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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 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

ssys

`ssys` is a Python toolkit for exact algebraic transformation of ordinary differential equation (ODE) models into canonical S-system or Generalized Mass Action (GMA) form. Given a model in Antimony or SBML format, `ssys` produces a mathematically equivalent representation. The transformation introduces auxiliary variables as needed to decompose a broad class of nonlinearities into products of power-law terms. The recast is exact: the original and transformed systems have identical dynamics on the invariant constraint manifold defined by auxiliary variable definitions, given consistent initial conditions.

Hlavacek, William [Los Alamos National Laboratory]↗
DOE OSTI2026

fp-tools

The output of a molecular dynamics simulation is a data file containing properties of the motion of the simulated particles as a function of time (e.g., positions, velocities). From this output, scientists can extract various properties which give insight into the physics of the system; for example, the radial distribution function can be computed from the particle positions, which gives insight into how close the system is to melting or freezing. Many publicly available codes to perform molecular dynamics simulations exist and have been well adopted by the scientific community (e.g., LAMMPS, VASP). However, it remains standard practice for scientists to write their own post-processing scripts to extract various properties of interest from the molecular dynamics simulation data. Since in many cases scientists are interested in the same set of “textbook” properties, there is a large duplication of effort in writing these post-processing scripts. Our proposed code, FP-Tools, is a C++ toolkit designed to help scientists extract and analyze quantities of interest from the output of a molecular dynamics simulation, eliminating the need for them to write these codes themselves and thus reducing this duplication of effort. The quantities which are computed by our code are well documented in the literature (either in publications or textbooks), and the algorithms we implement to compute these properties are also well known in the field. We are not introducing new science or methods here; rather, our primary goal is to provide a useful tool to the community in the form of a well-documented, easy to use package.

Hartman, Leah↗
DOE OSTI2026

HPC ODA Commons [SWR-26-003]

HPC ODA Commons is a community-driven platform for standardizing HPC operational data analytics. HPC sites generate enormous volumes of operational data - scheduler logs, accounting records, monitoring streams - but turning that data into actionable insight is needlessly hard. Each site builds bespoke parsers, schemas, and evaluation pipelines. Results can't be compared across institutions. Promising analytics ideas stay siloed because there's no shared language for describing the data, the experiments, or the outcomes. HPC ODA Commons fixes this by establishing community-governed contracts - versioned schemas, canonical artifacts, and benchmark recipes - that make ODA workflows discoverable, reproducible, and comparable. It pairs these standards with a practical, CLI-first toolkit that lets operators and researchers go from raw logs to standardized results without sending data off-cluster.

Menear, Kevin [National Laboratory of the Rockies ↗
DOE OSTI2024

Beyond PCA: Additional Dimension Reduction Techniques to Consider in the Development of Climate Fingerprints

Abstract Dimension reduction techniques are an essential part of the climate analyst’s toolkit. Due to the enormous scale of climate data, dimension reduction methods are used to identify major patterns of variability within climate dynamics, to create compelling and informative visualizations, and to quantify major named modes such as El Niño–Southern Oscillation. Principal components analysis (PCA), also known as the method of empirical orthogonal functions (EOFs), is the most commonly used form of dimension reduction, characterized by a remarkable confluence of attractive mathematical, statistical, and computational properties. Despite its ubiquity, PCA suffers from several difficulties relevant to climate science: high computational burden with large datasets, decreased statistical accuracy in high dimensions, and difficulties comparing across multiple datasets. In this paper, we introduce several variants of PCA that are likely to be of use in climate sciences and address these problems. Specifically, we introduce non-negative , sparse , and tensor PCA and demonstrate how each approach provides superior pattern recognition in climate data. We also discuss approaches to comparing PCA-family results within and across datasets in a domain-relevant manner. We demonstrate these approaches through an analysis of several runs of the E3SM climate model from 1991 to 1995, focusing on the simulated response to the Mt. Pinatubo eruption; our findings are consistent with a recently identified stratospheric warming fingerprint associated with this type of stratospheric aerosol injection.

Weylandt, Michael↗
DOE OSTI2025

Exploring Flood Predictability in Taiwan through Coupled Atmospheric–Hydrological and High-Performance Hydrodynamic Models

Effective flood simulation capabilities can tremendously support early warning and disaster prevention. To examine the applicability of a fully physics-based and high-performance flood simulation and forecasting modeling framework for a flood-prone region in Taiwan, we conduct a numerical experiment that couples the Weather Research and Forecasting (WRF) Model, WRF-Hydrological modeling system (WRF-Hydro), and the Two-Dimensional Runoff Inundation Toolkit for Operational Needs (TRITON) to perform integrated rainfall, streamflow, and flood simulations. Furthermore, we first use the coupled WRF and WRF-Hydro (WWH) to predict rainfall and streamflow and then drive TRITON with the predicted streamflow hydrographs to simulate flood depth and inundation area. With the refined spatial resolution and parameterization, this framework can better predict rainfall with reasonable spatial patterns. Although WWH could overestimate the amount of rainfall in some areas, the uncertain rainfall–streamflow predictions produce reasonable flood maps able to pinpoint regions at risk of flooding. In terms of model efficiency, the graphics processing unit–based computation can yield a speed-up factor as high as ∼13 compared to the central processing unit–based computation, promoting the efficacy of the coupled modeling framework in practical real-time flood forecasting.

Coupled models↗
DOE OSTI2024

Integrating ytopt and libEnsemble to autotune OpenMC

Ytopt is a Python machine-learning-based autotuning software package developed within the ECP PROTEAS-TUNE project. The ytopt software adopts an asynchronous search framework that consists of sampling a small number of input parameter configurations and progressively fitting a surrogate model over the input-output space until exhausting the user-defined maximum number of evaluations or the wall-clock time. libEnsemble is a Python toolkit for coordinating workflows of asynchronous and dynamic ensembles of calculations across massively parallel resources developed within the ECP PETSc/TAO project. libEnsemble helps users take advantage of massively parallel resources to solve design, decision, and inference problems and expands the class of problems that can benefit from increased parallelism. In this paper we present our methodology and framework to integrate ytopt and libEnsemble to take advantage of massively parallel resources to accelerate the autotuning process. Specifically, we focus on using the proposed framework to autotune the ECP ExaSMR application OpenMC, an open source Monte Carlo particle transport code. OpenMC has seven tunable parameters some of which have large ranges such as the number of particles in-flight, which is in the range of 100,000 to 8 million, with its default setting of 1 million. Setting the proper combination of these parameter values to achieve the best performance is extremely time-consuming. Therefore, we apply the proposed framework to autotune the MPI/OpenMP offload version of OpenMC based on a user-defined metric such as the figure of merit (FoM) (particles/s) or energy efficiency energy-delay product (EDP) on Crusher at Oak Ridge Leadership Computing Facility. In conclusion, the experimental results show that we achieve the improvement up to 29.49% in FoM and up to 30.44% in EDP.

Autotuning↗
DOE OSTI2025

Exascale workflow applications and middleware: An ExaWorks retrospective

Exascale computers offer transformative capabilities to combine data-driven and learning-based approaches with traditional simulation applications to accelerate scientific discovery and insight. However, these software combinations and integrations are difficult to achieve due to the challenges of coordinating and deploying heterogeneous software components on diverse and massive platforms. Here, we present the ExaWorks project, which addresses many of these challenges. We developed a workflow Software Development Toolkit (SDK), a curated collection of workflow technologies that can be composed and interoperated through a common interface, engineered following current best practices, and specifically designed to work on HPC platforms. ExaWorks also developed PSI/J, a job management abstraction API, to simplify the construction of portable software components and applications that can be used over various HPC schedulers. The PSI/J API is a minimal interface for submitting and monitoring jobs and their execution state across multiple and commonly used HPC schedulers. We also describe several leading and innovative workflow examples of ExaWorks tools used on DOE leadership platforms. Furthermore, we discuss how our project is working with the workflow community, large computing facilities, and HPC platform vendors to address the requirements of workflows sustainably at the exascale.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Enabling kilometer-scale E3SM land model simulation over North America: A new integrated framework solution

This study introduces a novel framework designed to enhance the performance, scalability, and portability of the kilometer-scale E3SM Land Model (km-ELM) within the E3SM modeling infrastructure. By seamlessly integrating cutting-edge data tools, we address existing challenges such as slow performance, limited scalability, and difficulties in software integration in current data-driven ELM simulation over large geographic areas. Our innovative approach leverages the KiloCraft data toolkit to generate unified inputs for simulations ranging from a single-cite case, to a 72,083-cell regional case to a continental configuration encompassing 21.6 million land grid cells at a 1 km × 1 km resolution. We conduct extensive strong- and weak-scaling experiments on three state-of-the-art supercomputers, utilizing up to 100,800 CPU cores across 2400 compute nodes to evaluate end-to-end metrics including wall-clock time, simulation-years-per-day (SYPD), initialization costs, and I/O throughput. Our results reveal the land (LND) component’s efficient scaling, demonstrating near-ideal weak scaling and strong-scaling parallel efficiencies reaching up to 87% at 50,400 cores. We confirm portability and reproducibility through bitwise-equivalent outputs across different machines using identical inputs over supported machines. Notably, at extreme scales, we identify I/O as a critical bottleneck and that leads to effective solution with the SCORPIO/ADIOS stack. Collectively, these findings validate the deployment of km-ELM at a continental scale with high parallel efficiency and provide essential guidance on configuration, decomposition, and I/O settings for optimized kilometer-scale land simulations in E3SM. This work emphasizes the innovative design and practical solutions that enhance the operational capabilities of km-ELM, focusing on software performance and scalability while leaving detailed scientific evaluations of simulated land processes for future investigations.

E3SM land model (ELM), km-ELM, scalability, perfor↗
DOE OSTI2025

Genetic tools for engineering Zymomonas mobilis , Cereibacter sphaeroides and Novosphingobium aromaticivorans to improve production of bioenergy compounds

Limited genetic tools for non-model bacteria are one of the limiting factors for genetic studies. This review compiles genetic tools used for three non-model alpha-proteobacteria, such as Zymomonas mobilis, Cereibacter (Rhodobacter) sphaeroides, and Novosphingobium aromaticivorans, which hold significant potential to produce industrially essential bioenergy compounds due to their distinctive metabolic pathways and resilience in extreme environments. Each of these strains has a unique genetic profile that enables them to efficiently carry out key reactions relevant to producing bioenergy compounds, such as converting sugars into bioenergy compounds and breaking down lignotoxins. Genetic tools can further optimize these strains for enhanced bioenergy compound production. This review explores the metabolic advantages of these organisms. It highlights the available array of genetic toolkits that can be shared among them to unlock their full potential for sustainable biofuel production.

Biofuel↗
DOE OSTI2026

Data for Development, Optimization, and Application of an Episomal Plasmid System for Rhodotorula toruloides

Rhodotorula toruloides is an emerging oleaginous yeast with strong potential as a microbial cell factory for the production of acetyl-CoA-derived bioproducts. However, engineering of this organism has been limited by the absence of a functional episomal plasmid system, a foundational genetic tool for rapid gene expression, pathway testing, and CRISPR-based genome engineering. Here, we report the first episomal plasmid system for R. toruloides . Through systematic screening of candidate autonomously replicating sequences (ARSs) from diverse sources, we identified multiple functional ARS elements and selected C63F4, a fragment derived from Contig 63 of R. toruloides CBS14, because of its stable performance. The resulting pC63F4 plasmid was maintained episomally, supported GFP reporter expression, exhibited a copy number of 2.39 ± 0.13, and showed good stability during long term cultivation. To overcome poor transformation efficiency, we developed a Cre-loxP-mediated in vivo re-circularization strategy that enabled reliable delivery of the episomal plasmid. Using this improved system, we demonstrated functional episomal expression of metabolic engineering genes and multi-gene pathways for the production of triacetic acid lactone, fatty alcohols, and limonene. Finally, we leveraged this platform to establish a redesigned CRISPR system that enables seamless genome editing in R. toruloides for the first time, while also simplifying marker recycling. Together, this work establishes a long-needed episomal plasmid platform and associated CRISPR toolkit that will accelerate metabolic engineering, synthetic biology, and fundamental studies in R. toruloides .

Gene Editing↗
DOE OSTI2025

Dataset for Leveraging CryoEM and AI-Driven Morphological Feature Analysis for Insights on Bacterial Structures

This repository hosts an AI-assisted image segmentation and analysis pipeline for Pantoea sp. YR343 cryo-electron microscopy (cryoEM) datasets. The workflow automates membrane thickness measurements, flagella detection, and field-of-view (FOV) screening from low-dose, high-resolution cryoEM micrographs eliminating the need for slow manual annotation. By integrating deep-learning based segmentation (YOLOv11) with quantitative post-processing, this toolkit provides a scalable and reproducible way to study bacterial morphology under hydrated, near-native conditions. The GitHub repository for AI-based tools for cryoEM bacteria ultrastructures can be found here: https://github.com/Sireesiru/Cryo-EM-Ultrastructures/tree/main

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

CROCUS Air Quality Data at Northeastern Illinois University Rooftop

This dataset is from the Department of Energy Office of Science funded project, Community Research on Urban and Climate Science (CROCUS) (https://crocus-urban.org/). The AQT (Vaisala AQT530) instrument provides observations on meteorological conditions, including particulate matter (PM2.5, PM10), gas species concentrations (NO, NO2, O3, CO), and environment temperature and moisture. These measurements are critical for understanding air quality. These measurements are useful for understanding changes in aerosol properties, air quality research, and comparing to model experiments especially in urban environments.Datasets are stored in the netCDF data format, and we we encourage users to make use the associated toolkits available from Unidata (https://www.unidata.ucar.edu/software/netcdf/), Project Pythia (https://foundations.projectpythia.org/core/data-formats/netcdf-cf.html), and our “Instrument Cookbooks” (https://crocus-urban.github.io/instrument-cookbooks) for more information on how to process the metadata-rich datasets.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

CROCUS Weather Data at Northeastern Illinois University Rooftop

This dataset is from the Department of Energy Office of Science funded project, Community Research on Urban and Climate Science (CROCUS) (https://crocus-urban.org/). Vaisala WXT sensor is an all-in-one weather instrument that provides 6 of the most important weather parameters: barometric pressure, temperature, relative humidity, rainfall, wind speed and direction. Temperature, pressure, relative humidity, and rainfall are sampled at 1 second frequency, while wind speed/direction is measured at ten per second (10Hz) frequency. These measurements are useful for looking at characterizing local weather, identifying unique weather events, and studying local turbulence, especially given the high temporal resolution of the wind measurements.Datasets are stored in the netCDF data format, and we we encourage users to make use the associated toolkits available from Unidata (https://www.unidata.ucar.edu/software/netcdf/), Project Pythia (https://foundations.projectpythia.org/core/data-formats/netcdf-cf.html), and our “Instrument Cookbooks” (https://crocus-urban.github.io/instrument-cookbooks) for more information on how to process the metadata-rich datasets.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

CROCUS Dual Polarization Ceilometer Data at Northeastern Illinois University Rooftop

This dataset is from the Department of Energy Office of Science funded project, CROCUS Urban Integrated Field Laboratory (https://crocus-urban.org/). The dual-polarization ceilometer (Vaisala CL61) is an autonomous lidar system operating at 910 nm wavelength, providing valuable measurements for understanding atmospheric boundary layer evolution, air quality, and cloud-aerosol interactions. The CL61 measures the backscattered signal intensity alternating between parallel- and cross-polarization signals. The unique depolarization measurement capability improves discrimination between different particle types, such as liquid droplets, ice crystals, and aerosols. The depolarization is highly dependent on the scatterer shape and orientation (spherical vs non-spherical particles), with the linear depolarization ratio providing a measure of dominant backscatter signal component from atmospheric particles at various heights, essentially allowing discrimination between liquid and solid particles. With its efficient optical system, CL61’s improved signal-to-noise ratio compared to traditional ceilometers allows studying detailed vertical profiles of aerosols and clouds up to 15 km height.Datasets are stored in a netCDF data format, and we we encourage users to make use of the associated toolkits available from Unidata (https://www.unidata.ucar.edu/software/netcdf/), Project Pythia (https://foundations.projectpythia.org/core/data-formats/netcdf-cf.html), and our “Instrument Cookbooks” (https://crocus-urban.github.io/instrument-cookbooks) for more information on how to process the metadata-rich datasets.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

CROCUS Urban Canyons - Space Science and Engineering Center (SPARC) Doppler lidar data

This is the netCDF format output from the Halo Photonics Streamline XR Doppler lidar that was deployed next to the Space Science and Engineering Center (SPARC) trailer at the University of Illnois-Chicago greenhouse parking lot during CROCUS Urban Canyons. The purpose of collecting this dataset is to provide vertical and horizontal wind profiles for studying the characteristics of turbulence over the urban canyon of Chicago. This data contains the radial velocity, intensity, and backscatter from the vertical profile, range height indicator, and sector scans that were performed over both Intensive Operating Period 1 and 2 of CROCUS Urban Canyons. There are four different types of files: * The Range Height Indicator (RHI) files contain scans that are along a constant azimuth, spanning the entire hemisphere of elevation values above the surface. * The Velocity Azimuth Display (VAD) files contain the raw radial velocity data from the 6-beam, 60 degree scans. * The User1 files contain stacked Plan Position Indicator scans over a 45 degree quadrant over downtown Chicago. * The Stare files contain vertically pointing scans. These are standard netCDF files that can be opened using xarray. The VAD scans can be processed from their raw radial velocities to horizontal wind speeds with the Atmospheric data Community Toolkit (https://arm-doe.github.io/ACT/).

EARTH SCIENCE > ATMOSPHERE > ATMOSPHERIC WINDS↗
DOE OSTI2024

Carbon Management Projects (CONNECT) Database and Explorer

Overview The Carbon Management Projects (CONNECT) Toolkit is an online exploratory visualization tool developed by the U.S. Department of Energy's (DOE) Office of Fossil Energy and Carbon Management (FECM) with support from other federal agencies such as the U.S. Environmental Protection Agency (EPA) and the U.S. Department of Transportation (DOT). It provides a single point of access to authoritative information on federal agency investment in a portfolio of research, development, and demonstration (RD&D) projects that have been publicly announced to advance technologies for point source carbon capture, carbon dioxide removal, transport, storage, and conversion, collectively referred to as carbon management. The RD&D programs covered in this tool are authorized by annual congressional appropriations ("Base Program") and the 2021 Infrastructure Investment and Jobs Act (IIJA). The tool also incorporates public information on other federal initiatives, such as the Regional Clean Hydrogen Hubs, and public information released by other government agencies, such as the Environmental Protection Agency's (EPA) and Primacy States’ Underground Injection Control Class VI permits and EPA’s facility level greenhouse gas (GHG) emissions. Developed in a geographic information system, the tool organizes carbon management projects into five groups based on the primary technology that a project aims to advance, each visually represented as a digital layer ("carbon management project layer"). Only federally funded projects are included, which can be awarded projects that are completed or ongoing, or projects that have been selected but are currently under negotiation. Project information can be viewed in the map or in the attribute table below it when turned on. In the map view, each project is displayed at either its host site (for field work), where available, or its performer site (project lead's location, further explained in the table below). Host sites and performer sites are represented in distinct icons. Several reference layers offer additional public information on infrastructural and natural resource environment for carbon management. These reference layers, combined with multiple geographical basemaps, enable users to visualize the carbon management project layers in context. Carbon management project information will be updated monthly based on feedback and information availability. Carbon management project layers Point Source Carbon Capture (PSC) This layer contains DOE-funded projects focused on capturing carbon dioxide (CO2) from power plants or industrial facilities. Carbon Dioxide Removal (CDR) This layer contains DOE-funded projects focused on capturing CO2 from the atmosphere, including direct air capture (DAC) and DAC hubs, direct ocean capture, enhanced mineralization, and biomass carbon removal and storage. For projects with multiple host sites, each of the sites are displayed individually with the project cost and cost sharing information representing the total for the entire project. Carbon Transport This layer contains DOE- and DOT-funded projects focused on CO2 transport. The Transport Research and Development sublayer contains projects that do not involve physical infrastructure; the Proposed Transport Corridor sublayer contains projects for which either a route for the transport infrastructure has been proposed or a general area for the transport infrastructure has been identified. Carbon Storage This layer contains DOE-funded key projects focused on CO2 storage. For projects with multiple field-work sites, each of the sites are displayed individually on the map with the project cost and cost sharing information representing the overall total for the entire project. Carbon Conversion This layer contains DOE-funded projects focused on converting CO2 into economically valuable products. Reference layers The following layers provide additional information in the geographic proximity of carbon management projects. Users should reference the original sources for more details (weblinks provided below and in pop-up windows on the map). Regional Clean Hydrogen Hub and Facility These layers illustrate the approximate areas of the Regional Clean Hydrogen Hubs announced by DOE's Office of Clean Energy Demonstrations (OCED) and the approximate locations of individual facilities that constitute the hubs (see "Where are the H2Hubs located?" on the webpage linked above). EPA Facility Level GHG Emissions (direct emitter) This layer shows direct CO2 emissions from stationary sources in 2022, using data extracted from EPA's Facility Level Information on GreenHouse gases Tool (FLIGHT). Captured and injected CO2 are not deducted from direct emitters’ total emissions. Contact EPA for additional details. Underground Injection Control Class VI permit/permit application This layer shows the locations of CO2 injection wells that are granted or in the process of applying for an Underground Injection Control Class VI permit by EPA or a Primacy State (currently Louisiana, North Dakota, and Wyoming). The URLs for the permits or permit applications are provided in the pop-up windows associated with the well locations. Contact EPA for additional details. Carbon Storage Resource This layer contains information on prospective CO2 storage resources in saline formations and oil and gas reservoirs provided by the National Carbon Sequestration Database and Geographic Information System (NATCARB) spatial database. Contact NETL for additional details. Existing CO2 pipeline This layer shows active CO2 pipelines based on information digitized from the map issued by the Pipeline and Hazardous Materials Safety Administration (PHMSA). Contact PHMSA for additional details.

Carbon Conversion↗
DOE OSTI2024

IDAES-PSE 2.7.0 Release

The Institute for the Design of Advanced Energy Systems (IDAES) Integrated Platform is a versatile computational environment offering extensive process systems engineering (PSE) capabilities for optimizing the design and operation of complex, interacting technologies and systems. IDAES enables users to efficiently search vast, complex design spaces to discover the lowest cost solutions while supporting the full process modeling lifecycle, from conceptual design to dynamic optimization and control. The extensible, open platform empowers users to create models of novel processes and rapidly develop custom analyses, workflows, and end-user applications. IDAES-PSE 2.7.0 Release Highlights New features: AutoScaler and CustomScalerBase classes: Such tools are the core of the new scaling framework being implemented in IDAES. Wider adoption of scaling tools among users will result in quicker and more robust model solutions. Scaler for equilibrium reactor and saponification properties: These scaler models are examples to follow for how to use the new scaling tools. ONNX Surrogate support from Optimization & Machine Learning Toolkit (OMLT): ONNX is an open standard format to save and load ML/AI models that is widely supported by all major frameworks. This capability makes it easier for IDAES users to create surrogate models and use them without having to support each framework individually. 1D Membrane Model for CO2 Capture and Utilization: Supports ongoing efforts for modeling and optimizing polymer membrane processes for CO2 capture and conversion into formic acid. StreamScaler unit model: Unrelated to the CustomScalerBase, this unit model allows a stream’s extensive variables to be scaled by a fixed factor. This allows streams being processed by multiple units in parallel to be scaled down to unit scale and scaled back up to process scale. Bug fixes or improvements: Scaling, EoS, Diagnostics tool, Modular Properties, tests & documentation Deprecations: Old Cubic EoS

AS↗
DOE OSTI2024

Computational simulations and beamline optimizations for an electron beam degrader at CEBAF

An electron beam degrader is under development with the objective of measuring the transverse and longitudinal acceptance of the Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Lab. This project is in support of the CE+BAF positron capability. Computational simulations of beam-target interactions and particle tracking were performed integrating the GEANT4 and Elegant toolkits. A solenoid was added to the setup to control the beam's divergence. Parameter optimization of the solenoid field and magnetic quadrupoles gradient was also performed to further reduce particle loss through the rest of the injector beamline.

Lizárraga-Rubio, V.↗