Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “FUNDAMENTAL”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 199 records · Page 11

Fundamental Power Coupler Technical Development - Final CRADA Report

The SLAC ‘Linac Coherent Light Source -II’ project (LCLS II) is a hard X-ray Free Electron Laser now under construction in support of photon-based material science. LCLS II uses a superconducting linac design based on the twenty year-long TESLA- Technology development effort. The TESLA proposal, the European XFEL (EU-XFEL) project, and the ILC design employ a pulsed superconducting linac with roughly 0.5% duty factor. This aspect was changed for LCLS II so that the FEL could be operated continuous-wave (CW) namely with a 100% duty factor. Several critical changes to the linac design were required including RF power distribution, cryogenic heat-load management and cavity preparation. This note lists the changes required to the fundamental power coupler (FPC). All of these changes were made by the SLAC physics and engineering teams and reviewed by the cryomodule design lead (Fermilab) and international partners. Testing was done by the LCLS II cryomodule teams (Jefferson Lab and Fermilab). The SLAC LCLS II project team managed the design and procurement process. The LCLS II fundamental power coupler design is based upon the DESY TESLA Test Facility (TTF-3) design. DESY shared their drawings with LCLS II and SLAC copied and modified them to meet the LCLS II CW operation power and heat-load requirements. LCLS II had an external reviewer evaluate and compare SLAC drawings to EU-XFEL drawings. SLAC used the same industrial partners that EU-XFEL used.

47 OTHER INSTRUMENTATION↗

Fundamental Mechanisms of C-X bond Transformations on Complex Molten Surfaces

Investigations of fundamental and applied catalysis science began in 1989 with surface science studies of single crystal surfaces and moved into work understanding and measuring direct electronic excitations from chemisorption on metals as "hot electrons", to studies of C-H bond activation on metals. Later studies of metal oxide catalysts led to greater understanding C-X bond activation and transformation on complex surfaces including liquids. In addition to an improved fundamental understanding of important industrial reactions, a primary outcome of this work funded by the U.S. taxpayers has been the large number of graduate and undergraduate students and post-docs who have been educated in catalysis science and engineering with support from this program.

03 NATURAL GAS↗

Experimental Study of the Fundamental Properties of Warm Dense Mixtures

The aim of the proposed research was to provide a multi-scale study of the properties of warm dense hydrocarbons, by studying the thermodynamic properties through the equation of state and the microscopic properties by x-ray scattering. Understanding the fundamental properties of warm dense mixtures is an intellectual challenge due to the complexity of the system. Unlike liquids or gases, where constituent particle interactions occur through collisions or bonding between valence electrons, in these strongly coupled systems the atoms will be partially ionized and compressed so tightly together that interactions between the inner core electrons can play a role in the systems chemistry. Advances in computational capabilities and development of new theoretical models have been used to predict the properties of mixtures but there is currently no experimental data of the fundamental interaction between the particles in mixtures to test these predictions against. The proposed research was to experimentally investigate the interaction of the different species in hydrocarbons by measuring the compressibility of substances with different carbon and hydrogen ratios and the complexity of the microscopic interactions through elastic and inelastic x-ray scattering. To study the bulk properties of warm dense hydrocarbons we established the Warm Dense Matter Research Laboratory (WDMRL) in the Institute for Shock Physics at Washington State University. The goal was for experiments in the WDMRL to determine shock loading conditions of interest in the hydrocarbon mixtures. We planned on using Hugoniot EOS measurements and a range of carbon and hydrogen concentrations to determine conditions when the EOS of the mixture varied significantly from that of the classical mixing model. Even though shock transit measurements through aluminum foils suggested pressures upto 400GPa, the experiments in the WDMRL were unsuccessful in getting usable shockwave compression data above 100GPa in polystyrene which was below the pressure of interest for hydrocarbon mixtures (>200GPa). To complete the project, we tested a technique using x-ray phase contrast imaging to map the location of tracer layers in a test sample of polycarbonate to record the material motion in dynamically compressed samples. A technique that will be useful for future warm dense matter experiments. These experiments used <200nm gold layers in polycarbonate samples to measure the material velocity and shock speed using x-ray phase contrast imaging. These results were compared to continuum surface measurements performed at ISP and show that the tracer layer technique can measure hydrodynamic properties accurately in dynamically compressed materials.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A Call to Arms Control: Synergies between Nonproliferation Applications of Neutrino Detectors and Large-Scale Fundamental Neutrino Physics Experiments (A Snowmass White Paper)

The High Energy Physics community can benefit from a natural synergy in research activities into next-generation large-scale water and scintillator neutrino detectors, now being studied for remote reactor monitoring, discovery and exclusion applications in cooperative nonproliferation contexts. Since approximately 2010, US nonproliferation researchers, supported by the National Nuclear Security Administration (NNSA), have been studying a range of possible applications of relatively large (100 ton) to very large (hundreds of kiloton) water and scintillator neutrino detectors. In parallel, the fundamental physics community has been developing detectors at similar scales and with similar design features for a range of high-priority physics topics, primarily in fundamental neutrino physics. These topics include neutrino oscillation studies at beams and reactors, solar, and geological neutrino measurements, supernova studies, and others. Examples of ongoing synergistic work at U.S. national laboratories and universities include prototype gadolinium-doped water and water-based and opaque scintillator test-beds and demonstrators, extensive testing and industry partnerships related to large area fast position-sensitive photomultiplier tubes, and the development of concepts for a possible underground kiloton-scale water-based detector for reactor monitoring and technology demonstrations. Some opportunities for engagement between the two communities include bi-annual Applied Antineutrino Physics conferences, collaboration with U.S. National Laboratories engaging in this research, and occasional NNSA funding opportunities supporting a blend of nonproliferation and basic science R&D, directed at the U.S. academic community.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Fundamental Structure/Property Studies of Gas Separation Membrane Polymers

Solution-processable polybenzimidazoles (PBIs) present opportunities for new gas separation membranes. We plan to develop systematic structure/property relations for this relatively new class of membrane materials. The fundamental questions we will address are: (1) How do chemical structure modifications of PBIs influence their gas solubility, diffusivity and permeability properties for a systematic series of gases? (2) Is the separation performance of PBIs affected by plasticization under operating conditions that are relevant to, for example, natural gas purification or olefin/paraffin separation and, if so, can this family of materials be tuned structurally to minimize deleterious effects of plasticization on separation properties? (3) What is the effect of water vapor on PBI separation performance? (4) What is the influence of physical aging on permeation properties of thin (i.e., <1 µm) PBI polymer films, and how does the rate of physical aging relate to polymer chemical structure? The primary focus of this research program is to develop a fundamental, molecular-based mechanistic understanding of the influence of chemical structure on the gas transport properties of PBIs and to establish structure/property relationships for this unique platform of materials.

08 HYDROGEN↗

Fundamental studies of thermal and electrical transport in microporous metal-organic frameworks

In this work, we established porous metal-organic frameworks (MOFs) as designer conductors of electrons and ions relevant to fundamental research and technological applications. MOFs are porous, crystalline materials composed of organic linkers and inorganic nodes. While most MOFs are insulating with respect to ionic and electronic charge carriers, a number of exceptions have been reported in recent years. Electrically conductive MOFs are highly attractive for applications including electrical energy storage, chemiresistive sensing, and optoelectronics because of their high surface areas and tunable chemical properties. Ion-conducting MOFs are desirable for the synthetically tunable size, shape, and polarity of their pore environments, allowing for the tailored development of solid state electrolytes for metal-ion batteries. We developed systematic strategies for the design of MOFs that conduct ions and electrons. For each objective, we leveraged the versatile chemistry of these materials to obtain frameworks with targeted properties towards electronic or ionic charge carriers. We studied the factors that govern electrical transport in MOFs in order to gain fundamental knowledge of this emerging class of materials. We took several approaches to tackle this problem from multiple angles. Namely, we synthesized and characterized new frameworks, investigated post-synthetic modifications to enhance conductivity, and correlated theory and experiment to uncover new mechanistic findings. These results, which put forth new design principles for conductive MOFs, move the field toward one of the DOE Basic Energy Sciences Grand Challenges: to “design and perfect atom- and energy-efficient synthesis of revolutionary new forms of matter with tailored properties.” In addition to investigating the movement of electrons in MOFs, we also studied the movement of other charged species in MOFs, such as protons, lithium, and magnesium. Proton-conducting frameworks could be appealing materials for solid state electrolytes in fuel cells. In addition, they contain crystallographically defined proton-conducting channels, in contrast with state-of-the-art polymer membranes such as Nafion, which are amorphous. Controlling pore size and polarity in MOFs can thus shed light on proton and other ion transport mechanisms, ultimately enabling the design of more advanced electrolyte materials and potentially novel electrical energy storage materials.

36 MATERIALS SCIENCE↗

Executive Summary of the Z Fundamental Science Program

The Z Fundamental Science (ZFS) Program is intended to provide access to the Z machine and its diagnostics for high energy density (HED) experiments in collaboration with a broad community of academic, industrial, and national laboratory research interests. ZFS experiments on the Z Facility focus on conducting fundamental research in HED science and help provide research experience necessary to maintain and grow the HED community, especially through involvement of researchers from academia. This report serves as an executive summary of the ZFS Program and provides a succinct synopsis of the history of the ZFS Program, metrics and impacts of the Program, as well as a brief list of the most impactful publications that have resulted from the various ZFS Projects relevant to laboratory astrophysics, plasma physics, and planetary physics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Fundamental Studies of the Vibrational, Electronic, and Photophysical Properties of Tetrapyrrolic Architectures

The ability to capture and utilize light in the near-ultraviolet (NUV), visible and near-infrared (NIR-I and NIR-II) spectral regions (i.e., 320–400, 400–700, 700–1000, 1000–1700 nm) is essential for any solar-energy conversion scheme. Nature employs chlorophylls and bacteriochlorophylls in light-harvesting architectures to absorb light in the blue and red/NIR regions. Accessory pigments (carotenoids, bilins) augment absorption of the (bacterio)chlorophylls in the green region. The harvested energy is funneled to a reaction center protein, where charge separation occurs. Subsequent migration of the electron and the hole stabilizes and stores the energy from light via redox chemistry. The long-term objective of the Bocian/Holten&Kirmaier/Lindsey research program under this DOE grant has been to develop tetrapyrrole-based molecular architectures that absorb sunlight, funnel energy and separate charge with high efficiency. Integral to the program has been iterative cycles of design, synthesis and characterization that provided deep insights into the relationships between chemical composition, electronic structure, and key static and dynamic properties (vibrational, redox, photophysical, energy/charge transfer) of tetrapyrrolic systems. Such architectures included monomers, dyads, larger arrays, and complexes with accessory components. The objective was to develop molecular designs and guiding principles to enhance current and future energy-conversion schemes. Molecular arrays targeted to address one or more fundamental questions concerning light harvesting and energy/charge transfer were constructed from analogues of the naturally occurring hemes, chlorophylls and bacteriochlorophylls. Diverse, tunable synthetic building blocks were prepared that spanned the three respective tetrapyrrole families, which are the porphyrins, chlorins and bacteriochlorins. Thus, the research focused on porphyrins as well as synthetic surrogates for chlorophylls (chlorins, 13 1 -oxophorbines and chlorin-imides) and bacteriochlorophylls (bacteriochlorins, bacterio-13 1 -oxophorbines and bacteriochlorin-imides), generically termed hydroporphyrins. Although the three tetrapyrrole classes (porphyrins, chlorins and bacteriochlorins) absorb light strongly in the violet-blue spectral region, the long-wavelength absorption band typically lies in the green-orange, red, and NIR regions, respectively, with increasing intensity. Understanding the spectra, electronic structure, and energy/charge-transfer properties of such tetrapyrrolic macrocycles is of central importance for the rational design of molecular architectures for solar-energy conversion. Our integrated program of molecular design and synthesis coupled with a variety of spectroscopic, electrochemical, and computational studies have probed from first principles how structural and electronic properties of tetrapyrrolic macrocycles dictate spectral properties as well as the rates of ground-state hole/electron transfer and excited-state energy flow in multicomponent architectures. Individual molecules and multicomponent architectures were designed to test ideas of fundamental importance, often requiring the development of new synthetic methodology. The members of the collaborative team had almost daily discussions by phone and/or e-mail concerning design of molecules, flow of compounds between the labs, planning of physical characterization studies, discussing results and analysis and integrating into design of next generation architectures, and the preparation of manuscripts. Furthermore, students and postdocs in the different labs routinely communicated with one another to facilitate the advancement of the research activities. In short, a highly integrated and collaborative research program was well established among the groups. The research effort involved molecular design and synthesis of synthetic molecular architectures by the Lindsey group integrated with physicochemical and photophysical characterization by the Bocian group and the Holten&Kirmaier group (Figure 2). The Bocian group carried out electrochemical, electron paramagnetic resonance (EPR), resonance Raman (RR), and Fourier-transform infrared (FT-IR) studies, as well as density functional theory (DFT) calculations and the time-dependent extension (TDDFT) to gain insight into excited-state properties. The Holten&Kirmaier group carried out static and time-resolved absorption and fluorescence spectroscopy studies and simulated absorption spectra using molecular orbital (MO) energies from DFT as input to the four-orbital model to complement the TDDFT calculations. The combined measurements provided understanding of the vibrational/electronic properties of the individual molecules and the changes that occur upon incorporation into multicomponent architectures. This information underpinned elucidating the mechanisms and timescales of ground-state hole/electron transfer and excited-state energy and charge transfer.

14 SOLAR ENERGY↗

Unraveling fundamental mechanisms of silicon nitride crystallization in microelectronics manufacturing

This research project investigates the fundamental mechanisms of silicon nitride (SiN) crystallization, aiming to enhance the understanding of this critical material in microelectronics manufacturing. Through a collaborative effort between Sandia National Laboratories, the University of Tennessee, and the University of Florida, we developed a comprehensive framework that integrates experimental techniques, atomistic modeling, meso-scale simulations, and an integrated multi-scale model to capture this physical phenomenon on multiple time and length scales . The project developed a new machine learning based atomistic potential and utilized advanced phase field modeling to capture the complexities of polycrystalline growth and the influence of mechanical stresses on crystallization dynamics. By employing a grain tracker algorithm, the meso-scale model effectively identified and tracked individual crystal grains, enabling the simulation of anisotropic growth behaviors reflective of SiN’s physical properties. The integration of atomistic simulations with meso-scale modeling created a powerful multi-scale framework that validated atomistic inputs and enhanced predictive accuracy for crystallization dynamics at larger scales, validated experimentally. This adaptable modeling capability not only accelerates development times by informing manufacturing processes but also serves as a valuable starting point for understanding crystallization physics in similar materials. The insights gained from this research unlock new opportunities for the development of advanced materials tailored for future microelectronics and photonics applications. Overall, this project represents a significant advancement in understanding of fundamental physics of SiN and establishes a foundation for future research in material science, bridging the gap between atomic-level phenomena and macroscopic material behaviors for practical applications.

36 MATERIALS SCIENCE↗

A new method of studying the fundamental mechanisms involved in pigment liberation from recycle papers

Deinking flotation is the most efficient and widely used method of removing ink particles from printed papers to improve the recyclability. A prerequisite for successful deinking flotation is detachment of pigments from paper fibers, a subprocess known as liberation. The degree of liberation is usually determined via hyperwashing tests, which are costly and time consuming. Furthermore, they provide no information on the fundamental mechanisms controlling liberation. In the present work, we developed a new method in which ?-potentials of the particles in a pulp are measured and analyzed. If pigments are not liberated from paper fibers, a frequency distribution plot gives a single peak, while two peaks appear when they are liberated. One can readily determine the degrees of liberation from the peak positions and peak heights. In addition, the ?-potential data can be used to construct disjoining pressure isotherms using the DLVO theory that are useful to better understand the fundamental mechanisms involved and the roles of different reagents used to improve pigment liberation.

42 ENGINEERING↗

Fundamental physics studies in time domain and multi-messenger astronomy

The era of ime domain and multi-messenger astronomy is not only leading to the development of a much broader set of detectors and instruments for astrophysical observations, but is also providing the means for astronomy to tie directly to cutting-edge studies in physics. In this manner, fundamental physics (theory and experiment) coupled with a strong theoretical understanding of astrophysical phenomena (guided by high-performance computing simulations) can tie directly to the amazing new observations in astronomy. This paper discusses how physics, astrophysical models, and observations can not only help astronomy probe fundamental physics but guide the needs for next-generation astrophysical missions.

79 ASTRONOMY AND ASTROPHYSICS↗

Fundamentals and Applications of Hybrid LWFA-PWFA

Fundamental similarities and differences between laser-driven plasma wakefield acceleration (LWFA) and particle-driven plasma wakefield acceleration (PWFA) are discussed. The complementary features enable the conception and development of novel hybrid plasma accelerators, which allow previously not accessible compact solutions for high quality electron bunch generation and arising applications. Very high energy gains can be realized by electron beam drivers even in single stages because PWFA is practically dephasing-free and not diffraction-limited. These electron driver beams for PWFA in turn can be produced in compact LWFA stages. In various hybrid approaches, these PWFA systems can be spiked with ionizing laser pulses to realize tunable and high-quality electron sources via optical density downramp injection (also known as plasma torch) or plasma photocathodes (also known as Trojan Horse) and via wakefield-induced injection (also known as WII). These hybrids can act as beam energy, brightness and quality transformers, and partially have built-in stabilizing features. They thus offer compact pathways towards beams with unprecedented emittance and brightness, which may have transformative impact for light sources and photon science applications. Furthermore, they allow the study of PWFA-specific challenges in compact setups in addition to large linac-based facilities, such as fundamental beam–plasma interaction physics, to develop novel diagnostics, and to develop contributions such as ultralow emittance test beams or other building blocks and schemes which support future plasma-based collider concepts.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

High-Entropy Alloys (HEA): Fundamentals and Applications

This book provides a systematic and comprehensive description of high-entropy alloys (HEAs). The authors summarize key properties of HEAs from the perspective of both fundamental understanding and applications, which are supported by in-depth analyses. The book also contains computational modeling in tackling HEAs, which help elucidate the formation mechanisms and properties of HEAs from various length and time scales.<br>High-entropy alloys (HEAs) [1,2] loosely refer to multi-principal-element solid solution alloys due to their high configurational entropy, in contrast to traditional alloys, which focus on the edge or corner of phase diagrams with one principal component. The unique compositions and the resulting attractive properties of HEAs have stimulated growing research interest due to scientific curiosity and potential industrial applications [3,4]. In order to balance the properties for targeted applications, the microstructure of HEAs can be a single phase or multiphases, and traditional physical metallurgy principles have been applied to develop a variety of HEAs, including high-entropy stainless steels, high-entropy superalloys, high-entropy refractory alloys, high-entropy light-weight alloys, high-entropy oxides, high-entropy metallic compounds, etc. However, great challenges still remain in the fundamental understanding of HEAs formation and their properties, and potential high-performance HEAs are yet to be explored. This special issue is meant to collect contributions from authors working in the various fields of HEAs to timely disseminate the rapid progress in this fascinating and expanding class of advanced materials.

Gao, Michael↗

Fundamental Plane of Black Hole Activity in the Quiescent Regime

A correlation among the radio luminosity (L{sub R}), X-ray luminosity (L{sub X}), and black hole (BH) mass (M{sub BH}) in active galactic nuclei (AGNs) and BH binaries is known to exist and is called the “fundamental plane” of BH activity. Yuan and Cui predict that the radio/X-ray correlation index, ξ{sub X}, changes from ξ{sub X}≈0.6 to ξ{sub X}≈1.2--1.3 when L{sub X}/L{sub Edd} decreases below a critical value of ∼10{sup −6}. While many works favor such a change, there are also several works claiming the opposite. In this paper, we gather from the literature the largest quiescent AGN (defined as L{sub X}/L{sub Edd}≲10{sup −6}) sample to date, consisting of 75 sources. We find that these quiescent AGNs follow a ξ{sub X}≈1.23 radio/X-ray relationship, in excellent agreement with the Yuan and Cui prediction. The reason for the discrepancy between the present result and some previous works is that their samples contain not only quiescent sources but also “normal” ones (i.e., L{sub X}/L{sub Edd}≳10{sup −6}). In this case, the quiescent sources will mix up with those normal ones in L{sub R} and L{sub X}. The value of ξ{sub X} will then be between 0.6 and ∼1.3, with the exact value being determined by the sample composition, i.e., the fraction of the quiescent and normal sources. Based on this result, we propose that a more physical way to study the fundamental plane is to replace L{sub R} and L{sub X} with L{sub R}/L{sub Edd} and L{sub X}/L{sub Edd}, respectively.

79 ASTRONOMY AND ASTROPHYSICS↗

The Optical Two- and Three-dimensional Fundamental Plane Correlations for Nearly 180 Gamma-Ray Burst Afterglows with Swift/UVOT, RATIR, and the Subaru Telescope

Gamma-ray bursts (GRBs) are fascinating events due to their panchromatic nature. We study optical plateaus in GRB afterglows via an extended search into archival data. We comprehensively analyze all published GRBs with known redshifts and optical plateaus observed by many ground-based telescopes (e.g., Subaru Telescope, RATIR) around the world and several space-based observatories such as the Neil Gehrels Swift Observatory. We fit 500 optical light curves, showing the existence of the plateau in 179 cases. This sample is 75% larger than the previous one, and it is the largest compilation so far of optical plateaus. We discover the 3D fundamental plane relation at optical wavelengths using this sample. This correlation is between the rest-frame time at the end of the plateau emission, ${T}_{\mathrm{opt}}^{* }$, its optical luminosity, L opt , and the peak in the optical prompt emission, L peak,opt , thus resembling the three-dimensional (3D) X-ray fundamental plane (the so-called 3D Dainotti relation). We correct our sample for redshift evolution and selection effects, discovering that this correlation is indeed intrinsic to GRB physics. We investigate the rest-frame end-time distributions in X-rays and optical (${T}_{\mathrm{opt}}^{* }$, ${T}_{{\rm{X}}}^{* }$), and conclude that the plateau is achromatic only when selection biases are not considered. We also investigate if the 3D optical correlation may be a new discriminant between optical GRB classes and find that there is no significant separation between the classes compared to the Gold sample plane after correcting for evolution.

79 ASTRONOMY AND ASTROPHYSICS↗

A Fundamentals Approach to Plant Capacity Testing

This paper provides a recommended method for evaluating the AC capacity of a photovoltaic (PV) generating station. It also presents companion guidance on setting the facilitys capacity guarantee value. This is a principles-based approach that incorporates plant fundamental design parameters such as loss factors, module coefficients, and inverter constraints. This method has been used to prove contract guarantees for over 700 MW of installed projects. The method is transparent, and the results are deterministic. In contrast, current industry practices incorporate statistical regression where the empirical coefficients may only characterize the collected data. Though these methods may work well when extrapolation is not required, there are other situations where the empirical coefficients may not adequately model actual performance.This proposed Fundamentals Approach method provides consistent results even where regression methods start to lose fidelity.

14 SOLAR ENERGY↗

Critical configurations of fundamental range networks.

A range network is defined to consist of ground stations and targets where only distances between the two sets of points are observed. Such a network is said to be fundamental when only those six constraints are used that are needed to define the coordinate system for an adjustment. When ground stations or targets have certain configurations, a unique adjustment in terms of coordinates may be impossible, even when the number of observations is sufficient and the coordinate system is uniquely defined. Such configurations, resulting in the singular solutions, are said to be critical. Attention is therefore focused on singular solutions rather than on numerical problems in some ill-conditioned systems of fundamental range networks. The critical configurations are presented in two separate groups. The first deals with ground stations lying all in a plane and the second deals with ground stations generally distributed. The two kinds of problems require different mathematical treatments and lead to quite different conclusions.

Blaha, G.↗

Type III solar radio bursts and the fundamental-harmonic hypothesis

The observational evidence is reviewed for the occurrence of type III solar radio bursts in pairs with frequency ratio two to one. We show that the observations can be explained under the hypothesis that there is a tendency for a type III burst to be followed by a second burst within approximately one second. This explanation leads to fewer difficulties than the hypothesis that type III bursts occur in pairs, one member being emitted at the fundamental of the local coronal plasma frequency, the other at its second harmonic. We conclude that in general, type III bursts are emitted at the second harmonic of the plasma frequency and that type III theories should account for this and only under very special circumstances (which are rare) for the emission at the fundamental and the second harmonic.

Rosenberg, H.↗