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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 199 records · Page 11

Nonlinear gyrokinetic modelling of high confinement negative triangularity plasmas

Abstract Nonlinear gyrokinetic simulations correctly predict particle as well as ion and electron energy fluxes of high confinement plasmas with a negative triangularity cross sectional shape, showing that core transport in these plasmas is well described by standard gyrokinetic models. Experimentally inferred power balance fluxes are mostly reproduced within one standard deviation across a wide portion of the minor radius. Experimental conditions are reproduced by ion scale simulations, without the need to include density and temperature profile curvature effects. The experimental case is used as baseline to predict that the non-dimensional confinement scaling in negative triangularity plasmas increases strongly with plasma current while slightly degrading at increasing normalized pressure and decreasing collisionality. Recent experiments showed that low toroidal rotation negatively impacts confinement; consistent with the experiment, simulations predict that low rotational shear significantly affects confinement unless the plasma effective charge is maintained above a minimum level. Core confinement is predicted to significantly degrade in low aspect ratio devices.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A mineral precipitation model based on the volume of fluid method

A novel volume of fluid method is presented for mineral precipitation coupled with fluid flow and reactive transport. The approach describes the fluid-solid interface as a smooth transitional region, which is designed to provide the same precipitation rate and viscous drag force as a sharp interface. Specifically, the governing equation of mineral precipitation is discretized by an upwind scheme, and a rigorous effective viscosity model is derived around the interface. The model is validated against analytical solutions for mineral precipitation in channel and ring-shaped structures. It also compares well with interface tracking simulations of advection-diffusion-reaction problems. Here, the methodology is finally employed to model mineral precipitation in fracture networks, which is challenging due to the low porosity and complex geometry. Compared to other approaches, the proposed model has a concise algorithm and contains no free parameters. In the modeling, only the pore space requires meshing, which improves the computational effciency especially for low-porosity media.

58 GEOSCIENCES↗

Techno-economic design of a linear Fresnel reflector for industrial process heat

A techno-economic model of a Concentrating Solar Thermal (CST) system using a Linear Fresnel Reflector (LFR) has been developed. LFRs can deliver process heat suitable for a range of industries, including food and beverage production. This model uses an adaptive algorithm to calculate the optimal secondary reflector shape given the geometry and optical properties of the rest of the system. A ray-tracing program is used to calculate optical efficiency over a wide range of longitudinal and transversal incidence angles and subsequently evaluate the annual efficiency at a given geographical location. A specific LFR design developed by Hyperlight Energy was modelled, and this industrial partner provided a detailed cost breakdown which was used as the basis of an economic model. Combining the technical and economic data facilitates the calculation of the Levelized Cost of Heat (LCOH). The influence of a number of parameters on the annual efficiency and LCOH is explored; notable parameters include the absorber height, the number, width, and spacing of the primary mirrors, the aim point, and the secondary reflector shape and width. By identifying an optimal combination of these parameters, we reduce the LCOH of the industry partner’s system design by 9.2%, from 14.4 $\$/MWh_{th}$ to 13.0 $\$/MWh_{th}$. In comparison, the LCOH of a natural gas boiler delivering the same annual quantity of heat is 29 $\$/MWh_{th}$, which indicates that LFRs can be a competitive heat source for industrial processes.

14 SOLAR ENERGY↗

Experiment-modeling studies comparing energy dissipation in the DIII-D SAS and SAS-VW divertors

Recent DIII-D experiments on Small Angle Slot (SAS) divertors have confirmed that a combination of divertor closure and target shaping can enhance cooling across the divertor target and increase energy dissipation, but with significant dependence on B T (toroidal magnetic field) direction. In these novel divertors, the roles of closure, target shaping, drifts, and scale lengths are all interconnected in optimizing dissipation, with the separatrix electron density n eSEP being the key parameter associated with the level of dissipation/detachment. After modifying the original flat-targeted graphite SAS to include a V shape with a tungsten coating on the outer side of the divertor (SAS-VW), matched series of discharges were run to compare to detailed SOLPS-ITER modeling. Experimentally, when run as designed with the outer strike point at the slot vertex, SAS-VW requires nearly identical n eSEP for detachment as the original SAS, with little difference in dissipation for the new geometry. This is in contrast to (1) earlier modeling predictions that a small change of the SAS geometry to a V shape should enhance dissipation at the same n eSEP for magnetic configurations having better H-mode access (ion B × ∇B drift directed into the divertor), and (2) despite the achievement of significantly higher (2-7x) neutral pressures and compression in the SAS-VW slot. Comparisons of experimental density scans to the most recent SOLPS-ITER modeling with ExB drifts show reasonable agreement for dissipation/detachment onset when using separatrix density as the independent parameter. In order to help understand the discrepancy in modeled vs actual performance for the new configuration, additional measurements varying gas injection location and impurity injection were undertaken. In-slot D 2 gas fueling is more effective (5–22 %) in promoting detachment, in accord with modeling. In-slot impurity injection (N 2 or Ne) can yield 30 % lower core Z eff and 15 % less confinement degradation after detachment compared to main chamber puffing, as well as relatively lower tungsten leakage from the divertor. Modeling can also reproduce the improved detachment seen as the strike point moves inboard of the slot vertex. While we can explain the effects of the most important parameters causing energy dissipation in these slot divertors, it remains that many aspects of their behavior cannot be accurately modeled using state-of-art codes such as SOLPS-ITER. This is of concern for future model-driven designs utilizing similar V-shaped geometries.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Nonlinear behavior of urban flood peaks in the U.S. Mid-Atlantic region

Urbanization, i.e., increasing urban development areas in a watershed, is well known as a major cause of increasing flood magnitudes. This study analyzes the observed flood peaks at 262 watersheds in the U.S. Mid-Atlantic region with varying levels of urban development and free from reservoir impacts. Our analysis reveals an interesting, V-shaped nonlinear behavior: flood peaks first decrease and then increase with increasing percentage of urban development area at the watershed scale (PDAW), with the shift occurring at a PDAW threshold of around 10%. Regression analyses suggest that the V-shaped pattern primarily results from complex interactions among climate conditions (e.g., storm-event rainfall) and landscape properties (e.g., elevation, distance to the coast). A neural network model was then developed to capture such interactions, satisfactorily reproducing the V-shaped pattern with an R-squared value of 0.58, RMSE of 6.72 mm/day, and NSE of 0.55. These findings highlight the need to account for nonlinear dynamics in flood prediction and management in the coastal environment.

flood peaks↗

Effect of particle size and moisture on flow performance of loblolly pine anatomical fractions: Experimental findings and model predictions

The rising energy demand has highlighted biomass as a promising next-generation energy source. However, commercializing biomass-derived energy faces challenges, particularly in handling biomass feedstock. Factors like particle size, shape, moisture content, and surface roughness significantly impact biomass flowability. This study addresses a crucial knowledge gap by examining the effects of particle size and moisture content on the flow behavior and shear properties of different anatomical fractions of loblolly pine (Pinus taeda). The bulk shear behavior was examined using a Schulze ring shear tester, while flow performance was tested through gravity-driven flow experiments in a variable wedge-shape hopper. Results were incorporated into empirical and machine learning-based flow prediction models to evaluate their accuracy and limitations. The study found that samples with higher moisture content show higher unconfined yield strength. The critical arching distance increased with particle size, e.g., from approximately 13 and 33 mm for 2- and 6-mm whole chips, respectively at a 32-degree inclination angle. Conversely, the flow rate decreased for a given hopper opening as particle size increased. For instance, at a 60-mm hopper opening and a 32-degree inclination angle, the mass flow rates for 2- and 6-mm whole chips were 7.83 and 6.42 tonne/h, respectively. The empirical model consistently overpredicted the mass flow rate for all anatomical fractions, while the machine learning model more accurately predicted the central tendency of flow rate but was insensitive to varying tissue proportions. These novel findings provide comprehensive characterization of anatomical fractions, reveal significant combined effects of particle size and moisture content on biomass flow behavior, and demonstrate a better predictive accuracy of a machine learning model, all of which are useful for optimizing material handling strategies and biomass utilization technologies in the industry.

09 - BIOMASS FUELS↗

Residual stress distribution in an additively manufactured complex structure by neutron diffraction measurement

Residual stress in an aerodynamically shaped Ni-based superalloy airfoil fabricated by laser powder bed fusion was measured by neutron diffraction. The experiment was conducted by considering the complex shape, implementing computer aided experiment planning, and automatic alignment at each rapid measurement. The 3-dimensional (3D) residual stress distribution in the airfoil is presented in this work, which lacks symmetry due to the complex geometry of the airfoil. In conclusion, the results provide theoretical thermal processing models a complete residual stress dataset of simulation validation on 3D shape complex structure.

Residual stress↗

End-Use Savings Shapes Measure Documentation: Boiler Replacement with Air-Source Heat Pump Boiler and Natural Gas Boiler Backup

Building on the successfully completed effort to calibrate and validate the U.S. Department of Energy's ResStock (™) and ComStock (™) models over the past three years, the objective of this work is to produce national data sets that empower analysts working for federal, state, utility, city, and manufacturer stakeholders to answer a broad range of analysis questions. The goal of this work is to develop energy efficiency, electrification, and demand flexibility end-use load shapes (electricity, gas, propane, or fuel oil) that cover a majority of the high-impact, market-ready (or nearly market-ready) measures. "Measures" refers to energy efficiency variables that can be applied to buildings during modeling. An end-use savings shape is the difference in energy consumption between a baseline building and a building with an energy efficiency, electrification, or demand flexibility measure applied. It results in a time-series profile that is broken down by end use and fuel (electricity or on-site gas, propane, or fuel oil use) at each timestep. ComStock is a highly granular, bottom-up model that uses multiple data sources, statistical sampling methods, and advanced building energy simulations to estimate the annual subhourly energy consumption of the commercial building stock across the United States. The baseline model intends to represent the U.S. commercial building stock as it existed in 2018. The methodology and results of the baseline model are discussed in the final technical report of the End-Use Load Profiles project. This documentation focuses on a single end-use savings shape measure - boiler replacement with air-source heat pump boiler with natural gas boiler backup. This measure replaces natural gas boilers for HVAC application by air-source heat pump boilers when applicable and use natural gas boiler backup when the heat pump boiler could not operate due to outdoor air conditions which are below its cutoff temperature. This measure helps to quantify the decarbonization as well as the energy savings potential from the replacement. The measure resulted higher savings in natural gas consumption compared to the increase in electricity consumption, with a ratio of 3. The total natural gas energy consumption was reduced by 41%, whereas the total electricity consumption was increased by 5.3%.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Divertor shaping with neutral baffling as a solution to the tokamak power exhaust challenge

Exhausting power from the hot fusion core to the plasma-facing components is one fusion energy’s biggest challenges. The MAST Upgrade tokamak uniquely integrates strong containment of neutrals within the exhaust area (divertor) with extreme divertor shaping capability. By systematically altering the divertor shape, this study shows the strongest evidence to date to our knowledge that long-legged divertors with a high magnetic field gradient (total flux expansion) deliver key power exhaust benefits without adversely impacting the hot fusion core. These benefits are already achieved with relatively modest geometry adjustments that are more feasible to integrate in reactor designs. Benefits include reduced target heat loads and improved access to, and stability of, a neutral gas buffer that ‘shields’ the target and enhances power exhaust (detachment). Analysis and model comparisons shows these benefits are obtained by combining multiple shaping aspects: long-legged divertors have expanded plasma-neutral interaction volume that drive reductions in particle and power loads, while total flux expansion enhances detachment access and stability. Containing the neutrals in the exhaust area with physical structures further augments these shaping benefits. These results demonstrate strategic variation in the divertor geometry and magnetic topology is a potential solution to one of fusion’s power exhaust challenge.

magnetically confined plasmas↗

Deep learning for time series forecasting: a survey of recent advances

Time series forecasting plays a critical role in numerous real-world applications, such as finance, healthcare, transportation, and scientific computing. In recent years, deep learning has become a powerful tool for modeling complex temporal patterns and improving forecasting accuracy. This survey provides an overview of recent deep learning approaches for time series forecasting, involving various architectures including RNNs, CNNs, GNNs, transformers, large language models, MLP-based models, and diffusion models. We first identify key challenges in the field, such as temporal dependency, efficiency, and cross-variable dependency, which drive the development of forecasting techniques. Then, the general advantages and limitations of each architecture are discussed to contextualize their adaptation in time series forecasting. Furthermore, we highlight promising design trends like multi-scale modeling, decomposition, and frequency-domain techniques, which are shaping the future of the field. This paper serves as a compact reference for researchers and practitioners seeking to understand the current landscape and future trajectory of deep learning in time series forecasting.

97 MATHEMATICS AND COMPUTING↗

Evidence for the Collective Nature of Radial Flow in Pb+Pb Collisions with the ATLAS Detector

Anisotropic flow and radial flow are two key probes of the expansion dynamics and properties of the quark-gluon plasma (QGP). While anisotropic flow has been extensively studied, radial flow, which governs the system’s radial expansion, has received less attention. Notably, direct experimental evidence for the global and collective nature of radial flow fluctuations has been lacking. This Letter presents the first measurement of transverse momentum (𝑝 T ) dependence of radial flow fluctuations (𝑣 0 ⁡(𝑝 T )) over 0.5 < 𝑝 T < 10 GeV and demonstrates its collective nature using a two-particle correlation method in Pb+Pb collisions at $\sqrt{𝑠_{NN}}$ = 5.02 TeV. The data reveal three key features supporting the collective nature of radial flow: long-range correlation in pseudorapidity, factorization in 𝑝 T , and centrality-independent shape in 𝑝 T . The comparison with a hydrodynamic model demonstrates the sensitivity of 𝑣 0 ⁡(𝑝 T ) to bulk viscosity, a crucial transport property of the QGP. These findings establish a new, powerful tool for probing collective dynamics and properties of the QGP.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Multi-Factor-Coupled, Ahead-of-Time Aggregation of Power Flexibility Under Forecast Uncertainty

The increasing penetration of distributed energy resources (DERs) is significantly reshaping the role of distribution systems under active energy management. To aggregate the active-reactive power flexibility of DERs dispersed at the feeder and provide capacity support to the transmission system, it is essential to efficiently identify feasible substation power injection trajectories. This paper introduces a novel ahead-of-time flexibility characterization method to address it. First, a polyhedral non-feeder-level power flexibility region (PFR) is constructed, accounting for various time-dependent, power-coupled, and forecast error uncertainties. Then, a polyhedral feeder-level PFR is analytically derived through a coordinate transformation, which can reveal the uncertainty propagation path, i.e., how uncertainty applies to the feeder-level PFR. To facilitate the high-level application, a tractable chance-constrained Chebyshev centering optimization model is further developed to find a ball-shaped inner approximation of the feeder-level PFR. Finally, the proposed method is validated on a modified IEEE 123-bus test system. Here, both theoretical and experimental results show that, with appropriate robustness parameter settings, the proposed method can make the approximated PFR less conservative with abundant robustness against forecast error uncertainty.

24 POWER TRANSMISSION AND DISTRIBUTION↗

TEAMER – Harvesting Subsea Water Motion to Provide Clean Electrical Power (Abstract)

Power generation from vortex induced vibration (VIV) is an emerging field with new technologies that are just beginning to be field tested. In this TEAMER project, WITT Energy will be field testing the power production of its pendulum system in two different configurations to evaluate its performance. The amount of power produced by a VIV instrument depend on the frequency at which it vibrates. The vibrational frequency is controlled by the device shape and its interaction with the flow velocity. Computer models are used to predict vibration frequencies as a function of flow velocity but they may be inaccurate due to complicated bathymetry and bottom roughness that is not captures by the models. This project will test the WITT VIV device in the Sequim Bay channel over a range of tidal velocities. Two tests will be completed with different pipe lengths that are expected to vary the vibrational frequency and therefore the power produced. PNNL will use an acoustic doppler current profiler (ADCP) to monitor the flow conditions during the tests. These tests will help WITT Energy evaluate how closely field operations follow computer model predictions and how best to configure their device for electricity production.

16 TIDAL AND WAVE POWER↗

Deep Learning for Fish Identification from Sonar Data (CRADA 481 Final Report)

In eastern regions of the United States, the American eel is a species of management and regulatory concern because of significant population declines, despite the species’ previous abundance in all tributaries of rivers flowing into the Atlantic Ocean. The American eel is also a candidate for listing under the U.S. Endangered Species Act. While hydropower construction and operation are only one of several factors contributing to this population decline, such a listing could impose additional regulatory challenges for a large number of hydropower projects. In this CRADA project, we improved technologies for identifying migrating eels with the goal of reducing the cost and time required for future American eel hydropower impact assessment and mitigation studies, while maintaining accuracy. We built on results from a previous FOA project (FOA# DE-FOA-0001662), led by the Electric Power Research Institute (EPRI), which developed a highly accurate, deep-learning method for identifying migrating eels from imaging sonar data. The current study aimed to further optimize this deep-learning model, originally designed for image classification, and to develop an object detection software capable of identifying fish from sonar videos in real time, enabling the detection of events like fish migrations and specific species, such as the American eel, at hydropower dams. The data conversion algorithms were packaged as software with a graphical user interface, and the software is evaluated by external collaborators. We focused on the American eel in this project and explored the transferability of the developed deep learning models to the sea lamprey, given the similar body shape and swimming behavior between the two species.

13 HYDRO ENERGY↗

End-Use Savings Shapes Measure Documentation: Boiler Replacement with Air-Source Heat Pump Boiler and Electric Boiler Backup

Building on the successfully completed effort to calibrate and validate the U.S. Department of Energy's ResStock TM and ComStock TM models over the past three years, the objective of this work is to produce national data sets that empower analysts working for federal, state, utility, city, and manufacturer stakeholders to answer a broad range of analysis questions. The goal of this work is to develop energy efficiency, electrification, and demand flexibility end-use load shapes (electricity, gas, propane, or fuel oil) that cover a majority of the high-impact, market-ready (or nearly market-ready) measures. "Measures" refers to energy efficiency variables that can be applied to buildings during modeling. An end-use savings shape is the difference in energy consumption between a baseline building and a building with an energy efficiency, electrification, or demand flexibility measure applied. It results in a time-series profile that is broken down by end use and fuel (electricity or on-site gas, propane, or fuel oil use) at each timestep. ComStock is a highly granular, bottom-up model that uses multiple data sources, statistical sampling methods, and advanced building energy simulations to estimate the annual sub hourly energy consumption of the commercial building stock across the United States. The baseline model intends to represent the U.S. commercial building stock as it existed in 2018. The methodology and results of the baseline model are discussed in the final technical report of the End-Use Load Profiles project. This documentation focuses on a single end-use savings shape measure—boiler replacement by air-source heat pump boiler. This measure replaces space heating natural gas boilers by air-source heat pump boilers when applicable and helps quantify the decarbonization as well as the energy savings potential from the replacement. The measure resulted higher savings in natural gas consumption compared to the increase in electricity consumption, with a ratio of 2.9. The total natural gas energy consumption was reduced by 20%, whereas the total electricity consumption was increased by 2.5%.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Mechanism of shape symmetry breaking in surfactant-mediated crystal growth

We present a dynamical model of crystal growth, in which it is possible to reliably achieve asymmetric products, beginning from symmetric initial conditions and growing within an isotropic environment. The asymmetric growth is the result of a positive feedback mechanism that amplifies the effect of thermal fluctuations in the coverage of surfactants on the growing crystalline facets. Within our simple model, we are able to understand the kinetic and thermodynamic factors involved in both the onset of symmetry breaking and the persistence of anisotropic growth. We demonstrate that the mechanism is general by studying models with increasing complexity. We argue that this mechanism of symmetry breaking underpins observations of colloidal, seed-mediated syntheses of single crystalline metal nanorods capped with strongly interacting surfactants. The parameters within our model are related to experimental observables such as the concentration, hydrophobicity, and binding strength of the surfactants, which suggests a potential route to optimize the yield of asymmetric products in colloidal nanoparticle syntheses.

Oaks-Leaf, Sam↗

NSA Site Science: Use of ARM Observations from Northern Alaska to Evaluate and Improve Prediction Capabilities

The Arctic is warming at a rate nearly double that of the rest of the planet, leading to profound changes in atmospheric, oceanic, and ice processes. The U.S. Department of Energy's (DOE) Atmospheric Radiation Measurement (ARM) user facility has played a significant role in Arctic research, operating observatories in Alaska's North Slope for over 25 years. These observatories provide a rich, and wide-reaching dataset that offers insight into atmospheric processes in northern Alaska. This report details the results of a nine-year research project (2015–2024) supported by the DOE Atmospheric Systems Research (ASR) program, that leverages data from ARM’s deployment of observing facilities at Utqiaġvik (known as the North Slope of Alaska, or NSA, site) and Oliktok Point, Alaska. The project was conducted in two phases: - Phase 1 (2015–2019): Focused on understanding key atmospheric processes at Oliktok Point, including cloud formation, high-latitude precipitation, aerosol-cloud interactions, and cloud properties. - Phase 2 (2019–2024): Extended the research to the broader North Slope region, using data from both Oliktok Point and Utqiaġvik. Topics explored included surface energy budgets, atmospheric stability, ice nucleation processes, and microphysics in Arctic clouds. The project resulted in numerous research products, including 50 peer-reviewed publications and dissertations, 169 presentations, and 10 data products. These products cover a variety of topics, including: - Cloud Macro- and Microphysical Properties: Arctic clouds play a crucial role in energy transfer, and accurate representation in models is critical. The study explored cloud transitions, ice crystal shapes, and dual-wavelength radar data to understand ice crystal habits and size distributions. - Aerosol Properties and Processes: The team examined aerosol sources in the Arctic, including industrial emissions and natural sources. Observations showed significant spatial gradients in aerosol concentrations due to human activities and wildfire smoke. The influence of aerosols on cloud formation and the surface energy budget was also assessed. - Aerosol-Cloud Interactions: Research revealed that aerosols might suppress cloud ice production, affecting cloud radiative forcing and precipitation. The impact of local industrial emissions on cloud properties was also investigated. - Contextualizing the North Slope of Alaska in the context of the broader Arctic: To understand broader trends, the project evaluated large-scale circulation patterns and the influence of weather systems on the Arctic. Studies indicated that large-scale processes play a significant role in temperature patterns and the timing of snowmelt. - Advancing ARM Observational and Modeling Capabilities: The project developed new radar data products and advanced measurement techniques, including clutter mitigation and drizzle detection. Uncrewed aerial systems (UAS) and tethered balloon systems (TBS) were deployed to gather detailed atmospheric data. Additionally, the project supported 10 early career scientists, providing training and mentorship to undergraduate interns, graduate students, postdoctoral researchers, and early career researchers. These efforts contributed to the advancement of ARM research capabilities and fostered a new generation of scientists skilled in Arctic atmospheric research. Ultimately, this ASR-supported project has provided valuable insights into Arctic atmospheric processes and their broader climate implications. Recommendations for future work include continuing support for long-term observing at Arctic locations to foster additional research, further exploration of aerosol-cloud interactions and the potential impacts of enhanced industrialization of the Arctic, and expanded use of uncrewed systems to gather data in this remote and harsh environment. Additionally, the data products developed by this work, and the data products developed through the ARM infrastructure, leave a treasure-trove of additional information that should be explored for many years to come to gain additional insight into physical processes in the Arctic atmosphere that drive the rapid changes occurring in at high latitudes and their global impact.

58 GEOSCIENCES↗

Charged-particle multiplicity distributions over a wide pseudorapidity range in p–Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV

This paper presents the primary charged-particle multiplicity distributions in proton–lead collisions at a centre-of-mass energy per nucleon–nucleon collision of $\sqrt{s_{NN}}$ = 5.02 TeV. The distributions are reported for non-single diffractive collisions in different pseudorapidity ranges. The measurements are performed using the combined information from the Silicon Pixel Detector and the Forward Multiplicity Detector of ALICE. The multiplicity distributions are parametrised with a double negative binomial distribution function which provides satisfactory descriptions of the distributions for all the studied pseudorapidity intervals. The data are compared to models and analyzed quantitatively, evaluating the first four moments (mean, standard deviation, skewness, and kurtosis). The shape evolution of the measured multiplicity distributions is studied in terms of KNO variables and it is found that none of the considered models reproduces the measurements. This paper also reports on the average charged-particle multiplicity, normalised by the average number of participating nucleon pairs, as a function of the collision energy. The multiplicity results are then compared to measurements made in proton–proton and nucleus–nucleus collisions across a wide range of collision energies.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗