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At least 1,171 records · Page 65
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

A theoretical study of the upper bound of surface elevation variance in the Phillips initial stage during wind-wave generation

The resonance mechanism in the initial of wind-wave generation proposed by Phillips is a foundation of wind-wave generation theory, but a precise theoretical quantification of wave energy growth in this initial stage has not been obtained yet after more than six decades of research. In this study, we aim to address this knowledge gap by developing an analytical approach based on a novel complex analysis method to theoretically investigate the temporal evolution of the wave energy in the Phillips initial stage. We quantitatively derive and analyse the growth behaviour of the surface wave energy and obtain an analytical solution for its upper bound. Our result highlights the crucial effects of surface tension. Because the phase velocity of gravity–capillary waves has a minimal value at a critical wavenumber, gravity–capillary waves and gravity waves (which neglect surface tension) exhibit distinct resonance curve properties and wave energy growth behaviours. For gravity waves, the resonance curve extends indefinitely; for gravity–capillary waves, it either forms a finite-length curve or does not exist, depending on the wind speed. The leading-order term of the upper-bound solution of the energy of gravity waves increases linearly over time, while for gravity–capillary waves, the term increases linearly over time under strong wind conditions but remains finite under weak wind conditions. This theoretical study provides an analytical framework for the generation of wind-waves in the Phillips initial stage, which may inspire further theoretical, numerical and experimental research.

58 GEOSCIENCES↗
DOE OSTI2023

Chaotic and integrable magnetic fields in one-dimensional hybrid Vlasov–Maxwell equilibria

The construction of kinetic equilibrium states is important for studying stability and wave propagation in collisionless plasmas. Thus, many studies over the past decades have been focused on calculating Vlasov–Maxwell equilibria using analytical and numerical methods. However, the problem of kinetic equilibrium of hybrid models is less studied, and self-consistent treatments often adopt restrictive assumptions ruling out cases with irregular and chaotic behaviour, although such behaviour is observed in spacecraft observations of space plasmas. In this paper, we develop a one-dimensional (1-D), quasineutral, hybrid Vlasov–Maxwell equilibrium model with kinetic ions and massless fluid electrons and derive associated solutions. The model allows for an electrostatic potential that is expressed in terms of the vector potential components through the quasineutrality condition. The equilibrium states are calculated upon solving an inhomogeneous Beltrami equation that determines the magnetic field, where the inhomogeneous term is the current density of the kinetic ions and the homogeneous term represents the electron current density. We show that the corresponding 1-D system is Hamiltonian, with position playing the role of time, and its trajectories have a regular, periodic behaviour for ion distribution functions that are symmetric in the two conserved particle canonical momenta. For asymmetric distribution functions, the system is nonintegrable, resulting in irregular and chaotic behaviour of the fields. The electron current density can modify the magnetic field phase space structure, inducing orbit trapping and the organization of orbits into large islands of stability. Thus, the electron contribution can be responsible for the emergence of localized electric field structures that induce ion trapping. We also provide a paradigm for the analytical construction of hybrid equilibria using a rotating two-dimensional harmonic oscillator Hamiltonian, enabling the calculation of analytic magnetic fields and the construction of the corresponding distribution functions in terms of Hermite polynomials.

Kaltsas, Dimitrios A. (ORCID:0000000300769015)↗
DOE OSTI2020

Rapid Determination of Uranium Isotopic Abundance from Cotton Swipes: Direct Extraction via a Planar Surface Reader and Coupling to a Microplasma Ionization Source

The collection of solid particulates and liquids from surfaces by the use of cloth swipes is fairly ubiquitous. In such methods, there is a continuous concern regarding the ability to locate and quantitatively sample the analyte species from the material. In this effort, we demonstrate the initial coupling of an Advion Plate Express plate reader to a liquid sampling–atmospheric pressure glow discharge (LS-APGD) microplasma ionization source with an Orbitrap mass spectrometer to perform uranium isotopic analyses of solution residues on cotton swipes. The Plate Express employs a sampling probe head to engage and seal against the swipe surface. Subsequentially, the analyte residues are desorbed and transported within a 2% HNO 3 electrolyte flow to the ionization source. Quantitative recoveries were observed following a single 30 s extraction step, with the absolute mass sampled per extraction being ~100 ng. While the intrasample variability in the analytical responses for triplicate sampling of the same swipe yield ~30% RSD, this lack of precision is offset by the ability to determine isotope ratios for enriched uranium specimens with a precision of better than 10% RSD. Pooled, intersample precision ( n = 9) was found to be <5%RSD across the various sample compositions. Finally, 235 U/ 238 U determinations (ranging from 0.053 to 1.806) were accurate with errors of <10%, absolute. The 234 U- and 236 U-inclusive ratios were determined with similar accuracy in enriched samples. While the driving force for the effort is in the realm of nuclear nonproliferation efforts, the ubiquitous use of cloth swipes across many application areas could benefit from this convenient approach, including the use of versatile, reduced-format mass spectrometer systems.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2025

Advanced Method Optimization with Categorical and Constrained Continuous Parameters

Traditional approaches to analytical method optimization (e.g., univariate and “guess-and-check”) can be time-consuming, costly, and often fail to identify true optima within the parameter space. Previous work defined and implemented a generalized technique for method optimization for continuous method parameters, but a knowledge gap remains for the incorporation of categorical variables into these advanced method optimization schemes. This work presents and validates a generalized optimization approach that incorporates both continuous and categorical variables while also utilizing a multivariate, multiobjective optimization scheme with Karush–Kuhn–Tucker conditions to bound the optimization space to solutions within the physical limitations of the parameter space. Method optimization from a case study using GC–MS for the analysis of 11 analytical standards with objectives to minimize peak width and maximize peak height resulted in a 3 orders of magnitude improvement in the average peak height and a 2 orders of magnitude improvement in the average peak width compared to the least optimal (but reasonable) instrumental parameters utilized in this study. This approach to optimization allows for a customizable method optimization in which users can include both continuous and categorical variables to achieve objectives specific to their analytical goals. This approach significantly reduces the labor and cost associated with traditional method development approaches and can be applied in a variety of scientific fields across a range of laboratory techniques (e.g., instrument method development, sample preparation, and extraction techniques).

Amorphous materials↗
DOE OSTI2020

Results of the International Energy Agency Bioenergy Round Robin on the Analysis of Heteroatoms in Biomass Liquefaction Oils

A round robin study evaluating the analysis of biomass liquefaction oils (BLOs) from fast pyrolysis and hydrothermal liquefaction (HTL) was performed, involving fifteen laboratories in seven countries in order to assess the current status of analytical techniques for the determination of nitrogen, sulfur, and chlorine content in BLOs and evaluate potential differences in origin (i.e. fast pyrolysis vs HTL). The BLOs were produced from a range of feedstocks including pine, mixed softwoods, forest residues, micro-algae, miscanthus, and wheat straw to cover a variety in nitrogen, sulfur, and chlorine content and speciation. Nine samples were distributed, comprised of eight separate BLOs and one blind duplicate produced by five producers. The samples were analyzed for water, carbon, hydrogen, nitrogen, sulfur, and chlorine content. No analytical test method was mandated; laboratories were encouraged to utilize whichever method they determined would be most applicable, relying on the existing body of BLO literature as a guide. The results of this round robin study are presented in this paper. The results of the carbon, hydrogen, and water measurements as reference analyses had relative standard deviations (2.9%, 3.5, and 5.6%, respectively) that were comparable to those found in past round robin studies on fast pyrolysis bio-oil. The analysis of nitrogen, sulfur, and chlorine showed higher levels of variability. Laboratories mostly chose the same method for water, carbon, hydrogen and nitrogen determination whereas there were a variety of methods chosen for sulfur and chlorine determination. The results suggest that specific analytical methods for the determination of nitrogen, sulfur, and chlorine should be further refined to ensure reproducible and accurate results for BLO analysis due to their importance on emissions, material selection, and catalyst activity.

Biomass, IEA Bioenergy, pyrolysis, hydrothermal li↗
DOE OSTI2026

Exploring Approaches for Accelerated Mass Spectrometric Detection of Fluorochemicals from Aqueous Solutions Using Indirect, Adsorbent-Facilitated Desorption Ionization

There is a growing need for rapid, low-cost analytical tools to screen water supplies for persistent contaminants. Due to their ubiquitous presence in the environment and their detrimental effects on human health, there is a public interest in widespread testing for perfluoroalkyl substances (PFAS). However, the most common methods for PFAS analysis can be time-intensive, requiring a preconcentration step followed by liquid chromatography–mass spectrometry (LC–MS), and are cost-prohibitive for most members of the public. To address these challenges, this study explores a novel method for rapid analysis of aqueous analytes by concentrating analytes on solid adsorbents and detecting them using mass spectrometric analysis via desorption ionization directly from the adsorbent surface. We demonstrate this general approach of indirect solution analysis (ISA) with desorption electrospray ionization (ISA-DESI) and laser desorption ionization (ISA-LDI). Various adsorbent materials were screened, including commercial mesoporous carbons, alumina, and metal–organic frameworks (MOFs). Using ISA-DESI, we consistently detect concentrations as low as 5–100 parts per trillion (ppt) for perfluorooctanoic acid (PFOA) and 10–100 ppt for perfluoroundecanoic acid (PFUnDA). This approach enables rapid detection in under 5 min, making it suitable for applications requiring trace detection with fast response times. We further demonstrate the use of ISA-DESI on a range of environmentally relevant contaminants. Advantages of this indirect solution analysis approach include simplified sample preparation, accelerated analysis, and low cost with readily available materials, making it a promising tool to accelerate mass spectrometric PFAS detection for identifying contaminated sites, performing laboratory studies, and monitoring industrial waste streams.

Bays, Nathan Robert [Sandia National Laboratories ↗
DOE OSTI2025

Real-Time Screening for Uranium Enrichment by Paper Spray Ionization Mass Spectrometry for Field Applications

A rapid isotope ratio screening technique for uranium enrichment is demonstrated by utilizing paper spray ionization (PSI) high-resolution mass spectrometry (HRMS). Measurements were conducted using an ambient ionization mass spectrometer coupled to a custom-made JEOL PSI attachment apparatus, with de minimus sample preparation requirements. The current method detection limit for individual isotopes (e.g., 235 U and 238 U) is approximately 50 pg, with subsequent optimization expected to further improve U isotopic sensitivity. The PSI analytical method described herein can support rapid analysis (both in-field and in-lab screening) of isotopes-of-interest, as demonstrated by empirical differentiation of depleted uranium (DU) and low enriched uranium (LEU) analytical aliquots. Furthermore, this analytical workflow holds promise for applications in nuclear forensics, international nuclear safeguards, and nonproliferation missions.

Anions↗
DOE OSTI2021

Parsing Weather Variability and Wildfire Effects on the Post-Fire Changes in Daily Stream Flows: A Quantile-Based Statistical Approach and Its Application

Determining wildland fire impacts on streamflow can be problematic as the hydrology in burned watersheds is influenced by post-fire weather conditions. Here, this study presents a quantile-based analytical framework for assessing fire impacts on low and peak daily flow magnitudes, while accounting for post-fire weather influences. This framework entails (a) the bootstrap method to compute the relative change in the post-fire annual flow and weather statistics, (b) double mass analysis to detect if post-fire baseflow and quick-flow yield ratios are significantly altered, and (c) a quantile regression method to parse fire effects on flow at a specific quantile. We illustrate the applicability of this analytical framework using 44 western US streams with at least 5% of their watershed area burned. Results indicate that large, high-severity burns in upland watersheds can raise the streamflow magnitude at the 0. 05 th and 0. 95 th quantiles for at least the five post-fire years. Quantile regression results show that the median fire-related increase in flow for the five post-fire years can be up to 5,000% (Standard Error; S.E. < 2%) at the 0. 05 th E quantile and 161% (S.E. < 10%) at the 0. 95 th quantile. The fire-related increase in flow was often pronounced at the 0. 05 th quantile for streams in the Pacific Northwest and California regions. The difference in fire effects on flow (at both quantiles) across streams was related to post-fire weather, pyrology, physiography, and land cover. The proposed analytical framework can be useful for detecting and quantifying fire effects on the low and peak stream flows in burned watersheds without overlapping disturbances.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Learning perturbation-inducible cell states from observability analysis of transcriptome dynamics

Abstract A major challenge in biotechnology and biomanufacturing is the identification of a set of biomarkers for perturbations and metabolites of interest. Here, we develop a data-driven, transcriptome-wide approach to rank perturbation-inducible genes from time-series RNA sequencing data for the discovery of analyte-responsive promoters. This provides a set of biomarkers that act as a proxy for the transcriptional state referred to as cell state. We construct low-dimensional models of gene expression dynamics and rank genes by their ability to capture the perturbation-specific cell state using a novel observability analysis. Using this ranking, we extract 15 analyte-responsive promoters for the organophosphate malathion in the underutilized host organism Pseudomonas fluorescens SBW25. We develop synthetic genetic reporters from each analyte-responsive promoter and characterize their response to malathion. Furthermore, we enhance malathion reporting through the aggregation of the response of individual reporters with a synthetic consortium approach, and we exemplify the library’s ability to be useful outside the lab by detecting malathion in the environment. The engineered host cell, a living malathion sensor, can be optimized for use in environmental diagnostics while the developed machine learning tool can be applied to discover perturbation-inducible gene expression systems in the compendium of host organisms.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Learning protocols for the fast and efficient control of active matter

Exact analytic calculation shows that optimal control protocols for passive molecular systems often involve rapid variations and discontinuities. However, similar analytic baselines are not generally available for active-matter systems, because it is more difficult to treat active systems exactly. Here we use machine learning to derive efficient control protocols for active-matter systems, and find that they are characterized by sharp features similar to those seen in passive systems. We show that it is possible to learn protocols that effect fast and efficient state-to-state transformations in simulation models of active particles by encoding the protocol in the form of a neural network. We use evolutionary methods to identify protocols that take active particles from one steady state to another, as quickly as possible or with as little energy expended as possible. Our results show that protocols identified by a flexible neural-network ansatz, which allows the optimization of multiple control parameters and the emergence of sharp features, are more efficient than protocols derived recently by constrained analytical methods. Our learning scheme is straightforward to use in experiment, suggesting a way of designing protocols for the efficient manipulation of active matter in the laboratory.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Non-Contact Vapor Detection of Illicit Drugs via Atmospheric Flow Tube-Mass Spectrometry

Real-time, non-contact detection of illicit drugs is a desirable goal for the interdiction of these controlled substances, but the relatively low vapor pressures of such species present a challenge for trace vapor detection technologies. The introduction of atmospheric flow tube-mass spectrometry (AFT-MS), which has previously been demonstrated to detect gas-phase analytes at low parts-per-quadrillion levels for explosives and organophosphorus compounds, also enables the potential for non-contact drug detection. With AFT-MS, direct vapor detection of cocaine and methamphetamine from ~5 µg residues at room temperature is demonstrated herein. Furthermore, thermal desorption of low- to sub-picogram levels of cocaine, methamphetamine, fentanyl, and heroin is observed via AFT-MS using a carrier flow rate of several L/min of air. These low levels can permit non-contact sampling through collection of vapor, effectively preconcentrating the analyte before desorption and analysis. Quantitative evaluation of the thermal desorption approach has yielded limits of detection (LODs) on order of 10 fg for cocaine and fentanyl, 100 fg for methamphetamine, and 1.6 pg for heroin. The LOD for heroin was lowered to 200 fg by using tributyl phosphate as a dopant to form a proton-bound heterodimer with heroin. When used with AFT-MS, the intentional formation of specific drug-dopant adducts has the potential to enhance detection limits and selectivity of additional drug species. Species that are prone to form adducts present a challenge to analysis, but that difficulty can be overcome by the intentional addition of a dopant. Molecules unlikely to form adducts will remain essentially unimpacted, but the adduct-forming species will interact with the dopant to compress the analyte signal into a single peak. This approach would be valuable in the application of non-contact screening for illicit substances via vapor collection followed by thermal desorption for analysis.

methamphetamine, cocaine, heroin, fentanyl, atmosp↗
DOE OSTI2025

Introducing bioderived solvents for safer and more sustainable 19 F benchtop NMR analysis of pyrolysis oils

The development of increasingly sustainable analytical chemistry techniques is a growing area of research. Detailed knowledge of bio-oil composition is crucial for the wider use of this alternative, sustainable fuel product, whether by guiding and optimising the pyrolysis processes or for indicating appropriate upgrading methods. The oxygen-containing species in the oil are most important to analyse as they are key to the long-term stability and further processing of the oil. A common analytical method is derivatisation, inserting 19 F nuclei only into specific compounds in the sample, so that a sparser NMR spectrum of a subset of the compounds present can be acquired with even a benchtop NMR spectrometer. However, the derivatisation reactions themselves are not benign, with the most commonly used method relying on DMF throughout. While DMF is highly effective in facilitating the derivatisation reaction, it is not only harmful but increasingly restricted in use. By substituting DMF with ethyl lactate, the reaction is rendered safer and more sustainable. The change in solvent does not affect the NMR results, with estimates of total carbonyl content comparable with those produced by titration. The spectra acquired are detailed enough to also allow the quantification of the different carbonyl functional groups present. By switching to ethyl lactate, it is possible to increase the amount of water in the solvent mixture, further reducing the environmental impact, user risks and cost of the analytical method. By replacing harmful solvents with greener alternatives, benchtop NMR analyses of pyrolysis oils are increasingly safer to run, increasingly cheaper to run, and increasingly more accessible to a wide range of different users.

Tang, Bridget [Aston University, Birmingham (Unite↗
DOE OSTI2020

Theory of ignition and burn propagation in inertial fusion implosions

A detailed analytic model is presented here to investigate the physics of burn propagation in inertially confined plasmas. The onset of ignition and burn propagation occurs when alpha heating of the hot spot causes rapid ablation of shell mass into the hot spot. This allows large energy gains to be achieved since most of the fuel mass is located in the shell. Here, we first present a comprehensive review of previous analytic models that have been used to describe the physics of hot-spot evolution and ignition; we then show that a proper description of a propagating burn wave requires a comprehensive model of hot spot and shell evolution that includes proper mass conservation in the shell, fusion reactivity, and fuel depletion. The analytic theory is in good agreement with detailed radiation-hydrodynamic simulations that predict the onset of burn propagation as occurring when the yield enhancement caused by alpha heating is between 15- and 25-fold, $f_α$ ~ 1.4, where $f_α$ = alpha energy deposited/hot-spot energy at bang time, and the hot-spot burnup fraction is approximately 2%. We show that the definition of ignition is not sensitive to the alpha-particle stopping power nor asymmetries provided that the absorbed fraction of alpha particles $θ_α$ is correctly accounted for. Finally, we use the results of 2-D simulations to show that even when $θ_α$ is small and unknown (as is true in hot spots with mid modes that have significant leakage of alpha particles into the surrounding cold bubbles), one can still relate the experimentally measureable parameter $\chi^{53}_α$ to the yield amplification and the burning-plasma parameter $Q^{\text{hs}}_α$ = alpha energy deposited/total input work delivered to the hot spot

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

An extended trajectory-mechanics approach for calculating two-phase flow paths

A technique originating in quantum dynamics is used to derive a trajectory-based, semi-analytical solution for two-phase flow. The partial differential equation governing the evolution of the aqueous phase is equivalent to a family of ordinary differential equations defined along a path through the porous medium. The trajectories may be found by solving the differential equations directly or by post-processing the output of a numerical solution to the full set of governing equations. The trajectories, which differ from conventional streamlines, are found to bend downward in response to gravitational forces. The curvature is more pronounced as the dip of the porous layer containing the flow increases. Subtle changes in the relative permeability curve can lead to significant variations in the trajectories. The ordinary differential equation for the trajectory provides an expression for the travel time along the path. The expression produces a semi-analytical approximation to the model parameter sensitivities, the partial derivatives of the travel times with respect to changes in the permeability model. The semi-analytical trajectory-based sensitivities generally agree with those computed using a numerical reservoir simulator and a perturbation approach. The sensitivities are useful in tomographic imaging algorithms designed to estimate the spatial variation in permeability within a porous medium using multiphase observations.

58 GEOSCIENCES↗
DOE OSTI2021

Driven resonant current amplification in self-organized plasma configurations with uniform λ and plasma pressure confinement

Driven resonant current amplification in uniform λ=$^{μoJ}_{B}$, self-organized plasma configurations with plasma pressure confinement is studied. This work extends previous analyses of force-free states (J ∥ B) to equilibria with plasma pressure gradients (∇P = J × B ≠ 0). An analytical treatment shows that in equilibria with uniform λ and a plasma pressure gradient that varies linearly with poloidal magnetic flux, driven resonances are either downshifted or upshifted from their force-free values. Additionally, a modification of off resonance current amplification is observed in pressure confining equilibria. Computational results add support to analytical predictions, and also include driven resonance behavior with equilibrium profiles not considered analytically. Furthermore, these results suggest not only persistence, but also modification of driven resonant current amplification in sustained spheromak configurations with plasma pressure confinement when compared to force-free states. By providing a basis for the existence of driven, high current amplification, pressure confining equilibria, this work provides insight into the accessibility of sustained spheromak states of most interest for potential fusion energy applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

A unified thermionic and thermionic-field emission (TE–TFE) model for ideal Schottky reverse-bias leakage current

We present a unified thermionic emission (TE) and thermionic-field emission (TFE) model for the ideal reverse-bias leakage current in Schottky junctions. The unified TE–TFE analytical model advances upon previous analytical TFE models by Murphy–Good and Padovani–Stratton, which are the two most widely adopted models by the community, in two major aspects: (i) the applicability of the TFE expression therein is extended to near-zero surface electric fields by an error-function correction, allowing for the calculation of the total current by a nontrivial sum of TE (over-the-barrier current) and TFE (below-the-barrier current) contributions; therefore, an accurate description of the TE-to-TFE transition region is captured analytically for the first time; (ii) image-force lowering is considered with much-simpler correction terms. Comparisons with the reference numerical model show that the unified TE–TFE model has excellent accuracy, as well as a 10 000× reduction in computation time. The unified model is further tested against experimental data from Schottky barrier diodes based on Si, 4H-SiC, GaN, and β-Ga 2 O 3 , revealing accurate extractions of barrier heights and correct descriptions of the ideal reverse leakage characteristics. With the extended applicable range, improved accuracy, and computational efficiency, the unified TE–TFE model is highly valuable for the design and analysis of devices based on Schottky junctions, as well as for potential integration in technology computer-aided design (TCAD) tools.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Multiple electron beam generation with different energies and comparable currents from a single cathode potential for high power traveling wave tubes (TWTs)

We present a technique for generating multiple electron beams with different energies and comparable currents from a single cathode stalk at a single potential using nested magnetically insulated coaxial diodes (MICDs). The application is for a multi-stream traveling wave tube. Particle-in-cell simulations are performed for an experimental parameter-based geometry where two thin-walled intense relativistic electron beams immersed in a strong uniform magnetic field propagate through a cylindrical vacuum channel. The analytically derived results are obtained by extending Fedosov’s solution for generating a hollow electron beam from an MICD on a cathode stalk in an infinite magnetic field. Two electron beams are generated and accelerated downstream assuming zero initial kinetic energy of the electrons from the cathodes. Results show both electron beam currents ranging from 66 to 2.8 kA with an energy difference ranging from 6% to 27% depending on voltages applied from 100 to 600 kV and the geometry of the two MICDs. An optimal geometry is a crucial factor in achieving the maximum energy difference between the electron beams for comparable currents. The analytical and numerical simulation results show good agreement. We are currently in the process of planning experiments using the electron beam accelerator (SINUS-6 at UNM) to validate the analytical and simulation results.

Islam, K. N. (ORCID:0000000214397710)↗
DOE OSTI2023

Impact of hohlraum cooling on ignition metrics for inertial fusion implosions

This paper extends the evaluation of ignition metrics to include the impact of hohlraum cooling before peak implosion velocity in radiation driven implosions. First, we provide an extension of the results for the key hot spot stagnation quantities from the 2018 paper. The modified analytic expressions presented here match the Hydra results for these National Ignition Facility scale implosions both with and without hohlraum cooling before peak velocity if the effective ablation pressure P abl (effective) = P abl (t pv - 0.5 ns) is used in the analytic formulas, where t pv is the time of peak implosion velocity. Second, we provide an analysis that enables a comparison of the Hydra radiation hydrodynamics code calculations utilized here with the predictions of the analytic piston model of an ICF implosion, which focused on sensitivity to time duration of the hohlraum cooling phase before peak velocity (often called the “coast time”) and the shell radius at peak velocity R pv . Third, we provide a set of ignition metrics that are valid across a wide range of capsule designs valid for implosions both with and without hohlraum cooling before peak implosion velocity is reached.

42 ENGINEERING↗