. Federal Aviation Administration (FAA) traffic flow managers and commercial airline dispatchers have used FACET technology for real-time operations planning. FACET integrates live air traffic data from FAA radar systems and weather data from the National Weather Service to summarize NAS performance. This information allows system operators to reroute flights around congested airspace and severe weather to maintain safety and minimize delay. FACET also supports the planning and post-operational evaluation of reroute strategies at the national level to maximize system efficiency. For the commercial airline passenger, strategic planning with FACET can result in fewer flight delays and cancellations. The performance capabilities of FACET are largely due to its architecture, which strikes a balance between flexibility and fidelity. FACET is capable of modeling the airspace operations for the continental United States, processing thousands of aircraft on a single computer. FACET was written in Java and C, enabling the portability of its software to a variety of operating systems. In addition, FACET was designed with a modular software architecture to facilitate rapid prototyping of diverse ATM concepts. Several advanced ATM concepts have already been implemented in FACET, including aircraft self-separation, prediction of aircraft demand and sector congestion, system-wide impact assessment of traffic flow management constraints, and wind-optimal routing.

FACET↗

NASA NTRS2003

Definition of International GPM GV Research Program

The Global Precipitation Measurement (GPM) Mission will consist of a constellation of rain-measuring satellites, the main member of which (the core satellite) will serve as the measurement reference to the other members of the constellation. The core satellite is being developed jointly by the National Aeronautics and Space Administration (NASA) and the newly-named Japan Aerospace Exploration Agency (JAXA -- previously NASDA) along with its government partner, the Communications Research Laboratory (CRL). The GPM mission was proposed as a follow-up mission to the Tropical Rainfall Measuring Mission (TRMM) by both NASA and NASDA based on the unparalleled scientific success of TRMM, and has recently been joined by the European Space Agency (ESA) via its formulation of the European GPM mission (i.e., EGPM). GPM is an ambitious mission designed to produce accurate and frequent global observations of precipitation (both rain and snow) made possible by replacing the TRMM satellite with the new core satellite carrying an advanced radar-radiometer system, and serving as the centerpiece for the constellation of some eight (8) additional satellites being provided through international cooperation. The core satellite is to be flown up to high latitudes (inclined some 65-70 degrees), and will carry a Ku/Ka-band, nadir-scanning, dual-frequency precipitation radar (DPR) that is being developed by JAXA and CRL, along with a large aperture, extended frequency-range, conically-scanning passive microwave radiometer being developed by NASA and its industrial partners. Each constellation satellite will also carry some type of multi-channel passive microwave radiometer (as well as a multi-beam Ka-band radar in the case of EGPM) whose rain estimates will be calibrated and referenced to those made by the core satellite, producing for the first time fully-global, continuous, and bias-free precipitation datasets. GPM data will be delivered in near-realtime, taking a major step toward the operational use of precipitation information for model initialization and data assimilation in a number of application areas such as hazardous weather forecasting, flood warning, fresh water resource assessment, and crop growth prediction. In addition, GPM data will complement the now-existing global temperature record, allowing for improved assessments of climate change, particularly those processes in which the global water cycle both forces and responds to climatic drifts in global temperature conditions. A foremost element of this international constellation mission is a parallel international ground validation (GV) network. This GV network is needed to determine uncertainties in the rain retrievals, critical for application of the retrieval information in weather and hydrometeorological modeling and climate diagnostics, as well as assurances that the satellite retrievals of surface rainfall are consistent with those actually measured at the surface. The key aspects of this network is that it must be worldwide and created through the GPM partnership process. Therefore the network will consist of a confederation of government agencies, academic organizations, private institutions, and individual scientists from a collection of nations who have initiated the process by gathering in Abingdon to develop the fundamentals of the international GPM GV research programme. Therefore in keeping with our responsibilities as the front-runners of the programme, the main objectives of this workshop are: (1) to present and share opinions on interests, perspectives, and concerns about GPM GV research; (2) to examine the conceptual and/or planned GPM GV site templates from NASA, NASDA, ESA, and other partners; (3) to define the main scientific objectives of the international GPM GV research programme; (4) to formulate a preliminary set of international GPM GV science and measurement requirements; and (5) to convene a Steering Committee to aid the organization of the GPM GV program, to document its science implementation plans, and to aid planning for follow-up GPM GV meetings.

Smith, Eric A.↗

DOE OSTI2025

Performance evaluations of signed and unsigned noisy approximate quantum Fourier arithmetic

The Quantum Fourier Transform (QFT) grants competitive advantages, especially in resource usage and circuit approximation, for performing arithmetic operations on quantum computers, and offers a potential route toward a numerical quantum-computational paradigm. In this paper, we utilize efficient techniques to implement QFT-based integer addition and multiplications. These operations are fundamental to various quantum applications including Shor’s algorithm, weighted-sum optimization problems in data processing and machine learning, and quantum algorithms requiring inner products. We carry out performance evaluations of these implementations based on IBM’s superconducting-qubit architecture using different compatible noise models. We isolate the sensitivity of the component quantum circuits on both one-/two-qubit gate error rates, and the number of the arithmetic operands’ superposed integer states. We analyze performance and identify the most effective approximation depths for unsigned quantum addition and quantum multiplication within the given context. We then perform a similar analysis of signed addition and compare to the unsigned results. We observe significant dependency of the optimal approximation depth on the degree of machine noise and the number of superposed states in certain performance regimes. Finally, we elaborate on the algorithmic challenges—relevant to signed, unsigned, modular and non-modular versions—that could also be applied to current implementations of QFT-based subtraction, division, exponentiation, and their potential tensor extensions. Here, we analyze the performance trends in our results and speculate on possible future developments within this computational paradigm.

Computational models↗

NASA NTRS1998

Study of a Wake Recovery Mechanism in a High-Speed Axial Compressor Stage

This work addresses the significant differences in compressor rotor wake mixing loss which exist in a stage environment relative to a rotor in isolation. The wake decay for a rotor in isolation is due solely to viscous dissipation which is an irreversible process and thus leads to a loss in both total pressure and efficiency. Rotor wake decay in the stage environment is due to both viscous mixing and the inviscid strain imposed on the wake fluid particles by the stator velocity field. This straining process, referred to by Smith (1993) as recovery, is reversible and for a 2D rotor wake leads to an inviscid reduction of the velocity deficit of the wake. A model for the rotor wake decay process is developed and used to quantify the viscous dissipation effects relative to those of inviscid wake stretching. The model is verified using laser anemometer measurements acquired in the wake of a transonic rotor operated in isolation and in a stage configuration at near peak efficiency and near stall operating conditions. Additional insight is provided by a time-accurate 3D Navier-Stokes simulation of the compressor stator flow field at the corresponding stage loading levels. Results from the wake decay model exhibit good agreement with the experimental data. Data from the model, laser anemometer measurements, and numerical simulations indicate that for the rotor/stator spacing used in this work, which is typical of core compressors, rotor wake straining (stretching) is the primary decay process in the stator passage with viscous mixing playing only a minor role. The implications of these results on compressor stage design are discussed.

VanZante, Dale E.↗

NASA NTRS2014

An Investigation of Low Earth Orbit Internal Charging

Low Earth orbit is usually considered a relatively benign environment for internal charging threats due to the low flux of penetrating electrons with energies of a few MeV that are encountered over an orbit. There are configurations, however, where insulators and ungrounded conductors used on the outside of a spacecraft hull may charge when exposed to much lower energy electrons of some 100's keV in a process that is better characterized as internal charging than surface charging. For example, the minimal radiation shielding afforded by thin thermal control materials such as metalized polymer sheets (e.g., aluminized Kapton or Mylar) and multilayer insulation may allow electrons of 100's of keV to charge underlying materials. Yet these same thermal control materials protect the underlying insulators and ungrounded conductors from surface charging currents due to electrons and ions at energies less than a few keV as well as suppress the photoemission, secondary electron, and backscattered electron processes associated with surface charging. We investigate the conditions required for this low Earth orbit "internal charging" to occur and evaluate the environments for which the process may be a threat to spacecraft. First, we describe a simple one-dimensional internal charging model that is used to compute the charge accumulation on materials under thin shielding. Only the electron flux that penetrates exposed surface shielding material is considered and we treat the charge balance in underlying insulation as a parallel plate capacitor accumulating charge from the penetrating electron flux and losing charge due to conduction to a ground plane. Charge dissipation due to conduction can be neglected to consider the effects of charging an ungrounded conductor. In both cases, the potential and electric field is computed as a function of time. An additional charge loss process is introduced due to an electrostatic discharge current when the electric field reaches a prescribed breakdown strength. For simplicity, the amount of charge lost in the discharge is treated as a random percentage of the total charge between a set maximum and minimum amount so a user can consider partial discharges of insulating materials (small loss of charge) or arcing from a conductor (large loss of charge). We apply the model to electron flux measurements from the NOAA-19 spacecraft to demonstrate that charging can reach levels where electrostatic discharges occur and estimate the magnitude of the discharge.

NeergaardParker, Linda↗

DOE OSTI2024

Deep-learning based artificial intelligence tool for melt pools and defect segmentation

Accelerating fabrication of additively manufactured components with precise microstructures is important for quality and qualification of built parts, as well as for a fundamental understanding of process improvement. Accomplishing this requires fast and robust characterization of melt pool geometries and structural defects in images. This paper proposes a pragmatic approach based on implementation of deep learning models and self-consistent workflow that enable systematic segmentation of defects and melt pools in optical images. Deep learning is based on an image-to-image translation–conditional generative adversarial neural network architecture. An artificial intelligence (AI) tool based on this deep learning model enables fast and incrementally more accurate predictions of the prevalent geometric features, including melt pool boundaries and printing-induced structural defects. We present statistical analysis of geometric features that is enabled by the AI tool, showing strong spatial correlation of defects and the melt pool boundaries. The correlations of widths and heights of melt pools with dataset processing parameters show the highest sensitivity to thermal influences resulting from laser passes in adjacent and subsequent layer passes. The presented models and tools are demonstrated on the aluminum alloy and datasets produced with different sets of processing parameters. However, they have universal quality and could easily be adapted to different material compositions. The method can be easily generalized to microstructural characterizations other than optical microscopy.

additive manufacturing↗

DOE OSTI2024

Effects of Size on Characteristics of Electroslag Remelted (ESR) HAYNES®282® alloy ingots

The effects of varying ingot diameters on the characteristics of round ESR ingots of 282 alloy are evaluated through a combined experimental and modeling study. Ingots of four different diameters --100 mm, 150 mm, 200 mm and 500 mm, were sectioned and analyzed using metallography to assess spatial variations in dendritic structure (primary / secondary dendrite arm spacings – PDAS/SDAS) across these ingots. Melt parameters of the processes were input into the simulation code, MeltFlow-ESR™ to theoretically predict PDAS/SDAS in the ingots. The values for PDAS/SDAS predicted by the simulations are compared with those measured by experiments and quantitative differences in these values are discussed in the context of the capability and limitations of the model and measurement methods. Both the predicted and measured values show that the PDAS/SDAS values increase with increasing ingot size. In addition, the relation with other ingot characteristics, such as local solidification time as well as the likelihood for freckle formation are discussed. The implication of these results for down-stream ingot processing and for ingot soundness are discussed.

Krishnamurthy, Ramanathan↗

NASA NTRS1980

The role of Ekman flow and planetary waves in the oceanic cross-equatorial heat transport

A numerical model is used to mechanistically simulate the oceans' seasonal cross-equatorial heat transport. The basic process of Ekman pumping and drift is able to account for a large amount of the cross-equatorial flux. Increased easterly wind stress in the winter hemisphere causes Ekman surface drift poleward, while decreased easterly stress allows a reduction in the poleward drift in the summer hemisphere. The addition of planetary and gravity waves to this model does not alter the net cross-equatorial flow, although the planetary waves are clearly seen. On comparison with Oort and Vonder Haar (1976), this adiabatic advective redistribution of heat is seen to be plausible up to 10-20 deg N, beyond which other dynamics and thermodynamics are indicated.

Schopf, P. S.↗

NASA NTRS2004

Properties of Minor Ions in the Solar Wind and Implications for the Background Solar Wind Plasma

The scope of the investigation is to extract information on the properties of the bulk solar wind from the minor ion observations that are provided by instruments on board NASA space craft and theoretical model studies. Ion charge states measured in situ in interplanetary space are formed in the inner coronal regions below 5 solar radii, hence they carry information on the properties of the solar wind plasma in that region. The plasma parameters that are important in the ion forming processes are the electron density, the electron temperature and the flow speeds of the individual ion species. In addition, if the electron distribution function deviates from a Maxwellian already in the inner corona, then the enhanced tail of that distribution function, also called halo, greatly effects the ion composition. This study is carried out using solar wind models, coronal observations, and ion calculations in conjunction with the in situ observations.

Wagner, William↗

DOE OSTI2024

Dynamic Modeling and Simulation of a Subcritical Coal-Fired Power Plant under Load-Following Conditions

Dynamic models for power plants that capture realistic general process trends and effects of manipulated variables are needed to improve load-following, while minimizing carbon footprint. In this work, a dynamic modeling approach and simulation results for subcritical coal-fired power plant components are presented. These encompass simulation of the dynamics in the fireside, including the effects of fuel, air combustion, and the dynamics of the entire waterside and power generation sections. This model development enables the simulation and analysis of the important short and long-time scale dynamics of components such as heaters, evaporative loop, and power generation units. Furthermore, additional variables in the power generation section are introduced to improve model accuracy, extending the prediction capability of subcritical power plant models and opening new opportunities for research in operator training, optimization, and advanced model-based controller design that are based on these models. The change in process gain for different ramp rates associated with disturbance signals that affect process variables is also explored and a correlation developed. This provides opportunities to study disturbance rejection control implementation and adaptation for scenarios with such variations in ramp rates. The prediction capabilities of selected components are compared to data available in literature, with the obtained root mean squared error ranges that reflect the model performance and quality of predictions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Decomposition and Algorithmic Approaches for Solving Large-Scale Process Family Design Problems

Our most recent work expands the water desalination case study from 76 variants to 10,897 variants using the equation-oriented model built in Pyomo as part of the PARETO project. Using the discretization formulation presented in Stinchfield (2024a), rather than solving for all 10,897 variants simultaneously, we decompose the formulation into subproblems containing subsets of variants from the process family. We solve the overall problem with Progressive Hedging (PH) deployed in parallel on a distributed HPC cluster using the open-source Python package mpi-sppy (Knueven et al., 2023). This approach allowed us to solve this process family design problem to ~1.5% relative optimality gap in about 5 hours; in comparison, Gurobi reached ~50% relative optimality gap in about 6 hours (Stinchfield et al., 2024b). However, this approach still requires discretization of the common unit module design ranges; additionally, PH acts as a heuristic for MILP’s with gap-closing capabilities. Ideally, we would not have to use ML surrogates or discretization to solve this problem, instead solving the process family design problem with the equation-oriented model directly to achieve the most accurate results. However, recall that we did not consider solving the MINLP directly due to complexity and size. In this work, we aim to decompose and solve this large-scale MINLP using a Structured Nonlinear Global Optimization algorithm presented by Cao and Zavala (2019).

Stinchfield, Georgia↗

NASA NTRS1990

Stability analysis of spacecraft power systems

The problems in applying standard electric utility models, analyses, and algorithms to the study of the stability of spacecraft power conditioning and distribution systems are discussed. Both single-phase and three-phase systems are considered. Of particular concern are the load and generator models that are used in terrestrial power system studies, as well as the standard assumptions of load and topological balance that lead to the use of the positive sequence network. The standard assumptions regarding relative speeds of subsystem dynamic responses that are made in the classical transient stability algorithm, which forms the backbone of utility-based studies, are examined. The applicability of these assumptions to a spacecraft power system stability study is discussed in detail. In addition to the classical indirect method, the applicability of Liapunov's direct methods to the stability determination of spacecraft power systems is discussed. It is pointed out that while the proposed method uses a solution process similar to the classical algorithm, the models used for the sources, loads, and networks are, in general, more accurate. Some preliminary results are given for a linear-graph, state-variable-based modeling approach to the study of the stability of space-based power distribution networks.

Halpin, S. M.↗

DOE OSTI2025

Hitting the Thermal Target for Leptophilic Dark Matter at Future Lepton Colliders

We study future lepton collider prospects for testing predictive models of leptophilic dark matter (DM) candidates with a thermal origin. We calculate experimental milestones for testing the parameter space compatible with freeze-out and the associated collider signals at past, present, and future facilities. This analysis places new limits on such models by leveraging the utility of lepton colliders. At 𝑒+⁢𝑒− machines, we make projections using precision 𝑍 -pole observables from 𝑒+⁢𝑒−→ℓ+⁢ℓ−+𝐸 signatures at large electron-positron collider and future projections for future circular collider (ee) in these channels. Additionally, a muon collider could also probe new thermal relic parameter space in this scenario via 𝜇+⁢𝜇−→𝑋+𝐸 , where 𝑋 is any easily identifiable standard model object. Collectively, these processes can probe much of the parameter space for which DM direct annihilation to ℓ+⁢ℓ− yields the observed relic density in Higgs-like models with mass-proportional couplings to charged leptons.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗