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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
NASA NTRS2015

Leak Rate Quantification Method for Gas Pressure Seals with Controlled Pressure Differential

An enhancement to the pressure decay leak rate method with mass point analysis solved deficiencies in the standard method. By adding a control system, a constant gas pressure differential across the test article was maintained. As a result, the desired pressure condition was met at the onset of the test, and the mass leak rate and measurement uncertainty were computed in real-time. The data acquisition and control system were programmed to automatically stop when specified criteria were met. Typically, the test was stopped when a specified level of measurement uncertainty was attained. Using silicone O-ring test articles, the new method was compared with the standard method that permitted the downstream pressure to be non-constant atmospheric pressure. The two methods recorded comparable leak rates, but the new method recorded leak rates with significantly lower measurement uncertainty, statistical variance, and test duration. Utilizing this new method in leak rate quantification, projects will reduce cost and schedule, improve test results, and ease interpretation between data sets.

seal↗
DOE OSTI2023

Optimization of metal-supported solid oxide electrolysis cells with infiltrated catalysts

We report metal-supported solid oxide electrolysis cells (MS-SOECs) are being developed for steam-to-hydrogen electrolysis, especially for utilization of dynamic or intermittent electrical power from renewable sources. Various aspects of the electrocatalyst processing and composition, and metal support structure were explored. Catalyst materials, infiltration temperature and infiltration cycles were optimized for high performance and durability. Numerous catalyst materials were screened for both oxygen and steam electrodes. The oxygen catalyst had moderate impact on both initial cell performance and durability. Reducing Ni content in the steam electrode had little effect on durability, but reduced initial performance. Ex-situ XRD analysis and cell assessment of catalyst infiltration temperature revealed that the optimal range is 750–850 °C. The best cell performance and durability was achieved with LSCF-SDC oxygen electrocatalyst and SDC-Ni (60:40 vol%) steam electrocatalyst infiltrated 11 times at 800 °C and operated at 700 °C. At low steam content, a significant mass transport limitation on the steam side results in limiting current behavior. Thinner and more porous metal supports were implemented, and found to improve steam mass transport at low steam content, relevant for SOECs operating under high H 2 recycle rate or high steam utilization.

08 HYDROGEN↗
NASA NTRS1999

"Ultra"-Fast Fracture Strength of Advanced Structural Ceramic Materials Studied at Elevated Temperatures

The accurate determination of inert strength is important in reliable life prediction of structural ceramic components. At ambient temperature, the inert strength of a brittle material is typically regarded as free of the effects of slow crack growth due to stress corrosion. Therefore, the inert strength can be determined either by eliminating active species, especially moisture, with an appropriate inert medium, or by using a very high test rate. However, at elevated temperatures, the concept or definition of the inert strength of brittle ceramic materials is not clear, since temperature itself is a degrading environment, resulting in strength degradation through slow crack growth and/or creep. Since the mechanism to control strength is rate-dependent viscous flow, the only conceivable way to determine the inert strength at elevated temperatures is to utilize a very fast test rate that either minimizes the time for or eliminates slow crack growth. Few experimental studies have measured the elevated-temperature, inert (or "ultra"-fast fracture) strength of advanced ceramics. At the NASA Lewis Research Center, an experimental study was initiated to better understand the "ultra"-fast fracture strength behavior of advanced ceramics at elevated temperatures. Fourteen advanced ceramics - one alumina, eleven silicon nitrides, and two silicon carbides - have been tested using constant stress-rate (dynamic fatigue) testing in flexure with a series of stress rates including the "ultra"-fast stress rate of 33 000 MPa/sec with digitally controlled test frames. The results for these 14 advanced ceramics indicate that, notwithstanding possible changes in flaw populations as well as flaw configurations because of elevated temperatures, the strength at 33 000 MPa/sec approached the room-temperature strength or reached a higher value than that determined at the conventional test rate of 30 MPa/sec. On the basis of the experimental data, it can be stated that the elevated-temperature, inert strength of an advanced ceramic material can be defined as the strength where no slow crack growth takes place at the temperature.

Choi, Sung R.↗
DOE OSTI2024

CEBAF Injector for K Long Beam Conditions

The Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Lab concurrently operates four experimental Halls with distinct bunch charge specifications and repetition rates. Numerous critical beam parameters within CEBAF are configured in the injector, some remaining unchanged throughout the accelerator. Consequently, the injector plays a crucial role in determining final beam characteristics, including bunch structure, beam sizes, bunch lengths, energy spread, and beam transmission. The Jefferson Lab KL experiment is scheduled to take place at CEBAF in Hall D, featuring a much lower bunch repetition rate of 7.80 MHz or 15.59 MHz, below the nominal values of 249.5 MHz or 499 MHz. Although the proposed average current of 5 ?A or 10 ?A is low compared to the maximum CEBAF cur- rent of approximately 180 ?A, the corresponding bunch charge is unusually high for CEBAF injector operation. This study focuses on the behavior of low-repetition-rate, high-bunch- charge (0.32 to 0.64 pC) beams in the CEBAF injector. We investigated the evolution and transmission of low-charge beams to space-charge dominated high-charge beams in the front end of the CEBAF injector for two configurations: the pre-existing CEBAF Phase 1 injector upgrade, operated at 130 kV, and the existing CEBAF Phase 2 injector upgrade, operated at 140 kV, 180 kV, and to be operated at 200 kV. The electron beam through the CEBAF injector is characterized using beam dynamics simulations and comparisons with the available measurements performed at 130 kV. Multi-objective genetic optimizations of the CEBAF injector were performed to determine the operating magnetic elements and RF settings for the evolution and transmission of low, moderate, and high charge beams in the CEBAF injector at 180 kV and 200 kV DC gun voltages. Subsequently, simulations at the same voltages were conducted to obtain the beam characteristics at the front end of the CEBAF injector. The laser spot size and laser pulse length at the cathode were varied to observe their effects on beam transmission in the injector at different voltages (130 kV, 180 kV, and 200 kV). Experimental studies at 130 kV, 140 kV, and 180 kV validate the simulations. Beam study measurements are carried out using EPICS tools, while optimizations and simulations are facilitated by General Particle Tracer. Based on the findings, optimal parameters for the upcoming Jefferson Lab KL experiment are proposed, utilizing a lower repetition rate and higher bunch charge

Pokharel, Sunil↗
NASA NTRS1971

Ion-thruster propellant utilization

The evaluation and understanding of maximum propellant utilization, with mercury used as the propellant are presented. The primary-electron region in the ion chamber of a bombardment thruster is analyzed at maximum utilization. The results of this analysis, as well as experimental data from a range of ion-chamber configurations, show a nearly constant loss rate for unionized propellant at maximum utilization over a wide range of total propellant flow rate. The discharge loss level of 1000 eV/ion was used as a definition of maximum utilization, but the exact level of this definition has no effect on the qualitative results and little effect on the quantitative results. There are obvious design applications for the results of this investigation, but the results are particularly significant whenever efficient throttled operation is required.

Kaufman, H. R.↗
DOE OSTI2026

Impact of Site Identity, Location, and Accessibility on Polyethylene Conversion Rates and Product Selectivities over Metal-Free MFI Zeolites

Brønsted (BAS), Lewis (LAS), and surface Brønsted (SBAS) acid sites have been investigated for polyethylene (PE) upcycling by zeolite catalysts, but there is no clear consensus regarding their catalytic roles, partly due to the complexity of the catalysts used and varying reaction conditions across studies. This work systematically determined how these sites impact PE conversion rates and product distributions by utilizing a suite of microporous MFI catalysts with varying Si/Al ratios, acid site densities, and inherent mesoporosities. PE conversion rates did not trend with total BAS or LAS densities due to a combination of internal mass transfer limitation and the apparent inability of LAS alone to cleave C–C bonds, but a strong, statistically significant correlation was present with respect to SBAS density and mesopore surface area, jointly, owing to accelerated polymer activation on external surfaces to smaller diffusion-limited chains. However, ingress of these SBAS-derived fragments ultimately remained rate limiting, as demonstrated by solid conversion rates that increased with mesopore surface area at similar SBAS density and likewise increased with SBAS density at similar mesopore surface area. In batch PE cracking reactions, light gaseous product selectivities were most sensitive to total BAS, with higher densities generally exhibiting higher selectivity to C 3 and linear C 4 –C 7 products and higher alkane/alkene product ratios, consistent with increased β-scission turnovers. Insights from this work help systematically clarify the roles of BAS, LAS, SBAS, and mesopores in PE cracking reactions and inform the development of tailored zeolite catalysts for efficient polyolefin upcycling.

accessibility↗
NASA NTRS2005

Axisymmetric Numerical Modeling of Pulse Detonation Rocket Engines

Pulse detonation rocket engines (PDREs) have generated research interest in recent years as a chemical propulsion system potentially offering improved performance and reduced complexity compared to conventional rocket engines. The detonative mode of combustion employed by these devices offers a thermodynamic advantage over the constant-pressure deflagrative combustion mode used in conventional rocket engines and gas turbines. However, while this theoretical advantage has spurred considerable interest in building PDRE devices, the unsteady blowdown process intrinsic to the PDRE has made realistic estimates of the actual propulsive performance problematic. The recent review article by Kailasanath highlights some of the progress that has been made in comparing the available experimental measurements with analytical and numerical models. In recent work by the author, a quasi-one-dimensional, finite rate chemistry CFD model was utilized to study the gasdynamics and performance characteristics of PDREs over a range of blowdown pressure ratios from 1-1000. Models of this type are computationally inexpensive, and enable first-order parametric studies of the effect of several nozzle and extension geometries on PDRE performance over a wide range of conditions. However, the quasi-one-dimensional approach is limited in that it cannot properly capture the multidimensional blast wave and flow expansion downstream of the PDRE, nor can it resolve nozzle flow separation if present. Moreover, the previous work was limited to single-pulse calculations. In this paper, an axisymmetric finite rate chemistry model is described and utilized to study these issues in greater detail. Example Mach number contour plots showing the multidimensional blast wave and nozzle exhaust plume are shown. The performance results are compared with the quasi-one-dimensional results from the previous paper. Both Euler and Navier-Stokes solutions are calculated in order to determine the effect of viscous effects in the nozzle flowfield. Additionally, comparisons of the model results to performance data from CalTech, as well as experimental flowfield measurements from Stanford University, are also reported.

Morris, Christopher I.↗
DOE OSTI2024

A custom 3D printed paddlewheel improves growth in flat panel photobioreactor

One of the main challenges with using flat panel photobioreactors for algal growth is uneven mixing and settling of cells in corners, especially when bubbling is the only method used for mixing. Here, in order to improve mixing in our flat panel reactor, we designed a custom paddlewheel. Paddlewheels are frequently used in outdoor algae raceway ponds to improve mixing and we are taking advantage of the same principle for mixing in the reactor. The paddlewheel is easily integrated into our PSI FMT150 1‐L flat panel photobioreactor and is printed on a 3D printer using high temperature poly lactic acid (HT‐PLA). With the inclusion of an annealing step, the paddlewheel is autoclavable. Addition of the paddlewheel in the reactor minimized cell settling and improved algal growth, as evidenced by a nearly 40% increase in oxygen production rates. Nutrient dispersion and utilization in the culture was also improved as evidenced by a corresponding 38% decrease in CO 2 concentration. The paddlewheel device presented here is a cost‐effective method for improving algal growth in a flat panel photobioreactor.

09 BIOMASS FUELS↗
DOE OSTI2020

Adaptive Laboratory Evolution for algal strain improvement: methodologies and applications

Originally developed in bacterial and fungal models, Adaptive Laboratory Evolution (ALE) experimentally selects for targeted phenotypes by allowing cells containing beneficial random genetic mutations to replicate more quickly in the presence of environmental stress. When applied to microalgae, this technique has been used to increase growth rate, stress tolerance, substrate utilization, and product yield. This review discusses ALE experimental design parameters, and summarizes key results and lessons learned from recent microalgal ALE studies. By documenting the current state of the field, we provide insight on the ways microalgal ALE might be used to develop commercially viable biotechnology strains.

09 BIOMASS FUELS↗
DOE OSTI2020

Benchmark of the KGMf with a coupled Boltzmann equation solver

The Kinetic Global Model framework (KGMf) is an open-source general-purpose global model (spatially averaged) simulation code developed to explore the reaction kinetics and pathways in plasma discharge systems. It contains species continuity and electron energy balance equations, with a time-dependent evaluated electron energy distribution function (EEDF) for electron impact reactions. The EEDF is utilized to determine the rate coefficients for electron impact reactions, which can have profound impact on the temporal evolutions of plasma parameters. Previously, the EEDF was commonly assumed as Maxwellian or an analytical function of the effective electron temperature. In this work, the KGMf is coupled with a Boltzmann equation (BE) solver to self-consistently compute the EEDF. The EEDF evolution frequency is determined based on relative changes of the reduced electric field. The KGMf is benchmarked with the ZDPlasKin code based on high-pressure low-temperature argon plasma discharge cases. Additionally, the temporal evolutions of reduced electric field, electron temperature, EEDF, reaction rates, and species densities, are obtained and compared under different discharge conditions, showing good agreement between the KGMf and the ZDPlasKin simulations. The application of the KGMf for predicting breakdown times in high power microwave discharges is also presented, which shows qualitative agreement with particle-in-cell simulations. The KGMf can be further applied for more complicated plasma discharge systems, where the reaction kinetics are more intricate (e.g., plasma-assisted combustion systems).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Mechanistic nuclear fuel performance modeling of uranium nitride

Uranium mononitride (UN) is a nuclear fuel candidate for advanced reactor designs and an alternative being considered for light water reactors due to its higher thermal conductivity and uranium density than UO 2 . As with any nuclear fuel, swelling and fission gas release are important factors for safety, while also being some of the hardest phenomena to predict with a high degree of confidence. Getting a grasp on the gas swelling behavior and release is crucial to lower the barrier for UN utilization. An accelerated swelling rate at high temperatures observed experimentally, sometimes referred to as “breakaway swelling,” further complicates the prediction of fuel performance of UN. A mechanistic model has been developed using a multiscale approach to describe the intragranular and intergranular fission gas behavior. Lower-length-scale calculations have been employed to inform models of the gas and self-diffusion behavior, resolution rate, and bubble shape. Leveraging previous work on high burnup UO 2 , two populations of intragranular bubbles are considered; small bulk bubbles and larger bubbles located along dislocations. The dislocation bubbles were found to be crucial to the overall swelling behavior, and the breakaway swelling transition was associated with the transition in the gas atom diffusion mechanism from an irradiation-induced athermal diffusion regime at lower temperatures to an intrinsic thermal equilibrium regime at higher temperatures, accelerating the growth of the dislocation bubbles. Similarly, the threshold for fission gas release was associated with the grain boundary vacancy diffusivity surpassing the gas atom diffusivity at sufficiently high temperatures, allowing the over-pressurized grain boundary bubble to grow in size and interconnect. Using thermo-mechanical models with the fission gas model, two integral fuel pin assessment cases were simulated. Finally, this work demonstrates the ability of a multiscale approach to accelerate the understanding of advanced fuel forms when experimental data is limited.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Rapid, efficient reduction of iron oxide with ammonia

Reducing iron oxide to iron metal with fossil fuels produces circa 4% of annual anthropogenic CO 2 , ca. 2 Gt/a, as direct chemical emissions from the process. Using ammonia instead of coke—releasing only water and nitrogen as byproducts—could be a widely deployable method of decarbonizing industrial ironmaking, because ammonia carries hydrogen and can be transported easily worldwide. However, initial reports suggest that the reaction of ammonia with iron oxide is slow and inefficient, completed only in hours and using only a few percent of the ammonia supplied. Drawing on thermodynamic and kinetic analysis of the reaction, we explored high-temperature, high-flow reaction conditions designed to increase the reaction rate and the ammonia utilization. We report the reduction of iron oxide in 1 min while using 64% of the ammonia supplied. We show that these insights translate to the gram scale and the reduction of pelletized ore, a common form used industrially.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Vibrational Spin-Orbit Coupling Contributions to Excited State Decay of Ligand-to-Ligand Charge Transfer States

Controlling excited state relaxation processes is important in a variety of photochemical and photophysical processes, including the generation of ground and excited state spin polarization for quantum information science applications. Here, we address how specific static distortions – based on vibrational spin-orbit active modes at C2v symmetry determined by group theory – in a series of low-symmetry ligand-to-ligand charge transfer complexes enable direct spin-orbit coupling contributions to T1 → S0 excited state decay. These results are used to address spin-vibronic coupling contributions to T1 → S0 decay in a high-symmetry (tBu2bpy)Pt(S,S) (tBu2bpy = 4,4’-di-tert-butyl-2,2’-bipyridine and S,S = benzene-1,2-dithiolate) ligand-to-ligand charge transfer complex with effective C2v symmetry, where T1 relaxation is both spin- and orbitally forbidden due to the direct spin-orbit coupling matrix element being zero by symmetry. Low-frequency vibrations that involve a pyridine-pyridine twisting motion within the bpy ligand generate large ∂/∂Qi values that will contribute significantly to T1 → S0 relaxation. The work advances ligand design strategies for the generation of tailored T1 → S0 relaxation rates, which can be utilized to optimize the generation of electron spin polarization in radical-elaborated ligand-to-ligand charge transfer complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Kinetic Model for the Reduction of Cu II Sites by NO + NH 3 and Reoxidation of NH 3 -Solvated Cu I Sites by O 2 and NO in Cu-SSZ-13

In this work, a kinetic model is developed for the reduction of Cu II sites by NO + NH 3 and the reoxidation of NH 3 -solvated Cu I sites by O 2 and NO in Cu-SSZ-13. Fourier transform infrared (FTIR) spectroscopy and spatially resolved capillary inlet mass spectrometry (SpaciMS) measurements during transient reactor experiments are utilized to identify the rate parameters associated with NO + NH 3 RHC (reduction half-cycle), proposed to occur via two distinct pathways involving adsorbed NH 3 and gas-phase NH 3 . The resulting NO + NH 3 RHC model is validated using spatiotemporal N 2 measurements covering a wide range of temperatures (200–450 °C) and space velocities (53,000–640,000 h –1 ). N 2 O formation is observed and modeled during NO + NH 3 RHC, with quantitative validation under standard selective catalytic reduction (SCR) conditions. Experimentally measured enthalpic and entropic changes associated with O 2 adsorption on NH 3 -solvated Cu I (ZCu(NH 3 ) 2 ) complexes [ Kamasamudram, K. Catal. Today 2010 , 151 (3–4), 212-222], along with activation energies estimated computationally for the intercage diffusion of ZCu(NH 3 ) 2 complexes [ Paolucci, C. Science 2017 , 357 (6 354), 898-903], are incorporated into a mean field kinetic model for the low-temperature oxidation half-cycle (OHC). Significant NH 3 release is observed during the isothermal oxidation of Cu I sites, attributed to desorption of NH 3 ligands from NH 3 -solvated Cu II dimers (Z 2 Cu 2 (NH 3 ) 4 O 2 ). Reduction of these dimeric complexes leads to the consumption of one NO/Cu II , contradicting the expected reduction stoichiometry. Inclusion of a global Arrhenius rate for the NO titration of Z 2 Cu 2 (NH 3 ) 4 O 2 complexes provides accurate representations of standard SCR on reduced and oxidized catalysts, predicting transient NO and NH 3 consumption between 150 and 250 °C as a function of hydrothermal aging. Deactivation of low-temperature standard SCR by NH 3 is observed at high NH 3 pressures, modeled via the formation of superoxo amino (ZCu(NH 3 ) 3 OO*) complexes during NH 3 titration of Z 2 Cu 2 (NH 3 ) 4 O 2 complexes [ Negri, C. J. Am. Chem. Soc. 2020 , 142 (37), 15884-15896]. The redox kinetic model presented here provides a foundational description of active site redox during low-temperature standard SCR, combining the recent kinetic, spectroscopic, and computational findings on the mechanism of standard SCR over Cu-SSZ-13.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Demonstration of neutron-yield enhancement by laser preheating and magnetization of laser-driven cylindrical implosions

Magnetized liner inertial fusion (MagLIF) is a fusion concept that uses magnetized, preheated fuel to reduce the implosion velocities and convergence ratios required for ignition. A scaled, laser-driven experimental platform to study MagLIF has been demonstrated on the OMEGA laser system, providing comprehensive experimental data on MagLIF scaling, utilizing the higher shot rate on OMEGA compared to the Z machine. Using this platform, a broader experimental space for MagLIF has been studied. Presented in this article are experimental results that demonstrate that the combination of preheat and magnetization enhances the neutron yield by 470% compared to a reference implosion, significantly more than the yield enhancement by the field or preheat alone. These results are achieved while maintaining a relatively low convergence ratio (<20). Here, the experiments were supported by one-, two-, and three-dimensional radiation-hydrodynamics simulations, all of which suggest that multiple sources of mix play different key roles depending on the scale of the MagLIF experiment.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Wide-Bandgap Semiconductor Amplifiers for Fusion Plasma Heating and Control

This paper discusses power electronics developed under the ARPA-E GAMOW program to support nuclear fusion power production. The goal of this project was to develop and assess the potential for wide-bandgap (WBG) semiconductor devices in power electronics to enable high-efficiency and high-voltage solid-state systems for fusion plasma generation, heating, and control. The power electronics use an architecture in which multiple high-power boards can be combined to produce megawatt-level power, where using multiple boards provides high reliability. Two main areas of power electronics boards are developed in this project for fusion plasma heating and control applications: (1) pulse generation and control and (2) radiofrequency generation. The first area is for boards capable of driving high-voltage millisecond pulses at high duty cycles. The envisioned application of these pulses is in plasma control of magnetohydrodynamic instabilities, plasma position, and edge-localized modes. Pulse-width modulation allows for the implementation of a wide variety of linear and nonlinear control systems. The boards developed for this project could actuate control coils based on digital input signals and can be parallelized to provide megawatts of output power. The design of the pulse generator is a low-side load switch. A load switch was designed and constructed that utilized 2-kV-rated field-effect transistor (FET)-based cascodes developed by Qorvo under this project to perform initial testing of these cascodes. The second area is being implemented using class E amplifiers with WBG devices and a reactance steering network to handle inductive or capacitive plasma loads. Applications include ion cyclotron resonance heating (ICRH) and high-harmonic fast-wave (HHFW) heating. A class E reactance steering network is demonstrated in modeling and experiment with a resistive-inductive load that models an inductively-coupled plasma. Power combining of boards with class E reactance steering networks is also simulated and demonstrated experimentally, to enable scaling up to high power. Modeling of high-power-density cooling and remaining useful life is conducted to enable reliable, effectively cooled high-power electronics for fusion applications.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Beam Profile Measurements Utilizing an Amplitude Modulated Pulsed Fiber Laser at PIP2IT

Fermilab is undertaking the development of a new 800 MeV superconducting RF linac to replace its present normal conducting 400 MeV linac. The PIP-II linac consists of a warm front-end generating 2 mA of 2.1 MeV H⁻ followed immediately by a series of superconducting RF cryomodules to 800 MeV. To limit the potential damage to the superconducting RF cavities, PIP-II will utilize laser-based monitors to obtain beam profiles via photoionization. This paper will present the results of transverse and longitudinal beam profile measurements using a prototype profile monitor that was tested with 2.1 MeV H⁻ beam at the PIP-II Injector Test (PIP2IT) accelerator. This prototype profile monitor utilizes a high repetition rate fiber laser and fiber optic transport into the PIP2IT enclosure. In addition, results will be shown of narrow-band electron detection from amplitude modulated laser pulses.

43 PARTICLE ACCELERATORS↗
DOE OSTI2020

Calculation of the First Moment of Energy Using D-T Reactivity Formalisms Under the Maxwell-Boltzmann Distribution (Pt. 1)

Nuclear fusion science is an example of a scientific field with a rich history of expert involvement and scientific publications, which together, form an expert-knowledge base. One example of this history is the utilization of published reaction rates from a variety of authors. Investigators for Deuterium-Tritium (D-T) ion fusion can choose from using frequently cited methods: the Bosch and Hale reactivity, thermonuclear reaction rates from Caughlan and Fowler, and the reactivity evaluation from Miley, Towner & Ivich which forms the basis of the Naval Research Lab (NRL) formulary. There are other choices available. Each of the reactivity formulations considered here, are based upon the Maxwell- Boltzmann velocity distribution for D-T fusion ion reactants. Numerical methods for computer codes simulating hot, energetic plasmas, include tabulations of the reactivity, and the first moment of energy. The purpose of this study is to answer the question: what is the first moment of energy, and how has it been formulated? This report is part of a series of reports by the authors on D-T fusion-reaction formalism. The present focus is on defining the mathematical relationship of the first moment of D-T fusion ion kinetic energy, $\langle$E$\rangle$, with the fusion crosssection, fusion reactivity and its derivative with respect to ion-temperature. Three variants of the first moment $\langle$E$\rangle$ are analytically developed and explored: 1) constant cross-section, 2) a normalized first moment, and 3) a particular function of the first moment. Much of the mathematical development is relegated to the Appendices, for a concise presentation of topics and results. A research component of this discussion is our comparison of some of the reactivity and its derivative results between evaluations (1) versus (2) and (3), which the authors have not found in any other publication to date. This investigation is useful for validation, verification (V&V) and uncertainty quantification (UQ) as it compares the work of several authors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗