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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

ON THE INTRINSIC CONTINUUM LINEAR POLARIZATION OF CLASSICAL BE STARS DURING DISK GROWTH AND DISSIPATION

We investigate the intrinsic continuum linear polarization from axisymmetric density distributions of gas surrounding classical Be stars during the formation and dissipation of their circumstellar disks. We implement a Monte Carlo calculation of the Stokes parameters with the use of the non-LTE radiative transfer code of Sigut and Jones to reproduce the continuous polarimetric spectra of classical Be stars. The scattering of light in the nonspherical circumstellar envelopes of classical Be stars produces a distinct polarization signature that can be used to study the physical nature of the scattering environment. In this paper, we highlight the utility of polarimetric measurements as important diagnostics in the modeling of these systems. We illustrate the effects of using self-consistent calculation of the thermal structure of the circumstellar gas on the characteristic wavelength-dependence of the polarization spectrum. In showing that the principal features of the polarization spectrum originate from different parts of the disk, we emphasize the capability of polarimetric observations to trace the evolution of the disk on critical scales. We produce models that approximate the disk formation and dissipation periods and illustrate how the polarimetric properties of these systems can have a pivotal role in determining the mechanism for mass decretion from the central star.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

THE IONIZED CIRCUMSTELLAR ENVELOPES OF ORION SOURCE I AND THE BECKLIN-NEUGEBAUER OBJECT

The 229 GHz ({lambda}1.3 mm) radio emission from Orion-KL was mapped with up to 0.''14 angular resolution with CARMA, allowing measurements of the flux densities of Source I ({sup S}rcI{sup )} and the Becklin-Neugebauer Object (BN), the two most massive stars in this region. We find integrated flux densities of 310 {+-} 45 mJy for SrcI and 240 {+-} 35 mJy for BN. SrcI is optically thick even at 229 GHz. No trace of the H30{alpha} recombination line is seen in its spectrum, although the v {sub 2} = 1, 5(5,0)-6(4,3) transition of H{sub 2}O, 3450 K above the ground state, is prominent. SrcI is elongated at position angle 140 Degree-Sign , as in 43 GHz images. These results are most easily reconciled with models in which the radio emission from SrcI arises via the H{sup -} free-free opacity in a T < 4500 K disk, as considered by Reid et al. By contrast, the radio spectrum of BN is consistent with p {sup +}/e {sup -} free-free emission from a dense (n{sub e} {approx} 5 Multiplication-Sign 10{sup 7} cm{sup -3}), but otherwise conventional, hypercompact H II region. The source is becoming optically thin at 229 GHz, and the H30{alpha} recombination line, at V {sub LSR} = 23.2 {+-} 0.5 km s{sup -1}, is prominent in its spectrum. A Lyman continuum flux of 5 Multiplication-Sign 10{sup 45} photons s{sup -1}, consistent with that expected from a B star, is required to maintain the ionization. Supplementary 90 GHz observations were made to measure the H41{alpha} and H42{alpha} recombination lines toward BN. Published 43 and 86 GHz data suggest that SrcI brightened with respect to BN over the 15 year period from 1994 to 2009.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Hard X-ray morphological and spectral studies of the galactic center molecular cloud SGR B2: Constraining past SGR A{sup ⋆} flaring activity

In 2013, NuSTAR observed the Sgr B2 region and for the first time resolved its hard X-ray emission on subarcminute scales. Two prominent features are detected above 10 keV: a newly emerging cloud, G0.66−0.13, and the central 90″ radius region containing two compact cores, Sgr B2(M) and Sgr B2(N), surrounded by diffuse emission. It is inconclusive whether the remaining level of Sgr B2 emission is still decreasing or has reached a constant background level. A decreasing X-ray emission can be best explained by the X-ray reflection nebula scenario, where the cloud reprocesses a past giant outburst from Sgr A{sup ⋆}. In the X-ray reflection nebula (XRN) scenario, the 3–79 keV Sgr B2 spectrum allows us to self-consistently test the XRN model using both the Fe Kα line and the continuum emission. The peak luminosity of the past Sgr A{sup ⋆} outburst is constrained to L{sub 3−79keV}∼5×10{sup 38} erg s{sup −1}. A newly discovered cloud feature, G0.66−0.13, shows different timing variability. We suggest that it could be a molecular clump located in the Sgr B2 envelope reflecting the same Sgr A{sup ⋆} outburst. In contrast, if the Sgr B2 X-ray emission has reached a constant background level, it would imply an origin of low-energy cosmic-ray (CR) proton bombardment. In this scenario, from the NuSTAR measurements we infer a CR ion power of dW/dt=(1−4)×10{sup 39} erg s{sup −1} and a CR ionization rate of ζ{sub H}=(6−10)×10{sup −15} H{sup −1} s{sup −1}. These measurements can become powerful tools to constrain the GC CR population.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

“Bloch wave” modification of stimulated Raman by stimulated Brillouin scattering

Using the reduced-description particle-in-cell (RPIC) method, we study the coupling of backward stimulated Raman scattering (BSRS) and backward stimulated Brillouin scattering (BSBS) in regimes where the reflectivity involves the nonlinear behavior of particles trapped in the daughter plasma waves. The temporal envelope of a Langmuir wave (LW) obeys a Schrödinger equation where the potential is the periodic electron density fluctuation resulting from an ion-acoustic wave (IAW). The BSRS-driven LWs in this case have a Bloch wave structure and a modified dispersion due to the BSBS-driven spatially periodic IAW, which includes frequency band gaps at kLW∼kIAW/2∼k0 (kLW, kIAW, and k0 are the wave number of the LW, IAW, and incident pump electromagnetic wave, respectively). This band structure and the associated Bloch wave harmonic components are distinctly observed in RPIC calculations of the electron density fluctuation spectra and this structure may be observable in Thomson scatter. Bloch wave components grow up in the LW spectrum, and are not the result of isolated BSRS. Self-Thomson scattered light from these Bloch wave components can have forward scattering components. The distortion of the LW dispersion curve implies that the usual relationship connecting the frequency shift of the BSRS-scattered light and the density of origin of this light may become inaccurate. The modified LW frequency results in a time-dependent frequency shift that increases as the IAW grows, detunes the BSRS frequency matching condition, and reduces BSRS growth. A dependence of the BSRS reflectivity on the IAW Landau damping results because this damping determines the levels of IAWs. The time-dependent reflectivity in our simulations is characterized by bursts of sub-picosecond pulses of BSRS alternating with multi-ps pulses of BSBS, and BSRS is observed to decline precipitously as soon as SBS begins to grow from low levels. In strong BSBS regimes, the Bloch wave effects in BSRS are strong and temporal anti-correlation with BSRS is due to pump depletion in addition to frequency detuning. In most cases studied, BSBS suppressed the time-averaged reflectivity of BSRS compared to the levels obtained with fixed ions (and therefore no BSBS). The strong spatial modulation of the Bloch Langmuir waves appears to weaken electron trapping and thereby lowers the inflated reflectivity levels of BSRS.

Dodd, E. S.↗
DOE OSTI2015

Copper ESEEM and HYSCORE through ultra-wideband chirp EPR spectroscopy

The main limitation of pulse electron paramagnetic resonance (EPR) spectroscopy is its narrow excitation bandwidth. Ultra-wideband (UWB) excitation with frequency-swept chirp pulses over several hundreds of megahertz overcomes this drawback. This allows to excite electron spin echo envelope modulation (ESEEM) from paramagnetic copper centers in crystals, whereas up to now, only ESEEM of ligand nuclei like protons or nitrogens at lower frequencies could be detected. ESEEM spectra are recorded as two-dimensional correlation experiments, since the full digitization of the electron spin echo provides an additional Fourier transform EPR dimension. Thus, UWB hyperfine-sublevel correlation experiments generate a novel three-dimensional EPR-correlated nuclear modulation spectrum.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2012

LONG-DURATION X-RAY FLASH AND X-RAY-RICH GAMMA-RAY BURSTS FROM LOW-MASS POPULATION III STARS

Recent numerical simulations suggest that Population III (Pop III) stars were born with masses not larger than {approx}100 M {sub Sun} and typically {approx}40 M {sub Sun }. By self-consistently considering the jet generation and propagation in the envelope of these low-mass Pop III stars, we find that a Pop III blue supergiant star has the possibility of giving rise to a gamma-ray burst (GRB) even though it keeps a massive hydrogen envelope. We evaluate observational characteristics of Pop III GRBs and predict that Pop III GRBs have a duration of {approx}10{sup 5} s in the observer frame and a peak luminosity of {approx}5 Multiplication-Sign 10{sup 50} erg s{sup -1}. Assuming that the E {sub p}-L {sub p} (or E {sub p}-E {sub {gamma},iso}) correlation holds for Pop III GRBs, we find that the spectrum peak energy falls at approximately a few keV (or {approx}100 keV) in the observer frame. We discuss the detectability of Pop III GRBs by future satellite missions such as EXIST and Lobster. If the E {sub p}-E {sub {gamma},iso} correlation holds, we have the possibility to detect Pop III GRBs at z {approx} 9 as long-duration X-ray-rich GRBs by EXIST. Conversely, if the E {sub p}-L {sub p} correlation holds, we have the possibility to detect Pop III GRBs up to z {approx} 19 as long-duration X-ray flashes by Lobster.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

AGC-2 Graphite Preirradiation Data Package

The NGNP Graphite R&D program is currently establishing the safe operating envelope of graphite core components for a Very High Temperature Reactor (VHTR) design. The program is generating quantitative data necessary for predicting the behavior and operating performance of the new nuclear graphite grades. To determine the in-service behavior of the graphite for pebble bed and prismatic designs, the Advanced Graphite Creep (AGC) experiment is underway. This experiment is examining the properties and behavior of nuclear grade graphite over a large spectrum of temperatures, neutron fluences and compressive loads. Each experiment consists of over 400 graphite specimens that are characterized prior to irradiation and following irradiation. Six experiments are planned with the first, AGC-1, currently being irradiated in the Advanced Test Reactor (ATR) and pre-irradiation characterization of the second, AGC-2, completed. This data package establishes the readiness of 512 specimens for assembly into the AGC-2 capsule.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2014

Dirac cones in the spectrum of bond-decorated graphenes

We present a two-band model based on periodic Hückel theory, which is capable of predicting the existence and position of Dirac cones in the first Brillouin zone of an infinite class of two-dimensional periodic carbon networks, obtained by systematic perturbation of the graphene connectivity by bond decoration, that is by inclusion of arbitrary π-electron Hückel networks into each of the three carbon–carbon π-bonds within the graphene unit cell. The bond decoration process can fundamentally modify the graphene unit cell and honeycomb connectivity, representing a simple and general way to describe many cases of graphene chemical functionalization of experimental interest, such as graphyne, janusgraphenes, and chlorographenes. Exact mathematical conditions for the presence of Dirac cones in the spectrum of the resulting two-dimensional π-networks are formulated in terms of the spectral properties of the decorating graphs. Our method predicts the existence of Dirac cones in experimentally characterized janusgraphenes and chlorographenes, recently speculated on the basis of density functional theory calculations. For these cases, our approach provides a proof of the existence of Dirac cones, and can be carried out at the cost of a back of the envelope calculation, bypassing any diagonalization step, even within Hückel theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

On the Relation of Silicates and SiO Maser in Evolved Stars

The SiO molecule is one of the candidates for the seed of silicate dust in the circumstellar envelope of evolved stars, but this opinion is challenged. In this work we investigate the relation of the SiO maser emission power and the silicate dust emission power. With both our own observation by using the PMO/Delingha 13.7 m telescope and archive data, a sample is assembled of 21 SiO v = 1, J = 2 − 1 sources and 28 SiO v = 1, J = 1 − 0 sources that exhibit silicate emission features in the ISO /SWS spectrum as well. The analysis of their SiO maser and silicate emission power indicates a clear correlation, which is not against the hypothesis that the SiO molecules are the seed nuclei of silicate dust. On the other hand, no correlation is found between SiO maser and silicate crystallinity, which may imply that silicate crystallinity does not correlate with mass-loss rate.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

High-resolution absorption spectroscopy of room-temperature and jet-cooled ammonia between 59,000 and 93,000 cm -1

Here, we present new high-resolution photoabsorption spectra of ammonia spanning the region between 59,000 cm -1 and 93,000 cm -1 that were recorded by using the Fourier Transform Spectrometer at the Synchrotron SOLEIL. This region extends from just above the Franck-Condon envelope for the $\tilde{A}$ 1 $A$ 2 " ← $\tilde{X}$ 1 $A$ 1 ' transition to well above the NH 3 + $\tilde{X}$ + 2 $A$ 2 " ionization threshold. The spectra were recorded at a measured resolution of 0.23 cm -1 in both a room-temperature cell (293 K) and in a slit-jet supersonic expansion (~70 K). The absolute photoabsorption cross section with an uncertainty of ±5% is also reported for the room-temperature spectrum. The present resolution is a factor of 10 – 100 times higher than in other recently reported broad band spectra of ammonia, and many of the observed bands show partially resolved rotational structure. We have attempted to assign this structure for a number of these bands. The oscillator strengths extracted from the data are in good agreement with previous measurements but, in the case of structured bands, the present higher resolution measurements return higher peak absorption cross sections, that increase further when the sample is cooled. The present higher resolution spectra suggest that a number of previous vibronic band assignments that were based on quantum defect considerations may require some revision. Finally, we discuss the substantial differences between the photoabsorption and photoionization data just above the first ionization threshold.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2014

Neutrino emission in the jet propagation process

Relativistic jets are universal in long-duration gamma-ray burst (GRB) models. Before breaking out, they must propagate in the progenitor envelope along with a forward shock and a reverse shock forming at the jet head. Both electrons and protons will be accelerated by the shocks. High-energy neutrinos could be produced by these protons interacting with stellar materials and electron-radiating photons. The jet will probably be collimated, which may have a strong effect on the final neutrino flux. Under the assumption of a power-law stellar-envelope density profile ρ∝r {sup –α} with index α, we calculate the neutrino emission flux by these shocks for low-luminosity GRBs (LL-GRBs) and ultra-long GRBs (UL-GRBs) in different collimation regimes, using the jet propagation framework developed by Bromberg et al. We find that LL-GRBs and UL-GRBs are capable of producing detectable high-energy neutrinos up to ∼PeV, from which the final neutrino spectrum can be obtained. Further, we conclude that a larger α corresponds to greater neutrino flux at the high-energy end (∼PeV) and to higher maximum neutrino energy as well. However, such differences are so small that it is not promising for us to be able to distinguish these in observations, given the energy resolution we have now.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

THE PROGENITOR OF SN 2011ja: CLUES FROM CIRCUMSTELLAR INTERACTION

Massive stars, possibly red supergiants, which retain extended hydrogen envelopes until core collapse, produce Type II plateau (IIP) supernovae. The ejecta from these explosions shocks the circumstellar matter originating from the mass loss of the progenitor during the final phases of its life. This interaction accelerates particles to relativistic energies which then lose energy via synchrotron radiation in the shock-amplified magnetic fields and inverse Compton scattering against optical photons from the supernova. These processes produce different signatures in the radio and X-ray parts of the electromagnetic spectrum. Observed together, they allow us to break the degeneracy between shock acceleration and magnetic field amplification. In this work, we use X-rays observations from the Chandra and radio observations from the Australia Telescope Compact Array to study the relative importance of processes which accelerate particles and those which amplify magnetic fields in producing the non-thermal radiation from SN 2011ja. We use radio observations to constrain the explosion date. Multiple Chandra observations allow us to probe the history of variable mass loss from the progenitor. The ejecta expands into a low-density bubble followed by interaction with a higher density wind from a red supergiant consistent with M{sub ZAMS} {approx}> 12 M{sub Sun }. Our results suggest that a fraction of Type IIP supernovae may interact with circumstellar media set up by non-steady winds.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

THE IMPRINT OF EXOPLANET FORMATION HISTORY ON OBSERVABLE PRESENT-DAY SPECTRA OF HOT JUPITERS

The composition of a planet’s atmosphere is determined by its formation, evolution, and present-day insolation. A planet’s spectrum therefore may hold clues on its origins. We present a “chain” of models, linking the formation of a planet to its observable present-day spectrum. The chain links include (1) the planet’s formation and migration, (2) its long-term thermodynamic evolution, (3) a variety of disk chemistry models, (4) a non-gray atmospheric model, and (5) a radiometric model to obtain simulated spectroscopic observations with James Webb Space Telescope and ARIEL. In our standard chemistry model the inner disk is depleted in refractory carbon as in the Solar System and in white dwarfs polluted by extrasolar planetesimals. Our main findings are: (1) envelope enrichment by planetesimal impacts during formation dominates the final planetary atmospheric composition of hot Jupiters. We investigate two, under this finding, prototypical formation pathways: a formation inside or outside the water iceline, called “dry” and “wet” planets, respectively. (2) Both the “dry” and “wet” planets are oxygen-rich (C/O < 1) due to the oxygen-rich nature of the solid building blocks. The “dry” planet’s C/O ratio is <0.2 for standard carbon depletion, while the “wet” planet has typical C/O values between 0.1 and 0.5 depending mainly on the clathrate formation efficiency. Only non-standard disk chemistries without carbon depletion lead to carbon-rich C/O ratios >1 for the “dry” planet. (3) While we consistently find C/O ratios <1, they still vary significantly. To link a formation history to a specific C/O, a better understanding of the disk chemistry is thus needed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Fluorescent lighting with aluminum nitride phosphors

A fluorescent lamp includes a glass envelope; at least two electrodes connected to the glass envelope; mercury vapor and an inert gas within the glass envelope; and a phosphor within the glass envelope, wherein the phosphor blend includes aluminum nitride. The phosphor may be a wurtzite (hexagonal) crystalline structure Al.sub.(1-x)M.sub.xN phosphor, where M may be drawn from beryllium, magnesium, calcium, strontium, barium, zinc, scandium, yttrium, lanthanum, cerium, praseodymium, europium, gadolinium, terbium, ytterbium, bismuth, manganese, silicon, germanium, tin, boron, or gallium is synthesized to include dopants to control its luminescence under ultraviolet excitation. The disclosed Al.sub.(1-x)M.sub.xN:Mn phosphor provides bright orange-red emission, comparable in efficiency and spectrum to that of the standard orange-red phosphor used in fluorescent lighting, Y.sub.2O.sub.3:Eu. Furthermore, it offers excellent lumen maintenance in a fluorescent lamp, and does not utilize "critical rare earths," minimizing sensitivity to fluctuating market prices for the rare earth elements.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Modification of conventional peak shapes to accurately represent spectral asymmetry: High-Resolution X-ray photoelectron spectra of [C 4 C 1 Pyrr][NTf 2 ] and [C 8 C 1 Im][NTf 2 ] ionic liquids

X-ray photoelectron spectroscopy (XPS) is one of the most widely used techniques for surface characterization. Analysis of XPS data is challenging and requires the analyst to fit the data with synthetic line shapes to reach physically meaningful interpretations. Experimental spectral envelopes, however, are complex and display asymmetric features that are often ignored or attributed to additional chemical components. The high-resolution XPS spectra of [C 4 C 1 Pyrr][NTf 2 ] and [C 8 C 1 Im][NTf 2 ] all exhibit a degree of asymmetry which is systematically observed at the higher binding energy side of photoemission envelopes. Here, we present the development of a refined fitting procedure for XPS spectra of these ionic liquid-based systems which include (a) Shirley background offset necessary to account for the insulator-like region and (b) spectral asymmetry in C 1s and N 1s regions. Further, Shirley and trapezoid components are applied to compensate for inelastic scattering taking place during electron transitions as high as 7.8 eV above the start of the fitting region in C 1s high-resolution spectrum. To demonstrate the fitness of this model, we present an analysis of a 2:1 mixture of [C 4 C 1 Pyrr][NTf 2 ]: [C 8 C 1 Im][NTf 2 ].

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2012

Regions of azimuthal instability in gyrotrons

This paper is devoted to the analysis of the instability of operating modes in high-power gyrotrons with cylindrically symmetric resonators. This instability manifests itself in destruction of the azimuthally uniform wave envelope rotating in a gyrotron resonator having a transverse size greatly exceeding the wavelength. The appearance of azimuthally nonuniform solutions can be interpreted as simultaneous excitation of modes with different azimuthal indices. This problem is studied self-consistently, i.e., taking into account the temporal evolution of both the azimuthal and axial structures of the wave envelope. The region of gyrotron operation free from this instability is identified. The efficiency achievable in this region can be only 1%-2% lower than the maximum efficiency. It is also possible to address the difference between the theory of mode interaction developed under assumption that all modes have fixed axial structure and the self-consistent theory presented here. As known, for fixed axial mode profiles, single-mode high-efficiency oscillations remain stable no matter how dense is the spectrum of competing modes, while the self-consistent theory predicts stable high-efficiency operation only when the azimuthal index does not exceed a certain critical value. It is shown that the azimuthal instability found in the self-consistent theory is caused by excitation of modes having axial structures different from that of the desired central mode.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2012

POWER ANISOTROPY IN THE MAGNETIC FIELD POWER SPECTRAL TENSOR OF SOLAR WIND TURBULENCE

We observe the anisotropy of the power spectral tensor of magnetic field fluctuations in the fast solar wind for the first time. In heliocentric RTN coordinates, the power in each element of the tensor has a unique dependence on the angle between the magnetic field and velocity of the solar wind ({theta}{sub B}) and the angle of the vector in the plane perpendicular to the velocity ({phi}{sub B}). We derive the geometrical effect of the high speed flow of the solar wind past the spacecraft on the power spectrum in the frame of the plasma P(k) to arrive at the observed power spectrum P(f, {theta}{sub B}, {phi}{sub B}) based on a scalar field description of turbulence theory. This allows us to predict the variation in the {phi}{sub B} direction and compare it to the data. We then transform the observations from RTN coordinates to magnetic-field-aligned coordinates. The observed reduced power spectral tensor matches the theoretical predictions we derive in both RTN and field-aligned coordinates, which means that the local magnetic field we calculate with wavelet envelope functions is an accurate representation of the physical axis of symmetry for the turbulence and implies that on average the turbulence is axisymmetric. We also show that we can separate the dominant toroidal component of the turbulence from the smaller but significant poloidal component and that these have different power anisotropy. We also conclude that the magnetic helicity is anisotropic and mostly two dimensional, arising from wavevectors largely confined to the plane perpendicular to B .

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Multi-octave visible to long-wave IR femtosecond continuum generated in Cr:ZnS-GaSe tandem

We report a technique for generation of broad and coherent femtosecond (fs) continua that span several octaves from visible to long-wave IR parts of the spectrum (0.4–18 µm). The approach is based on simultaneous amplification of few-cycle pulses at 2.5 µm central wavelength at 80 MHz repetition rate, and augmentation of their spectrum via three-wave mixing in a tandem arrangement of polycrystalline Cr:ZnS and single crystal GaSe. The obtained average power levels include several mW in the 0.4–0.8 µm visible, 0.23 W in the 0.8–2 µm near-IR, up to 4 W in the 2–3 µm IR, and about 17 mW in the 3–18 µm long-wave IR bands, respectively. High brightness and mutual coherence of all parts of the continuum was confirmed by direct detections of the carrier envelope offset frequency of the master oscillator.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗