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At least 1,333 records · Page 74
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Interconnection of Three Single-Phase Feeders in North America Distribution Systems

This paper proposes a solution for maintaining power balance within all three phases at residential level during islanded mode of operation. Grid abnormalities can lead to isolating the residential microgrid from the main grid, and as a result, distributed generation (DG) units take the full responsibility of supplying local loads. However, in such condition, some phases might face the challenge of meeting local load demand due to the lack of enough power generation, resulting in voltage drop and frequency variation across household loads. In order to resolve this issue, the proposed method in this paper seamlessly interconnects all three single-phase feeders during islanded mode and forms a unified single-phase residential microgrid. Consequently, the load demands in all three phases are met, leading to enhanced voltage and frequency profiles. For this purpose, a seamless transition algorithm is defined which monitors the system condition in real time, and coordinates the operation of all inverter-based DG units in residential microgrid accordingly during transitions. Case study results are provided to verify the validity of proposed method.

Pilehvar, Mohsen S.↗
DOE OSTI2020

Enhanced magnetocaloric performance in manganite bilayers

Bilayer films of La 0.8 Sr 0.2 MnO 3 and La 0.7 Ca 0.3 MnO 3 with different layer thicknesses and stacking sequences were synthesized via pulsed laser deposition. The magnetic properties and magnetocaloric effects were systematically investigated. We found that the phase transition associated with the layers tends to merge together at an optimal thickness and a stacking sequence. The operating temperature span of the entropy change broadens at the expense of its magnitude, leading to an enhancement of the refrigerant capacity by over 40%. The optimized bilayer film possesses a refrigerant capacity of ~6.0J/kg, compared to a value of ~4.2J/kg for the single-phase films. The phase transition broadening induced by epitaxial strain is responsible for the enhanced window of operating temperature as well as refrigerant capacity. Finally, the design principle developed here may be applied to ferroelastic and ferroelectric materials to enhance elastocaloric and electrocaloric effects.

36 MATERIALS SCIENCE↗
NASA NTRS1992

The FML compressor as a drive system for the LFSWT: A narrative

During 1988, a feasibility study was performed to decide how best to build a Laminar Flow Supersonic Wind Tunnel (LFSWT) at the NASA-Ames Fluid Mechanics Laboratory (FML) for boundary layer transition research. A full report was received in June 1988. The report was based on the following guidelines: continuous operation at Mach numbers within the range from 1.8-4.0 was required to impact the NASA 'HiStar' project; low disturbance flow is essential for transition research; minimum test section height is 8 inches; tunnel must fit in an FML test cell; tunnel design should be simple; and construction costs should be minimized. The study considered three drive system options: (1) use surplus JPL compressors and support equipment; (2) use of the FML compressor with ambient injectors; and (3) use of the FML compressor with injectors driven by the NASA-Ames 3000 psia air supply.

Laub, James↗
NASA NTRSDate not supplied

The Transition of RGB Imagery Applied to Fog and Low Clouds from NASA Capabilities within the GOES Proving Ground to the Present Era

A wide range of RGB Imagery products are now available from the GOES ABI instrument, but less than a decade earlier, these false-color imagery products were only seen over Europe and Africa within the suite of the EUMETSAT SEVIRI geostationary instrument. The issue of fog and low clouds as applied to aviation and ground transportation hazards has been a long-standing challenge where satellite imagery provides notable value to visually inspect large spatial areas vs relying on in situ point observations. A legacy channel difference product was the standard satellite imagery tool, but the Nighttime Microphysics RGB would soon be introduced with GOES-R and -S where users had no interpretation experience. As part of the GOES Proving Ground efforts, the SPoRT program utilized existing NASA LEO satellites to demonstrate the future ABI capabilities. Operational users were able to test and adopt the RGBs from NASA LEO instruments prior to the GOES-R launch in order to be ready for the wealth of new channels available from ABI. The transition experience and methods from these proxy RGBs to the start of the GOES-R ABI era to the present day provides insights to the value of these new qualitative products in operations and to how the transition method of such products can be successfully implemented as well as future needs in the RGB Imagery area.

Kevin Fuell↗
NASA NTRS1990

Thermal response of large area high temperature superconducting YBaCuO infrared bolometer

Thermal analysis of large area high temperature superconducting infrared detector operating in the equilibrium mode (bolometer) was performed. An expression for the temperature coefficient beta=1/R(dR/dT) in terms of the thermal conductance and the thermal time constant of the detector were derived. A superconducting transition edge bolometer is a thermistor consisting of a thin film superconducting YBaCuO evaporated into a suitable thermally isolated substrate. The operating temperature of the bolometer is maintained close to the midpoint of the superconducting transition region where the resistance R has a maximum dynamic range. A detector with a strip configuration was analyzed and an expression for the temperature rise (delta T) above the ambient due to a uniform illumination with a source of power density P(sub i) was calculated. An expression for the thermal responsivity of the detector was derived using the thermal diffusion analysis with appropriate boundary conditions. It was found that the thermal responsibility depends upon the spatial modulation frequency and the angular frequency of the incoming radiation. The problem of the thermal cross talk between different detector elements was addressed. In the case of monolithic HTS detector array with a row of square elements of dimensions 2a and CCD or CID readout electronics the thermal spread function was derived for different spacing between elements. This analysis can be critical for future design and applications of large area focal plane arrays as broad band optical detectors made of granular thin films HTS YBaCuO.

Khalil, Ali E.↗
NASA NTRS1991

Thermal response of large area high temperature superconducting YBaCuO infrared bolometers

Thermal analysis of large area high temperature superconducting infrared detector operating in the equilibrium mode (bolometer) was performed. An expression for the temperature coefficient beta = 1/R(dR/dT) in terms of the thermal conductance and the thermal time constant of the detector were derived. A superconducting transition edge bolometer is a thermistor consisting of a thin film superconducting YBaCuO evaporated into a suitable thermally isolated substrate. The operating temperature of the bolometer is maintained close to the midpoint of the superconducting transition region where the resistance R has a maximum dynamic range. A detector with a strip configuration was analyzed and an expression for the temperature rise (delta T) above the ambient due to a uniform illumination with a source of power density was calculated. An expression for the thermal responsibility depends upon the spatial modulation frequency and the angular frequency of the incoming radiation. The problem of the thermal cross talk between different detector elements was addressed. In the case of monolithic HTS detector array with a row of square elements of dimensions 2a and CCD or CID readout electronics the thermal spread function was derived for different spacing between elements.

Khalil, Ali E.↗
DOE OSTI2021

Thermodynamically Stable, Plasmonic Transition Metal Oxide Nanoparticle Solar Selective Absorbers towards 95% Optical-to-Thermal Conversion Efficiency at 750 °C

Generation 3 (Gen) concentrating solar power (CSP) systems requires a high operation temperature ≥750°C to increase the power-cycle efficiency towards ≥50%. However, such a high operation temperature poses a notable challenge to high temperature materials. On the receiver side, a critical challenge is the lack of solar selective absorbers that demonstrate both high optical-to-thermal energy conversion efficiency η therm approaching 95% and long-term thermal stability at >750°C in air. Existing solar absorbers either have limited η therm ≤89% or deteriorate significantly within 500 h at 750°C; some of these also require costly vacuum deposition for stringent thickness control. Therefore, it is highly desirable to simultaneously achieve η therm ~95% AND high thermal stability at 750°C for future generations of CSP receivers. This project has investigated and developed low-cost, highly scalable spray-coated transition metal oxide nanoparticle (NP) pigmented solar selective coatings on various types of Inconel alloy tube sections that are thermodynamically stable at 750-800°C in air, maintaining η therm >94.3%(93.2%) under a solar concentration ratio of C=1000 after 60 simulated day-night cycles at 750ºC (800ºC) (1 cycle=12 h at 750 or 800°C and 12h ramping down to 25°C). We have also coated up to 48 inches long receiver tubes for preliminary solar testing under Norwich Technology’s parabolic trough systems, demonstrating notably improved performance in solar heating compared to benchmark Pyromark 2500 coatings. Two key innovations have been developed in this project: (1) We achieved an unprecedented high thermal efficiency >94% by optimizing the d-band optical absorption spectra of transition metal ions, engineering their valences and stoichiometry; (2) We were able to maintain or even slightly increase the efficiency when operating at 750°C in air by engineering the interdiffusion of transition metal ions between the coating and the Inconel substrate to our advantage. Featuring high-temperature solar spectral selectivity and thermodynamic stability in air, as well as low-cost, highly scalable solution-chemical synthesis and spray coating techniques, this innovation in solar selective absorber technology alone accounts for nearly 40% of the targeted reduction in the levelized cost of electricity (LCOE) from the receiver, thermal energy storage, and operation & maintenance combined by 2030, as proposed by the U.S. Department of Energy. For a 110 MWe CSP power plant, this LCOE reduction from the solar selective coating alone transfers to ~$\$ $1.9 M increase in annual profit based on a sales price of 10¢/kWh (or an annual sale of $50 M/year). The high solar absorptance (~98%) NP pigment materials developed in this project are equally applicable to volumetric receivers either as a coating or as bigger ceramic microspheres after sintering, potentially benefiting Gen3 falling particle CSP technologies. All these contributions facilitate the larger scale deployment of CSP systems with energy storage capability to address the intermittency issue of solar energy towards dispatchable solar electricity, bridging the temporal gap between peak solar electricity production and peak electricity consumption. The collaboration with Norwich Technologies and Brayton Energy in this project will also facilitate the future commercialization of this new solar selective coating technology developed in this SIPS project.

14 SOLAR ENERGY↗
NASA NTRS1989

Analysis of low Reynolds number separation bubbles using semiempirical methods

The formation and growth of transitional separation bubbles can significantly affect boundary-layer development on airfoils operating at low chord Reynolds numbers. Of primary concern is the change in boundary-layer thickness between laminar separation and turbulent reattachment. This can be estimated using semiempirical methods, such as the one devised by Horton (1968), which are based on solutions to the integral forms of the boundary-layer equations. The applicability of these methods at low Reynolds numbers was investigated using hot-wire measurements of bubbles formed on an NACA 66(3)-018 airfoil at chord Reynolds numbers of 50,000-200,000. The momentum thickness growth between separation and transition was found to be similar to that predicted for a laminar half-jet and appears to be influenced by the momentum thickness Reynolds number at separation. This parameter also was found to have a noticeable effect on the Reynolds number based on the length of a bubble's laminar portion.

Schmidt, Gordon S.↗
DOE OSTI2020

CCE Phase 2: System-of-System Analysis

During Phase 1, Consequence Prioritization, the CCE Team identified High Consequence Events (HCEs) that can be accomplished through cyber means to impact critical functions, services, and processes. During Phase 2, System-of-Systems Analysis (SoS Analysis), the CCE Team will conduct a systematic review and analysis of information related to the equipment, systems, processes, operations, maintenance, testing, and procurement practices based on the HCEs identified in Phase 1.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2023

Turbulence and E × B flow correlations across the L-H transition in DIII-D deuterium and hydrogen plasmas

The isotope dependence of the low- to high confinement-mode (L- to H-mode) transition power threshold P LH presents significant challenges for the initial (non-nuclear) hydrogen operations phase of the international thermonuclear experimental reactor (ITER). Here, we examine the isotope dependence of turbulence and E × B flow correlation properties in the L-mode edge plasma, leading up to the L-H transition. At marginal auxiliary power (near P LH ), turbulence is initially suppressed periodically during limit cycle oscillations (LCO) that precede the transition to sustained H-mode confinement. Here, we present evidence that the long-range (toroidal) correlation of the E × B edge plasma flow across the LCO phase is much weaker in hydrogen than in deuterium in the DIII-D tokamak, congruent with the higher threshold power P LH required to access LCO and H-mode in hydrogen. Concomitantly, the time required to initially quench edge turbulence via localized edge E × B flow shear is significantly longer in hydrogen (1–1.5 ms) than in deuterium (approx. 100 µs). No toroidal long-range correlation of the turbulence amplitude is observed, in agreement with expectations based on the relatively short poloidal turbulence correlation length. Radial edge turbulence and flow correlation lengths are longer in deuterium than in hydrogen plasmas as one would expect from ‘naïve’ gyro-Bohm isotope transport scaling, despite the substantially higher thermal flux across the last closed flux surface in hydrogen before the L-H transition. This article is part of a discussion meeting issue 'H-mode transition and pedestal studies in fusion plasmas'.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Ten questions concerning energy flexibility in buildings

Demand side energy flexibility is increasingly being viewed as an essential enabler for the swift transition to a low-carbon energy system that displaces conventional fossil fuels with renewable energy sources while maintaining, if not improving, the operation of the energy system. Building energy flexibility may address several challenges facing energy systems and electricity consumers as society transitions to a low-carbon energy system characterized by distributed and intermittent energy resources. For example, by changing the timing and amount of building energy consumption through advanced building technologies, electricity demand and supply balance can be improved to enable greater integration of variable renewable energy. Although the benefits of utilizing energy flexibility from the built environment are generally recognized, solutions that reflect diversity in building stocks, customer behavior, and market rules and regulations need to be developed for successful implementation. In this paper, we pose and answer ten questions covering technological, social, commercial, and regulatory aspects to enable the utilization of energy flexibility of buildings in practice. In particular, we provide a critical overview of techniques and methods for quantifying and harnessing energy flexibility. We discuss the concepts of resilience and multi-carrier energy systems and their relation to energy flexibility. We argue the importance of balancing stakeholder engagement and technology deployment. Finally, we highlight the crucial roles of standardization, regulation, and policy in advancing the deployment of energy flexible buildings.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS2008

In-Flight Operation of the Dawn Ion Propulsion System - The First Nine Months

The Dawn mission, part of NASA's Discovery Program, has as its goal the scientific exploration of the two most massive main-belt asteroids, Vesta and Ceres. The Dawn spacecraft was launched from Cape Canaveral Air Force Station on September 27, 2007 on a Delta-II 7925H-9.5 (Delta-II Heavy) rocket that placed the 1218 kg spacecraft into an Earth-escape trajectory. On-board the spacecraft is an ion propulsion system (IPS) which will provide most of the delta-V needed for heliocentric transfer to Vesta, orbit capture at Vesta, transfer to Vesta science orbits, departure and escape from Vesta, heliocentric transfer to Ceres, orbit capture at Ceres, and transfer to Ceres science orbits. The Dawn ion engine design is based on the design validated on NASA's Deep Space 1 mission. However, because of the very substantial (11 km/s) delta-V requirements for this mission Dawn requires two engines to complete its mission objectives. The power processor units (PPU), digital control and interface units (DCIU) slice boards and the xenon control assembly (XCA) are also based on the DS1 design. The DCIUs and thrust gimbal assemblies (TGA) were developed at the Jet Propulsion Laboratory. The spacecraft was provided by Orbital Sciences Corporation, Sterling, Virginia, and the mission is managed by and operated from the Jet Propulsion Laboratory. Dawn partnered with Germany, Italy and Los Alamos National Laboratory for the science instruments. The mission is led by the principal investigator, Dr. Christopher Russell, from the University of California, Los Angeles. The first 80 days after launch were dedicated to the initial checkout of the spacecraft prior to the initiation of long-term thrusting for the heliocentric transfer to Vesta. The IPS hardware, consisting of three ion thrusters and TGAs, two PPUs and DCIUs, xenon feed system, and spacecraft control software, was investigated extensively. Thrust measurements, roll torque measurements, pointing capabilities, control characteristics, and thermal behavior of the spacecraft and IPS were carefully evaluated. The Dawn IPS fully met all its initial checkout performance objectives. Deterministic thrusting for cruise began on December 17, 2007. Over the subsequent approximately 330 days the IPS will be operated virtually continuously at full power thrusting (approximately 91 mN) leading to a Mars flyby in February 2009. The encounter with Mars provides a gravity assist for a plane change and is the only source of post-launch delta-V apart from the IPS. Following the Mars gravity assist IPS will be operated for approximately one year at full power and for 1.3 years at throttled power levels leading to rendezvous with Vesta in August of 2011. Following nine months of orbital operations with IPS providing the propulsion needed for orbit capture, science orbit transfer and orbit maintenance and Vesta escape, Dawn will transit to Ceres with an expected arrival date of February 2015. As of June 16, 2008 the ion thrusters on Dawn have operated for close to 3,846 hours and have delivered nearly 1 km/s of delta-V to the spacecraft. Dawn IPS operation has been almost flawless during the initial checkout and six months of cruise. This paper provides an overview of Dawn's mission objectives, mission and system design, and the results of the post-launch Dawn IPS mission operations through June 2008

Garner, Charles E.↗
NASA NTRSDate not supplied

Automatic Dependent Surveillance-Broadcast (ADS-B) In-Trail Procedures (ITP)

Aircraft in oceanic and remote non-radar airspace frequently fly for extended periods of time in the same direction, at the same time, along similar flight paths as other aircraft. Since there is no radar surveillance, controllers use procedural separation to ensure that aircraft remain separated. Procedural separation distances are typically larger than radar separation distances and as a result aircraft operating in oceanic airspace are sometimes held at non-optimal flight levels due to conflicting traffic at intervening flight levels. Automatic Dependent Surveillance-Broadcast (ADS-B) In-Trail Procedures (ITP) were developed to enable flight level change maneuvers that would otherwise not be possible with current procedural separation standards. Aircraft operators choosing to equip with an ADS-B transceiver and an appropriate onboard decision support system would be able to take advantage of these procedures when operating in proximity to aircraft equipped with a suitable ADS-B transmitter (“ADS-B Out”). The ability to perform in-trail maneuvers to achieve more time at optimum altitudes could result in more efficient and predictable flight profiles thereby saving fuel and in some cases allowing operators to make beneficial operational decisions. NASA first began developing ADS-B ITP in 2003 as a result of a desire to develop methodologies, concepts, and procedures to reduce separation requirements for future air transportation systems using airborne ADS-B. The objectives were to provide insight into the details necessary to reduce separation requirements for the future and to develop applications that could provide incentives for operators to voluntarily equip with transformational technologies. From 2003 to 2008, NASA conducted research that supported the development of ITP including batch simulations, human-in-the-loop experiments and avionics and separation standards development. This research showed enough maturity and benefit that in 2008, the FAA Surveillance and Broadcast Services (SBS) program adopted ADS-B ITP as one of their three key, near-term applications to make use of ADS-B-In. The FAA developed an agreement with NASA to transition the technology and established an FAA project for the purpose of performing an operational trial of ADS-B ITP in revenue service in the summer of 2011. The objectives of the project are to a) validate the operational performance and economic benefits of ITP; and b) develop and validate ADS-B ITP Minimum Operational Performance Specifications (MOPS) material. As a part of this project, the FAA established agreements with United Airlines and Honeywell. The agreements include the work necessary for the development, certification and installation of onboard systems for twelve United Airlines 747-400s. ITP system development is nearly complete and certification activities are underway. The FAA project has also been working with Oakland Oceanic Control Center (ZOA) and the FAA’s Oceanic and Offshore Operations Office to develop controller procedures and safety analyses that are required to support the flight trial. The FAA has also been working on the development of an ITP Operational Specification that should be approved this April. The presentation will cover some of the key aspects of the development, challenges, and integration required to successfully transition ADS-B ITP from a concept in 2003 to flight trials in revenue service in 2011.

Kenneth M Jones↗
NASA NTRS2015

Altitude Compensating Nozzle

The dual-bell nozzle (fig. 1) is an altitude-compensating nozzle that has an inner contour consisting of two overlapped bells. At low altitudes, the dual-bell nozzle operates in mode 1, only utilizing the smaller, first bell of the nozzle. In mode 1, the nozzle flow separates from the wall at the inflection point between the two bell contours. As the vehicle reaches higher altitudes, the dual-bell nozzle flow transitions to mode 2, to flow full into the second, larger bell. This dual-mode operation allows near optimal expansion at two altitudes, enabling a higher mission average specific impulse (Isp) relative to that of a conventional, single-bell nozzle. Dual-bell nozzles have been studied analytically and subscale nozzle tests have been completed.1 This higher mission averaged Isp can provide up to a 5% increase2 in payload to orbit for existing launch vehicles. The next important step for the dual-bell nozzle is to confirm its potential in a relevant flight environment. Toward this end, NASA Marshall Space Flight Center (MSFC) and Armstrong Flight Research Center (AFRC) have been working to develop a subscale, hot-fire, dual-bell nozzle test article for flight testing on AFRC's F15-D flight test bed (figs. 2 and 3). Flight test data demonstrating a dual-bell ability to control the mode transition and result in a sufficient increase in a rocket's mission averaged Isp should help convince the launch service providers that the dual-bell nozzle would provide a return on the required investment to bring a dual-bell into flight operation. The Game Changing Department provided 0.2 FTE to ER42 for this effort in 2014.

Ruf, Joseph H.↗
DOE OSTI2026

Engineering Na‐Rich P2‐Type Layered Oxides Through Li/Ti Dual Doping for Oxygen Redox Activation and Superior Structural Stability

Sodium layered oxides Na x MO 2 (x ≤ 1 and M = transition metal ions) have gained significant interest as sodium-ion battery (NIB) cathodes owing to their high operating voltages and potential for higher energy density compared with polyanion and Prussian blue–type cathodes. However, their practical applications are often hindered by the irreversible structural transitions leading to capacity fading during cycling. The nature and substitution of transition metal ions define the material properties and electrochemical performance. In this study, through comprehensive electrochemical characterization combined with multi-scale structural and spectroscopical analyses, we demonstrate the synergistic impacts of Lithium and Titanium doping, which not only increases overall capacity by boosting cation and anion cooperative redox contributions but also improves the rate capability and cycling stability. Specifically, Li + doping enhances the available sodium inventory for extraction, while Ti 4+ disrupts Na + /vacancy ordering at lower voltages (< 4 V) and mitigates the detrimental P2→OP4/O2 phase transition during cycling. The combined effect of Lithium and Titanium doping promotes more charge localization on Oxygen, which activates reversible lattice oxygen redox reactions at elevated voltages, contributing additional capacity beyond conventional cationic redox. This work provides crucial insights into the design of high-performance, high-capacity P2-type layered cathode materials for sodium-ion batteries.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Identification of Intraday False Data Injection Attack on DER Dispatch Signals

The urgent need for the decarbonization of power grids has accelerated the integration of renewable energy. Concurrently, increasing distributed energy resources (DER) and advanced metering infrastructure (AMI) have transformed the power grids into a more sophisticated cyber-physical system with numerous communication devices. While these transitions provide economic and environmental value, they also impose increased risk of cyber attacks and operation al challenges. This paper investigates the vulnerabilit y of the power grids with high renewable penetration against an intraday false data injection (FDI) attack on DER dispatch signals and proposes a kernel support vector regression (SVR) based detection model as a countermeasure. The intraday FDI attack scenario and the detection model are demonstrated in a numerical experiment using the HCE 187-bus test system.

Kim, Jip↗
DOE OSTI2020

Smart Inverters for Seamless Reconnection of Isolated Residential Microgrids to Utility Grid

This paper proposes an approach to achieve seamless reconnection of isolated residential microgrids to utility grid. Any abnormal condition on the grid side results in isolating the residential microgrid from utility grid, and giving the full responsibility of supplying household loads to local distributed generation (DG) units. However, after resolving the abnormal condition on the grid side, the residential microgrid needs to seamlessly reconnect to the main grid. To this end, a seamless transition algorithm is presented which monitors the system condition in real time, and coordinates the operation of all inverter-based DG units in residential microgrid before reconnection to the main grid. A modified control scheme is proposed for single-phase inverters which turns them into smart inverters enable to interact with seamless transition algorithm. The proposed approach synchronizes each phase voltage with its respective grid-side voltage in order to seamlessly reconnect the residential microgrid to the main grid. Case study results are carried out in PSCAD/EMTDC environment to verify the validity of proposed method.

Pilehvar, Mohsen S.↗
NASA NTRS1979

Concept for UF6-fueled self-critical DNPL reactor system

An analytical study of a self-critical nuclear pumped laser system concept was performed. The primary emphasis was on a reactor concept which would use gaseous uranium hexafluoride (UF6) as the fissioning material. A reference configuration was selected which has a 3.2 cu m lasing volume as the reactor core. The core is composed of a series of hexagonal graphite tubes which are surrounded by a reflector-moderator composed either of heavy water or beryllium. Laser transitions requiring average fission power densities less than approximately 1 kW/cu cm for excitation are most attractive. Operation at wavelengths greater than approximately 400 nm may be required because of limitations imposed by the opacity of gaseous UF6. Further research directed toward identification of UF6 compatible lasing transitions is required.

Rodgers, R. J.↗