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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 217 records · Page 12

X-Ray Spectroscopic Studies of X-Pinch Plasmas with 3-5 Picosecond Resolution: A Quest for Clear Experimental Evidence for Radiative Collapse in the X-ray Spectra (Final Report)

Dense Z-pinch plasmas produced from current-carrying exploding wires frequently produce very brief (less than 0.1 nanosecond), intense, bursts of soft X-rays from tiny (about 1 micrometer), very hot (10-30 million K) regions of the plasma. This project addresses the physical processes that lead to those tiny, high-energy density plasmas and develops means to measure the conditions just before and during the X-ray bursts. One possible relevant process is radiative collapse, which starts if the power radiated by a dense Z-pinch, proportional to the density-squared, exceeds the resistive heating rate from the current flow, thereby cooling the plasma and enabling the magnetic pinching force to exceed the outward plasma thermal pressure. As the resulting radius reduction further increases the radiation rate, this process produces a runaway magnetic implosion. A competing mechanism is a sausage-like instability that can develop in a Z-pinch plasma at a lower current than is needed to induce radiative collapse. This mechanism can also produce tiny hot spots in the neck regions of the sausage-shaped plasma column. It is also possible that these two mechanisms work together to produce the X-ray emitting hot spots. If radiative collapse does contribute to hot spot formation, it would be terminated when the plasma becomes so dense that the radiation cannot escape, enabling the plasma kinetic pressure to build up and stop the current-driven implosion. This project aims to study the development of the hot spots by means of high temporal and spatial resolution X-ray spectroscopy to determine if there is evidence for the presence of the radiative collapse mechanism. Progress toward this goal is presented. To summarize, during the four-year period 09/15/2017 - 9/14/2021, we have collected necessary spectroscopic data to determine the plasma conditions and continue to do so. We are also now in the process of calibrating diagnostic systems (especially the x-ray streak camera system) and analyzing data to determine plasma conditions as a function of time before, during and after the X-ray burst.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Climatic and Socioeconomic Drivers of Water Use and Their Spatio‐Temporal Patterns for Small and Mid‐Sized Cities in the Contiguous United States

This study explores the drivers of urban water use and their spatial-temporal patterns in 142 small and mid-sized cities across the Contiguous United States (CONUS) by analyzing the data directly collected from these cities and using advanced machine learning techniques. We identify five distinguished clusters across CONUS, each showing unique trends of the impact of drivers on water use. We find that socioeconomic factors significantly influence water use in eastern and southwestern cities, while climatic variables such as precipitation and temperature range dominate in central and northwestern regions. Temporal analysis reveals the impacts of major socioeconomic and climatic disruptions on urban water use in the period 2011–2021, including the COVID lockdown, the rapid growth of data centers, and the drought of 2012. In addition, our analysis suggests that economic growth in small and mid-sized US cities continues to be accompanied by rising water use, contrasting with the opposite trend observed in large cities in prior studies. This implies that as smaller cities develop, their water use may increase above current levels until incomes reach a higher threshold, highlighting the need to improve water use efficiency. This study also presents useful insights for developing effective water demand management strategies in response to climatic variability and socioeconomic growth in small and mid-sized cities.

54 ENVIRONMENTAL SCIENCES↗

Quantitative probing of the fast particle motion during the solidification of battery electrodes

Synchrotron x-ray tomography represents one of the most powerful imaging techniques that can visualize the three-dimensional microstructural complexity with a high spatial resolution. To date, however, the temporal resolution of this technique has been handicapped by the intrinsic limitations in the data acquisition speed and the lack of a suitable data processing method. The present study aims to fundamentally resolve this challenge by implementing a data analysis method that is based on differentiating discrete tomography reconstruction from a continuous scan reconstruction. With this methodological development, we capture and quantify the particle motion during the solidification of battery electrodes and reveal the statistics of the dynamically evolving motion in the drying process, which has been challenging to resolve. We discover that the particle motion exhibits a strong dependence on its geometric location within a drying electrode. Our results also imply that the final electrode quality can be controlled by balancing the solvent evaporation rate and the particle mobility in the region close to the drying surface.

25 ENERGY STORAGE↗

The spatial and temporal evolution of the Portland and Tualatin forearc basins, Oregon, USA

The Portland and Tualatin basins are part of the Salish-Puget-Willamette Lowland, a 900-km-long, forearc depression lying between the volcanic arc and the Coast Ranges of the Cascadia convergent margin. Such inland seaways are characteristic of warm, young slab subduction. We analyzed the basins to better understand their evolution and relation to Coast Range history and to provide an improved tectonic framework for the Portland metropolitan area. We model three key horizons in the basins: (1) the top of the Columbia River Basalt Group (CRBG), (2) the bottom of the CRBG, and (3) the top of Eocene basement. Isochore maps constrain basin depocenters during (1) Pleistocene to mid-Miocene time (0–15 Ma), (2) CRBG (15.5–16.5 Ma), and (3) early Miocene to late Eocene (ca. 17–35 Ma) time. Results show that the Portland and Tualatin basins have distinct mid-Miocene to Quaternary depocenters but were one continuous basin from the Eocene until mid-Miocene time. A NW-striking gravity low coincident with the NW-striking, fault-bounded Portland Hills anticline is interpreted as an older graben coincident with observed thickening of CRBG flows and underlying sedimentary rocks. Neogene transpression in the forearc structurally inverted the Sylvan-Oatfield and Portland Hills normal faults as high-angle dextral-reverse faults, separating the Portland and Tualatin basins. An eastward shift of the forearc basin depocenter and ten-fold decrease in accommodation space provide temporal constraints on the emergence of the Coast Range to the west. Clockwise rotation and northward transport of the forearc is deforming the basins and producing local earthquakes beneath the metropolitan area.

15 GEOTHERMAL ENERGY↗

An experimental comparison of a space-time multigrid method with PFASST for a reaction-diffusion problem

We consider two parallel-in-time approaches applied to a (reaction) diffusion problem, possibly non-linear. In particular, we consider PFASST (Parallel Full Approximation Scheme in Space and Time) and space-time multigrid strategies. For both approaches, we start from an integral formulation of the continuous time dependent problem. Then, a collocation form for PFASST and a discontinuous Galerkin discretization in time for the space-time multi-grid are employed, resulting in the same discrete solution at the time nodes. Strong and weak scaling of both multilevel strategies are compared for varying orders of the temporal discretization. Moreover, we investigate the respective convergence behavior for non-linear problems and highlight quantitative differences in execution times

97 MATHEMATICS AND COMPUTING↗

Light-Duty Vehicle Transportation Policy and Implication on Greenhouse Gas Emissions

The transportation sector accounts for 16% of global greenhouse gas (GHG) emissions and is under formidable pressure to decarbonize. With a growing number of countries making commitments to achieve carbon neutrality or “net-zero” emissions within the next few decades, it is imperative for transportation researchers and policymakers to understand the viable pathways towards achieving carbon neutrality for light-duty transport. This chapter discusses the transportation policies and GHG emissions of the three largest markets in the world—the U.S., China, and the European Union. The life cycle GHG emissions of various vehicle technologies are evaluated while highlighting the regional and temporal differences. We then use market penetration and fleet models, developed specifically for each market, to comprehensively assess the light-duty transport energy demand and GHG emissions under various scenarios. The modeling results show that battery electric vehicles (BEVs) will increase in market share, but internal combustion engine vehicles (ICEV) will continue to dominate the passenger vehicle stock in the next 20 years under most scenarios. Improving ICEV efficiency can play a critical role in meeting GHG regulations in the near- and medium-term. BEVs, whose GHG emissions are highly dependent on the source of electricity generation, will play an essential role in the long-term as the electric grid becomes cleaner. In summary, transportation policies should be technology agnostic and consider emissions based on the whole life cycle. Moreover, a holistic approach to reducing transportation GHG emissions is key to achieving global environmental goals.

Ou, Shawn↗

eCounter: Inline Per-IP Network Monitoring at Millisecond Resolution via eBPF

Scientific data acquisition (SciDAQ) systems are shifting from archive-based workflows to streaming paradigms, where real-time, fine-grained network monitoring becomes essential. While P4-enabled devices offer per-packet in-band observability, they require specialized switches and routers. Host-side tools like Prometheus exporters lack sufficient temporal granularity. To bridge this gap, we present eCounter, a lightweight, hardware-agnostic, inline telemetry agent built on extended Berkeley Packet Filter (eBPF). eCounter captures per-interface ingress and egress traffic, categorized by IP address and protocol, at millisecond to sub-millisecond resolution. In a 100 Gbps environment, it continuously exports up to 3,257 time-series bins per second with only 4% CPU utilization at a 35¿KiB/s data rate. We evaluate eCounter across diverse NIC MTU settings, hook types, CPU architectures and operating systems, and observed negligible impact on concurrent high-throughput streaming applications. Complexity analysis confirms that it can be readily scaled to distributed SciDAQ deployments.

Mei, Xinxin [Computational Sciences and Technology↗

STSR-INR: Spatiotemporal super-resolution for multivariate time-varying volumetric data via implicit neural representation

Implicit neural representation (INR) has surfaced as a promising direction for solving different scientific visualization tasks due to its continuous representation and flexible input and output settings. We present STSR-INR, an INR solution for generating simultaneous spatiotemporal super-resolution for multivariate time-varying volumetric data. Inheriting the benefits of the INR-based approach, STSR-INR supports unsupervised learning and permits data upscaling with arbitrary spatial and temporal scale factors. Unlike existing GAN- or INR-based super-resolution methods, STSR-INR focuses on tackling variables or ensembles and enabling joint training across datasets of various spatiotemporal resolutions. Here we achieve this capability via a variable embedding scheme that learns latent vectors for different variables. In conjunction with a modulated structure in the network design, we employ a variational auto-decoder to optimize the learnable latent vectors to enable latent-space interpolation. To combat the slow training of INR, we leverage a multi-head strategy to improve training and inference speed with significant speedup. We demonstrate the effectiveness of STSR-INR with multiple scalar field datasets and compare it with conventional tricubic+linear interpolation and state-of-the-art deep-learning-based solutions (STNet and CoordNet).

97 MATHEMATICS AND COMPUTING↗

A Continental-Scale Estimate of Soil Organic Carbon Change at NEON Sites and Their Environmental and Edaphic Controls

Current carbon cycle models focus on the effects of climate and land-use change on primary productivity and microbial-mineral dependent carbon turnover in the topsoil, while less attention has been paid to vertical soil processes and soil-dependent response to land-use change along the profile. In this study, a spatial-temporal analysis was used to estimate soil organic carbon (SOC) change in topsoil/A horizon and subsoil/B horizon at National Ecological Observatory Network (NEON) sites, USA over 30 years. To separate the effects of land-use, environmental, and edaphic factors on SOC change, space-for-time substitution was used in combination with the Continuous Change Detection and Classification algorithm and Structural Equation Modeling. Results showed that (a) under natural vegetation, Spodosols and Inceptisols found in the eastern NEON sites had substantial topsoil SOC accumulation (+0.4 to +1.2 Mg C ha –1 year –1 ), while Inceptisols and Andisols in the west had a comparable magnitude of topsoil SOC loss (–0.5 to –1.8 Mg C ha –1 year –1 ); (b) Mollisols and Alfisols in the Central Plains sites were susceptible to significant SOC loss under farming and grazing; (c) Runoff/erosion and leaching potential, vertical translocation, and mineral sorption were the most important factors controlling SOC variation across the NEON sites. Our work could be used to parameterize ecosystem models simulating SOC change.

54 ENVIRONMENTAL SCIENCES↗

High-Performance Accelerator Modeling: Toward Improving Controls and Diagnostics for High-Brightness Beams in Experiment

One of the main charges of beam physics is to improve the overall beam quality delivered to experiments and applications, which is generally quantified by the beam brightness. High brightness beams have numerous applications, including x-ray free electron lasers and ultrafast electron diffraction (UED). To these ends, this thesis details efforts to use high-performance models --- high-fidelity models that execute quickly --- for controls and diagnostics. To demonstrate the generality of these techniques, this thesis focuses on three of the most successful photoinjector designs currently used worldwide: the UCLA/SLAC/BNL-type high-gradient S-band gun, the continuous-wave high-repetition rate VHF APEX gun and the L-band DESY-PITZ-type gun. Work will be shown from Pegasus (UCLA), HiRES (LBNL) and FAST (FNAL).Specifically, data-driven models for online virtual diagnostics are presented, in this case, in the context of UED at HiRES, leading to a temporal resolution improvement. Methods for improving the fidelity of physics-based models are discussed, with examples at HiRES, Pegasus and FAST. Markov-chain Monte Carlo analysis is applied to match simulations, in the context of photocathode studies at HiRES and Pegasus. Lastly, the augmentation of online model-based predictions with model-independent optimization is explored in a fluctuating environment at Pegasus and HiRES. A central theme of this dissertation is working with parameter fluctuations when modeling an accelerator beamline. Long-term drifts and shot-to-shot jitter exist in every accelerator to a varying degree and therefore play an important role in every chapter of this dissertation. This thesis attempts to address the issues associated with these fluctuations when trying to develop faithful model representations of the system.

43 PARTICLE ACCELERATORS↗

Reconciliation of asynchronous satellite-based $\mathrm{NO_2}$ and $\mathrm{XCO_2}$ enhancements with mesoscale modeling over two urban landscapes

Fossil fuel carbon dioxide (CO 2ff ), the main driver of global warming and climate change, is often co-emitted with nitrogen oxides (NO x ) and precursors to ground-level ozone from anthropogenic sources like power plants or vehicles. In urban and suburban areas, satellite-based NO 2 can be used as a proxy to track the emissions of CO 2ff . Because of NO 2 ’s shorter lifetime, urban NO 2 plumes are more distinguishable from backgrounds and more sensitive to variations in emissions. However, the combination of these two gases is limited by the asynchrony among NO 2 and CO 2 monitoring satellites. We used CO 2ff simulated by the Weather Research and Forecasting model coupled with Chemistry (WRF-Chem) model to reconcile the tropospheric NO 2 vertical column density (VCD) from the Tropospheric Monitoring Instrument (TROPOMI) and column-averaged dry-air mole fractions of carbon dioxide enhancements (ΔXCO 2 ) from Orbiting Carbon Observatory 3 (OCO-3) Snapshot Area Maps (SAMs) over a multicity area, Washington D.C.-Baltimore (DC-Balt), and a basin city, Mexico City. NO 2 /CO 2ff ratios over DC-Balt are smaller than Mexico City, indicative of stricter emission restrictions, a more combustion-efficient vehicle fleet, and higher combustion efficiency due to lower altitude in DC-Balt. For single-track cases, the spatial correlations between NO 2 and ΔXCO 2 over Mexico City are stronger than DC-Balt because the NO 2 and CO 2 are mostly trapped in the valley of Mexico City, while DC-Balt is severely affected by distant sources (i.e., US East Coast cities). Using multi-track averaging, spatial correlation coefficients increase with the number of days used for averaging. The correlations reached a maximum when averaging >12 continuous images for DC-Balt and > 10 continuous images for Mexico City. This finding indicates that multi-track averaging using modeled CO 2ff as a proxy is helpful to filter the noise in single-track images, to cancel the interference from distant sources, and to magnify correlations between NO 2 and CO 2ff . Mexico City showed stronger spatial correlations but weaker temporal correlations than DC-Balt due to biomass burning hot spots and large transport errors caused by the trapping effects of the surrounding mountains. Tracking the 20-day moving average of CO 2ff emissions using TROPOMI NO 2 seems technically feasible, considering the relationship between correlation coefficients and the number of available satellite images.

54 ENVIRONMENTAL SCIENCES↗

A FAIR-compliant parts catalogue for genome engineering and expression control in Saccharomyces cerevisiae

The synthetic biology toolkit for baker's yeast, Saccharomyces cerevisiae, includes extensive genome engineering toolkits and parts repositories. However, with the increasing complexity of engineering tasks and versatile applications of this model eukaryote, there is a continued interest to expand and diversify the rational engineering capabilities in this chassis by FAIR (findable, accessible, interoperable, and reproducible) compliance. In this study, we designed and characterised 41 synthetic guide RNA sequences to expand the CRISPR-based genome engineering capabilities for easy and efficient replacement of genomically encoded elements. Moreover, we characterize in high temporal resolution 20 native promoters and 18 terminators using fluorescein and LUDOX CL-X as references for GFP expression and OD600 measurements, respectively. Additionally, all data and reported analysis is provided in a publicly accessible jupyter notebook providing a tool for researchers with low-coding skills to further explore the generated data as well as a template for researchers to write their own scripts. We expect the data, parts, and databases associated with this study to support a FAIR-compliant resource for further advancing the engineering of yeasts.

59 BASIC BIOLOGICAL SCIENCES↗

CodEx: A Modular Framework for Joint Temporal De-Blurring and Tomographic Reconstruction

In many computed tomography (CT) imaging applications, it is important to rapidly collect data from an object that is moving or changing with time. Tomographic acquisition is generally assumed to be step-and-shoot, where the object is rotated to each desired angle, and a view is taken. However, step-and-shoot acquisition is slow and can waste photons, so in practice fly-scanning is done where the object is continuously rotated while collecting data. However, this can result in motion-blurred views and consequently reconstructions with severe motion artifacts. In this paper, we introduce CodEx, a modular framework for joint de-blurring and tomographic reconstruction that can effectively invert the motion blur introduced in sparse view fly-scanning. The method is a synergistic combination of a novel acquisition method with a novel non-convex Bayesian reconstruction algorithm. CodEx works by encoding the acquisition with a known binary code that the reconstruction algorithm then inverts. Using a well chosen binary code to encode the measurements can improve the accuracy of the inversion process. The CodEx reconstruction method uses the alternating direction method of multipliers (ADMM) to split the inverse problem into iterative deblurring and reconstruction sub-problems, making reconstruction practical to implement. Here we present reconstruction results on both simulated and binned experimental data to demonstrate the effectiveness of our method.

42 ENGINEERING↗

Depth-dependent links between microbial taxa and nitrous oxide emissions in a long-term cotton cropping system employing soil health practices

Long-term management practices can shape soil microbial communities in ways that influence nitrogen (N) dynamics and nitrous oxide (N 2 O) emissions. We leverage a 41-year continuous cotton cropping experiment with contrasting tillage, cover cropping, and N fertilization regimes to investigate how these long-term strategies influence soil microbial communities and their associations with N 2 O fluxes during the cotton growing season. Using 16S rRNA gene metabarcoding, we assessed microbial composition in surface and subsurface soils and evaluated its relationship with temporal N 2 O emissions. Among the management practices, N fertilization – a known driver of N 2 O emissions – had the strongest effect on microbial community composition and was linked to a greater number of taxa correlated to N 2 O emissions, particularly in surface soils. Soil pH emerged as a key variable influencing microbial structure across depth and was negatively associated with both N 2 O emissions and microbial composition in the surface layers of fertilized soils. In total, 57 archaeal/bacterial taxa were correlated with N 2 O fluxes, but only seven were shared across depths, suggesting distinct microbial contributors in surface and subsurface soils. Several of these taxa have been previously reported to be associated with N and C cycling processes such as nitrate respiration or carbon turnover, indicating functional context to their correlation with N 2 O fluxes. Temporal shifts in the abundance of key taxa aligned with seasonal peaks in N 2 O emissions, notably in early and late August, and were most pronounced under conventional tillage, hairy vetch cover cropping, and N fertilization. While 16S-based associations cannot confirm functional gene presence or activity, these findings demonstrate that long-term fertilization and associated soil acidification are dominant drivers of microbial shifts linked to N 2 O emissions and highlight the importance of accounting for depth-specific and seasonal microbial dynamics when evaluating management impacts on greenhouse gas emissions.

16S rRNA gene sequencing↗

Biomass carbon removal can help sustainable aviation fuels achieve on-time arrival

Biofuels, including sustainable aviation and marine fuels, and biomass carbon removal and storage (BiCRS) are often viewed as potentially competing pathways for advancing climate and energy goals. Their comparative economic, environmental, and temporal advantages remain debated. Rather than identifying a “best-use” for biomass, we show that the relative economic advantages of BiCRS versus biofuels exist along a continuum shaped by energy- and decarbonization-focused market conditions. These pathways need not be adversarial: BiCRS can enable, rather than displace, future biofuel deployment. While the lignocellulosic biofuel sector continues to face barriers associated with underdeveloped supply chains and technologies that have not yet been commercialized at scale, emerging BiCRS approaches are comparatively feedstock-flexible, rapidly deployable, and responsive to carbon removal markets. Early BiCRS deployment can help establish reliable biomass supply chains, reducing investment risk for future lignocellulosic biorefineries. By easing initial supply chain constraints, BiCRS can serve as a practical stepping stone toward meeting both near-term carbon removal needs and long-term sustainable fuel objectives under uncertain future market and policy conditions.

bioenvironmental engineering↗

Absolute Neutron Rate Measurement and Non-Thermal/Thermonuclear Fusion Differentiation

The goal of fusion energy is to produce significantly more energy from fusion reactions than is input into the device. One of the products of fusion reactions is neutrons, which, due to their lack of charge, provide a unique view into the parameters of the device. Lawrence Livermore National Laboratory (LLNL) in collaboration with the University of California, Berkeley (UCB) have designed, assembled, and fielded a robust and portable neutron detection system known as PANDA (Portable and Adaptable Neutron Diagnostics for ARPA-E). This detector suite consists of three LaBr activation detectors that are calibrated to give a total neutron yield on shot, and twenty-four scintillators coupled to photo-multiplier tubes (SPMT). The SPMTs can be configured to attain spatial, temporal and/or energy information from fusion neutrons. The system was designed to be portable and is compartmentalized so that individual components can be used at different fusion facilities. During the duration of this work, part of the system was installed at the FuZE facility, a part of Zap Energy. Another component was installed that the CESZAR facility at the University of California, San Diego (UCSD) to support experiments by Magneto-Inertial Fusion Technologies, Inc. (MIFTI). The diagnostics were successful at both locations and the LLNL/UCB team supported the data analysis by creating and running analysis scripts and Monte-Carlo calculations. At Zap Energy the diagnostics demonstrated that the fusion from the FuZE device is thermonuclear in nature, a result that resulted in an invited talk at the American Physical Society Division of Plasma Physics and an invited paper. Additionally, temporal and spatial data was taken using the SPMTs to understand the duration and length of fusion production. At UCSD the neutron yield from the diagnostics was used to show improvements to fusion yields on their gas puff Z-pinch when using a gas shell surrounding the fuel. The success in this diagnostic has led to continued work at both Zap Energy and MIFTI, as well as follow on funding and interest at other fusion energy companies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Energy storage emerging: A perspective from the Joint Center for Energy Storage Research

Energy storage is an integral part of modern society. A contemporary example is the lithium (Li)-ion battery, which enabled the launch of the personal electronics revolution in 1991 and the first commercial electric vehicles in 2010. Most recently, Li-ion batteries have expanded into the electricity grid to firm variable renewable generation, increasing the efficiency and effectiveness of transmission and distribution. Important applications continue to emerge including decarbonization of heavy-duty vehicles, rail, maritime shipping, and aviation and the growth of renewable electricity and storage on the grid. This perspective compares energy storage needs and priorities in 2010 with those now and those emerging over the next few decades. The diversity of demands for energy storage requires a diversity of purpose-built batteries designed to meet disparate applications. Advances in the frontier of battery research to achieve transformative performance spanning energy and power density, capacity, charge/discharge times, cost, lifetime, and safety are highlighted, along with strategic research refinements made by the Joint Center for Energy Storage Research (JCESR) and the broader community to accommodate the changing storage needs and priorities. Innovative experimental tools with higher spatial and temporal resolution, in situ and operando characterization, first-principles simulation, high throughput computation, machine learning, and artificial intelligence work collectively to reveal the origins of the electrochemical phenomena that enable new means of energy storage. This knowledge allows a constructionist approach to materials, chemistries, and architectures, where each atom or molecule plays a prescribed role in realizing batteries with unique performance profiles suitable for emergent demands.

Trahey, Lynn↗

Rapidly tunable ultrabroadband flying focus using adaptive optics and an axiparabola

A programmable ultrabroadband flying focus was produced using adaptive optics and an axiparabola with a continuous wave superluminescent diode. A deformable mirror and spatial light modulator were used to add a programmable amount of radial group delay, and an axiparabola was used to create an extended focus by imparting spherical aberration. Three different flying focus trajectories were measured using spectral interferometry, two with uniform velocity and one with an accelerating velocity. Here, the temporal response function width of the flying focus optics alone was calculated to be 52 ± 6 fs, and the focal spot size was measured to be (1.2 ± 0.1) × larger than the diffraction-limited spot size through the extended focus.

Markland, H. S. [University of Rochester, NY (Unit↗