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NASA NTRS1982

The influence of stray magnetic fields on ion beam neutralization

An experimental investigation is described of a comparison between the ion beam neutralization characteristics of a local neutralizer (within approximately 5 cm of the beam edge) and those associated with a distant one (approximately 1 meter away from the thruster). The influence of magnetic fields in the vicinity of the neutralizer cathode orifice which are either parallel or normal to the neutralizer axis is assessed. The plasma property profiles which reflect the influence of the magnetic fields are measured. The results suggest that magnetic fields at the region of a neutralizer cathode orifice influence its ability to couple to the ion beam. They reveal that there is a potential jump from the neutralizer cathode orifice to the plasma which exists close to the orifice. This potential drop is found to increase as the axial component of magnetic flux density increases. A magnetic field perpendicular to the neutralizer axis induces a potential rise a few centimeters downstream from the neutralizer cathode.

Feng, Y.-C.↗

NASA NTRS1995

Dissecting the EUV spectrum of Capella

Extreme ultraviolet spectra of Capella, obtained at various orbital phases over the past two years by the EUVE satellite, show strong emission lines from a continuous distribution of temperatures (approximately 10(exp 5 -10(exp 7.3) K). In addition to the strong He II lambda 303.8, the spectra are dominated by emission lines of highly ionized iron. Strong lines of Fe IX, XV, XVI, and XVIII-XXIV are used to construct emission measure distributions for the individual pointings, which show several striking features, including a minimum near 10(exp 6) K and a local maximum at 10(exp 6.8) K. Furthermore, intensities of the highest temperature lines (Te is greater than 10(exp 7) K) show variations (factors of 2-3) at different orbital phases, while the lower temperature Fe lines show variations of about 30% or less. The low variability of most of the strong low temperature features motivates a detailed analysis of the summed spectrum. With approximately 280 ksec of total exposure time, we have measured over 200 emission features with S/N greater than or equal to 3.0 in the summed spectrum. We report here initial results from the analysis of this spectrum. We can now identify lines of Fe VIII and X-XIV, as well as a number of electron density and abundance diagnostic lines. We also report here the first direct measurement of the continuum flux around approximately 100 A in a cool star atmosphere with EUVE. The continuum flux can be predicted from the emission measure model based on Fe line emission, and demonstrates that the Fe/H abundance ratio is dose to the solar photospheric value.

Brickhouse, Nancy S.↗

DOE OSTI2022

Dynamic aspects of graphene deformation and fracture from approximate density functional theory

Graphene is one of the most intriguing two-dimensional carbon materials. Its mechanical strength and failure are key concerns for materials engineering and applications. Despite the success of fracture mechanics, the mechanism of how pristine materials fail remains an elusive problem. While many theoretical studies based on molecular dynamics using empirical forcefields have tried to address this question, atomic-scale mechanics are not clearly understood. Especially, a widely employed bond-breaking approach based on the critical bond length has not been rigorously tested. Here, utilizing molecular dynamics simulations with density functional based tight binding, we investigate how the failure of the pristine material initiates. The Wiberg bond order (W BO ) to estimate the change of chemical bonds shows a transition from sp 2 (W BO ~ 1.33) to sp 3 (WBO < 1.0) during the deformation. However, it reveals that a single threshold value for either the WBO or bond length is insufficient to decide failure of pristine material without free edges or defects. Instead, collective behaviors of the local atomic group govern the fracture initiation of pristine graphene. Overall, our study provides dynamic mechanical responses based on quantum mechanics, which have not been captured by empirical forcefields, opening opportunities to design properties by precisely coupling the mechanics and quantum mechanics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Theory of Plasmonic Hot-Carrier Generation and Relaxation

Hot-carrier (HC) generation from (localized) surface plasmon decay has recently attracted much attention due to its promising applications in physical, chemical, materials, and energy science. However, the detailed mechanisms of plasmonic HC generation, relaxation, and trapping are less studied. In this work, we developed and applied a quantum-mechanical model and coupled master equation method to study the generation of HCs from plasmon decay and their following relaxation processes with different mechanisms treated on equal footing. First, a quantum-mechanical model for HC generation is developed. Its connection to existing semiclassical models and time-dependent density functional theory (TDDFT) is discussed. Second, the relaxation and lifetimes of HCs are investigated in the presence of electron–electron and electron–phonon interactions. A GW-like approximation is introduced to account for the electron–electron scattering. The numerical simulations on the Jellium nanoparticles with a size up to 1.6 nm demonstrate the electron–electron scattering and electron–phonon scattering dominate different time scale in the relaxation dynamics. We also generalize the model to study the extraction of HCs to attached molecules. The quantum yield of extracting HCs for other applications is found to be size-dependent. In general, the smaller size of NP improves the quantum yield, which is in agreement with recent experimental measurements. Even though we demonstrate this newly developed theoretical formalism with Jellium model, the theory applies to any other atomistic models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Cosmological quasiparticles and the cosmological collider

The interplay between cosmology and strongly coupled dynamics can yield transient spectral features that vanish at late times, but which may leave behind phenomenological signatures in the spectrum of primordial fluctuations. Of particular interest are strongly coupled extensions of the standard model featuring approximate conformal invariance. In flat space, the spectral density for a scalar operator in a conformal field theory is characterized by a continuum with scaling law governed by the dimension of the operator, and is otherwise featureless. Anti–de Sitter/conformal field theory arguments suggest that for large 𝑁, in an inflationary background with Hubble rate 𝐻, this continuum is gapped. We demonstrate that there can be additional peak structures that become sharp and particlelike at phenomenologically interesting regions in parameter space, and we estimate their contribution to cosmological observables. We find phenomena that are potentially observable in future experiments that are unique to these models, including displaced oscillatory features in the squeezed limit of the bispectrum. These particles can be either fundamental, and localized to a UV brane, or composite at the Hubble scale, 𝐻, and bound to a horizon in the bulk of the 5D geometry. We comment on how stabilization of conformal symmetry breaking vacua can be correlated with these spectral features and their phenomenology.

conformal field theory↗

NASA NTRS1988

The GONG Data Reduction and Analysis System

Each of the six GONG observing stations will produce three, 16-bit, 256X256 images of the Sun every 60 sec of sunlight. These data will be transferred from the observing sites to the GONG Data Management and Analysis Center (DMAC), in Tucson, on high-density tapes at a combined rate of over 1 gibabyte per day. The contemporaneous processing of these data will produce several standard data products and will require a sustained throughput in excess of 7 megaflops. Peak rates may exceed 50 megaflops. Archives will accumulate at the rate of approximately 1 terabyte per year, reaching nearly 3 terabytes in 3 yr of observing. Researchers will access the data products with a machine-independent GONG Reduction and Analysis Software Package (GRASP). Based on the Image Reduction and Analysis Facility, this package will include database facilities and helioseismic analysis tools. Users may access the data as visitors in Tucson, or may access DMAC remotely through networks, or may process subsets of the data at their local institutions using GRASP or other systems of their choice. Elements of the system will reach the prototype stage by the end of 1988. Full operation is expected in 1992 when data acquisition begins.

Pintar, James A.↗

NASA NTRS1977

Mariner 9 Ultraviolet Spectrometer Experiment: Mars Atomic Oxygen 1304-A Emission

Selected results are presented for an analysis of Mariner 9 1304-A data from the first 100 passes. Based on a comparison of limb data, the exospheric temperature appears lower on several Mariner 9 passes than when Mariner 6 and 7 encountered the planet in 1969. Temperatures of 300 and 350 K are considered in the atmospheric modeling. At 300 K, derived values of the atomic oxygen concentration are typically between 0.5 and 1 percent of the total density at 135 km, based on fitting theoretical intensities to limb data from several passes. Structure in the limb data below 200 km suggests the possibility that approximately 0.2 kR of the observed approximately 0.8 kR near 150 km is due to dissociative excitation of CO2. There is variability in limb profiles indicating changes in the O distribution with time. The variability does not appear to follow a recognizable pattern. Interpretation of the 1304-A disc data shows a correlation in intensity with the 10.7 cm solar flux and larger O concentrations in the afternoon than in the morning. The correlation in intensity with the 10.7 cm flux is probably due largely to variation in the solar 1304-A fluxes. Selected disc data show localized and random enhancements in the intensity.

Strickland, D. J.↗

DOE OSTI2023

A New Plasma Radar Concept for Simultaneous Magnetic and Density Measurements

An innovative, compact 288GHz interferometer has been fabricated, tested, installed and successfully demonstrated on the LAPD-U magnetized plasma at UCLA. The system takes advantage of frequency modulated (FM) radar techniques to deliver a compact heterodyne system. In addition, the reflected power from the source is taken advantage of to eliminate the need for additional quasi-optical components. Electron density in LAPD-U plasma has recently been increased substantially thereby requiring a higher frequency/shorter wavelength interferometer to avoid deleterious refractive effects. This system satisfies those needs. The system uses a 96GHz varactor tuned Gunn oscillator which passes to a passive tripler. This tripler has ~3% conversion efficiency. The 288GHz radiation is then coupled to free space using a so-called dual-mode or Pickett horn. The output 288GHz beam is then coupled to an aspheric lens manufactured from low-loss, high-density polyethylene. This lens is employed to collimate the emerging beam. Small axial adjustment of the lens position can also be used to create a slowly focusing beam so as to optimize the measured signal. In addition, up-down or side-to-side adjustment of the lens can be utilized to steer the beam vertically or horizontally – again to optimize alignment. The propagating beam passes through a beam splitter and then through a water-free, bubble-free fused quartz window into the LAPD-U vacuum vessel. The beam-splitter is a thin sheet of G10 which reflects a small fraction of the incident power (~5 %) towards a zero-bias detector optimized for the frequency range from 220 to 300GHz. Note that waveguides at this frequency have dimensions of ~0.9mm x 0.45mm and so have very large conductive losses. This drives the use of quasi-optical propagation. The detector requires no DC bias and is very responsive (> 1V/mW into 1MΩ). Radiation is coupled to the detector via a similar lens-horn arrangement used for the launch. This reflected beam acts as the local oscillator or reference millimeter-wave beam for the detector. The remainder of the launched source beam then enters the LAPD-U vacuum vessel and passes through the plasma at the mid-plane until reaching the opposing port which is closed off with an aluminum flange. This flange is used as a mirror to retroreflect the incident 288GHz beam back along its path. The retroreflected beam exits the input port but does NOT couple directly into the zero-bias detector. Instead, the majority of the return power continues towards the 288GHz source. As mentioned above the transmitted beam enters the source a second time. This would appear undesirable. However, at these frequencies multipliers are highly non-linear elements which results in a significant portion of the return beam (~20%) re-emerging from the multiplier and horn and then coupling via the G10 beam-splitter to the zero-bias detector. This approach eliminated the need for a second quasi-optical beam-splitter. The system is extremely compact measuring approximately 28 inches x 20 inches. The above did not explain how heterodyne operation was achieved. As mentioned above the Gunn oscillator is able to be varactor tuned. This allows a low voltage to be applied to control the operating frequency of the Gunn oscillator. During heterodyne operation a sawtooth shaped voltage is applied to the varactor at 750kHz using an 80MHz Arbitrary Waveform Generator (AWG). This voltage changes the Gunn frequency linearly during the up-sweep which is then reset abruptly at the sawtooth crash to be immediately followed by another linear sweep. Passage through the 288GHz multiplier triples the frequency change experienced by the electromagnetic wave. These frequency changes are small – tens of megahertz. This FM radar approach results in the launched electromagnetic wave frequencies at the detector for the reference and plasma wave to be different. The approximately 10 ns delay propagation delay for the plasma beam results in the local oscillator and plasma beams NOT having an identical frequency – there is in fact a fixed difference frequency. The frequency tuning level of the Gunn oscillator is then adjusted so that there is ONE cycle of this difference frequency during each linear ramp. During the sawtooth crash or downward re-sweep this one cycle replays in reverse but on a very fast timescale. The process then repeats. Low-pass filtering eliminates the fast re-sweep to leave a pure sine wave heterodyne signal. When the plasma is present it introduces a phase delay in the sine wave (caused by the extremely small Doppler shift resulting from the optical path length change). Of course, to measure this phase change we need a reference. This is simply obtained from an arbitrary waveform generator which provides a synchronized output pulse train which again is low pass filtered to obtain a 750kHz sinusoidal voltage reference for the interferometer. The interferometer was installed on LAPD-U where it has worked reliably and has established that electron densities exceeding 1x10 13 cm -3 are routinely achieved. In addition, the system sensitivity was able to easily observe density fluctuation at frequencies up to 50kHz. FM Radar techniques have enabled a full demonstration of a compact, sensitive, high frequency (288GHz/1mm) heterodyne interferometer.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

How Many Bursts Does It Take to Form a Core at the Center of a Galaxy?

We present a novel method for systematically assessing the impact of the central potential fluctuations associated with bursty outflows on the structures of dark matter halos for classical and ultrafaint dwarf (UFD) galaxies. Specifically, we use dark-matter-only simulations augmented with a manually added massive particle that modifies the central potential and approximately accounts for a centrally concentrated baryonic component. This approach enables precise control over the magnitude, frequency, and timing of rapid outflow events. We demonstrate that this method can reproduce the established result of core formation for systems that undergo multiple episodes of bursty outflows. In contrast, we also find that equivalent models involving only single (or a small number of) burst episodes do not form cores with the same efficacy. This is important because many UFDs in the local Universe are observed to have tightly constrained star formation histories that are best described by a single early burst of star formation. Using a suite of cosmological zoom-in simulations, we identify the regimes in which single bursts can and cannot form a cored density profile. Our results suggest that it may be difficult to form cores in UFD-mass systems with a single early burst, regardless of its magnitude.

cold dark matter↗

NASA NTRS1980

Some possible effects of Jupiter's rings on the Jovian inner plasmasphere

The ionospheric plasma density on magnetic field lines threading the Jovian rings which are located inside approximately 1.8 Jupiter radii on the jovigraphic equatorial plane is calculated by using a rotating ion exosphere model. It is found that the bulk of the ionospheric particles on these field lines are on ballistic trajectories. On field lines approximately symmetric with respect to the jovigraphic equator, the ring, which to a first approximation would absorb the population of trapped particles, consequently has little effect. On field lines which are made asymmetric by the higher-order multipoles of Jupiter's field and the tilt of the dipole axis, the rings may have a significant effect. It is suggested that better definition of the rings' atmospheric and ionospheric properties is required to model these localized effects. If the rings are found to be an important plasma source for the inner magnetosphere, the present exospheric model will have to be revised.

Luhmann, J. G.↗

DOE OSTI2025

Simulations of Quantum Approximate Optimization Algorithm on HPC-QC Integrated Systems

The Quantum Approximate Optimization Algorithm (QAOA) has emerged as a promising tool for accelerating optimization processes in the Noisy Intermediate-Scale Quantum (NISQ) era. Compared to classical methods, QAOA efficiently solves optimization problems, often formulated as Quadratic Unconstrained Binary Optimization (QUBO) problems. Classical quantum simulators are crucial for evaluating quantum algorithms due to limited quantum resources. However, QAOA's performance can vary with different simulation methods. This study analyzes QAOA's performance using various quantum simulators (e.g., density _matrix, statevector, and matrix_product_state) and demonstrates the benefits of HPC-QC integrated systems in solving QUBO problems on an active learning workflow. By simulating QAOA on dense, large-matrix QUBO problems, we evaluate accuracy and problem-solving time. We also assess QAOA's performance on local computers and HPC-QC inte-grated systems, using Oak Ridge Leadership Computing Facility (OLCF)'s Frontier supercomputer with local Qiskit Aer and remote IBM Quantum simulators.

Kim, Seongmin [ORNL] (ORCID:0000000159063004)↗

NASA NTRS1983

The galactic spheroid

Analytic approximations and numerical simulations are used to derive the characteristic behavior of star counts in a galactic spheroidal population, whose visible stars' stellar luminosity function is obtainable for galactocentric distances between about 4 and 12 kpc from star count observations above 30 deg galactic latitude. The total densities of stars and of mass in the spheroid at the solar position are evaluated using different assumed luminosity functions, in order to extrapolate the measured values to a wider range of absolute magnitudes. The upper limits to the frequency of intermediate population stars are derived for the absolute visual magnitude range of 5-8. If such stars occur in either a flat disk with a scale height of 3 kpc or a spheroid with an ellipticity of 0.5, their local surface density is less than 1.8 times that of the spheroid.

Bahcall, J. N.↗

NASA NTRS1994

Effects of the Mount Pinatubo eruption on the radiative and chemical processes in the troposphere and stratosphere

The Lawrence Livermore National Laboratory two-dimensional zonally-averaged chemical-radiative-transport model of the global atmosphere was used to study the effects of the 15 June 1991 eruption of the Mt. Pinatubo volcano on stratospheric processes. SAGE 2 time-dependent aerosol surface area density and optical extinction data were used as input into the model. By 22 December 1991, a maximum equatorial change of -1.8 percent in column ozone was derived from heterogeneous chemical processes that convert NO(x) into HNO3 on sulfuric acid aerosols. Radiative feedbacks from increased aerosol optical thickness independently changes column ozone by approximately -3.5 percent for the same period. This occurs from increasing the net heating of the lower stratosphere, which indirectly increases chemical reaction rates via their temperature dependence and from changes in actinic fluxes, which directly modify photodissociation rates. Including both heterogeneous and radiative effects changes column ozone by -5.5 percent. The model-derived change overestimates the decrease in column ozone relative to the TOMS instrument on the Nimbus 7 satellite. Maximum local ozone decreases of 12 percent were derived in the equatorial region, at 25 km. Model-derived column NO2 peaked (-14 percent) at 30 deg S in October 1991. The timing of the NO2 peak is consistent with observation, but the model underestimates the magnitude of the decrease. Local concentrations of NO(x) (NO + NO2), ClO(x) (Cl + ClO), and HO(x) (OH + HO2), in the lower stratosphere between 30 deg S and 30 deg N, were calculated to have changed by -40 percent, +100 to +160 percent, and +120 to +140 percent respectively.

Kinnison, Douglas E.↗

DOE OSTI2022

Applying Thomson scattering to diagnosing turbulent density and velocity fluctuations in a gas-puff z-pinch

The electron plasma wave feature (EPW) in the time-resolved Thomson scattering spectrum is used to obtain the local electron density in imploding high energy density gas-puff z-pinch plasmas. The optical setup was optimized to allow the relatively weak EPW feature obtained from 1 MA imploding neon gas-puff z-pinches to be seen above the continuum emission as well as the brighter ion acoustic wave (IAW) feature. Using a frequency-doubled Nd:YLF laser (E = 10 J, λ = 526.5 nm, Δt= 2.3 ns, spot size ~ 250 μm) and two visible light streak cameras, we determined the average electron density in the imploding plasma sheath 40 ns prior to stagnation to be n e = 2.5 × 10 18 /cm 3 . At pinch time, it reached n e = 1.7 × 10 19 /cm 3 . Here, the electron temperature during implosion measured via the IAW (approximately 50 eV) was four times lower than the implosion electron temperature measured via the EPW (approximately 200 eV), assuming that neither feature is affected by turbulent fluctuations in the plasma. In order for the electron temperatures inferred from the EPW and IAW spectral features to be self-consistent, we find that it is necessary to include velocity fluctuations in the analysis of the IAW feature peaks and corresponding density fluctuation in the peak widths of the EPW feature.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

FINETUNA: fine-tuning accelerated molecular simulations

Abstract Progress towards the energy breakthroughs needed to combat climate change can be significantly accelerated through the efficient simulation of atomistic systems. However, simulation techniques based on first principles, such as density functional theory (DFT), are limited in their practical use due to their high computational expense. Machine learning approaches have the potential to approximate DFT in a computationally efficient manner, which could dramatically increase the impact of computational simulations on real-world problems. However, they are limited by their accuracy and the cost of generating labeled data. Here, we present an online active learning framework for accelerating the simulation of atomic systems efficiently and accurately by incorporating prior physical information learned by large-scale pre-trained graph neural network models from the Open Catalyst Project. Accelerating these simulations enables useful data to be generated more cheaply, allowing better models to be trained and more atomistic systems to be screened. We also present a method of comparing local optimization techniques on the basis of both their speed and accuracy. Experiments on 30 benchmark adsorbate-catalyst systems show that our method of transfer learning to incorporate prior information from pre-trained models accelerates simulations by reducing the number of DFT calculations by 91%, while meeting an accuracy threshold of 0.02 eV 93% of the time. Finally, we demonstrate a technique for leveraging the interactive functionality built in to Vienna ab initio Simulation Package (VASP) to efficiently compute single point calculations within our online active learning framework without the significant startup costs. This allows VASP to work in tandem with our framework while requiring 75% fewer self-consistent cycles than conventional single point calculations. The online active learning implementation, and examples using the VASP interactive code, are available in the open source FINETUNA package on Github.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Dynamical cluster approximation study of electron localization in the extended Hubbard model

We perform a detailed study of the phase transitions and mechanisms of electron localization in the extended Hubbard model using the dynamical cluster approximation on a 2×2 cluster. We explore the interplay of charge order and Mott physics. We find that a nearest-neighbor Coulomb interaction V causes “screening” effects close to the Mott phase transition, pushing the phase boundary to larger values of U. We also demonstrate the different effects of V on correlations in metallic and insulating regimes, and document the different correlation aspects of charge order and Mott states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1996

Model Insensitive and Calibration Independent Method for Determination of the Downstream Neutral Hydrogen Density Through Ly-alpha Glow Observations

Our knowledge of the various heliospheric phenomena (location of the solar wind termination shock, heliopause configuration and very local interstellar medium parameters) is limited by uncertainties in the available heliospheric plasma models and by calibration uncertainties in the observing instruments. There is, thus, a strong motivation to develop model insensitive and calibration independent methods to reduce the uncertainties in the relevant heliospheric parameters. We have developed such a method to constrain the downstream neutral hydrogen density inside the heliospheric tail. In our approach we have taken advantage of the relative insensitivity of the downstream neutral hydrogen density profile to the specific plasma model adopted. We have also used the fact that the presence of an asymmetric neutral hydrogen cavity surrounding the sun, characteristic of all neutral densities models, results in a higher multiple scattering contribution to the observed glow in the downstream region than in the upstream region. This allows us to approximate the actual density profile with one which is spatially uniform for the purpose of calculating the downstream backscattered glow. Using different spatially constant density profiles, radiative transfer calculations are performed, and the radial dependence of the predicted glow is compared with the observed I/R dependence of Pioneer 10 UV data. Such a comparison bounds the large distance heliospheric neutral hydrogen density in the downstream direction to a value between 0.05 and 0.1/cc.

Gangopadhyay, P.↗

NASA NTRS1999

Bidirectional Reflectance of a Macroscopically Flat, High-Albedo Particulate Surface: An Efficient Radiative Transfer Solution and Applications to Regoliths

Many remote sensing applications rely on accurate knowledge of the bidirectional reflection function (BRF) of surfaces composed of discrete, randomly positioned scattering particles. Theoretical computations of BRFs for plane-parallel particulate layers are usually reduced to solving the radiative transfer equation (RTE) using one of existing exact or approximate techniques. Since semi-empirical approximate approaches are notorious for their low accuracy, violation of the energy conservation law, and ability to produce unphysical results, the use of numerically exact solutions of RTE has gained justified popularity. For example, the computation of BRFs for macroscopically flat particulate surfaces in many geophysical publications is based on the adding-doubling (AD) and discrete ordinate (DO) methods. A further saving of computer resources can be achieved by using a more efficient technique to solve the plane-parallel RTE than the AD and DO methods. Since many natural particulate surfaces can be well represented by the model of an optically semi-infinite, homogeneous scattering layer, one can find the BRF directly by solving the Ambartsumian's nonlinear integral equation using a simple iterative technique. In this way, the computation of the internal radiation field is avoided and the computer code becomes highly efficient and very accurate and compact. Furthermore, the BRF thus obtained fully obeys the fundamental physical laws of energy conservation and reciprocity. In this paper, we discuss numerical aspects and the computer implementation of this technique, examine the applicability of the Henyey-Greenstein phase function and the sigma-Eddington approximation in BRF and flux calculations, and describe sample applications demonstrating the potential effect of particle shape on the bidirectional reflectance of flat regolith surfaces. Although the effects of packing density and coherent backscattering are currently neglected, they can also be incorporated. The FORTRAN implementation of the technique is available on the World Wide Web, and can be applied to a wide range of remote sensing problems. BRF computations for undulated (macroscopically rough) surfaces are more complicated and often rely on time consuming Monte Carlo procedures. This approach is especially inefficient for optically thick, weakly absorbing media (e.g., snow and desert surfaces at visible wavelengths since a photon may undergo many internal scattering events before it exists the medium or is absorbed. However, undulated surfaces can often be represented as collections of locally flat tilted facets characterized by the BRF found from the traditional plane parallel RTE. In this way the MOnte Carlo procedure could be used only to evaluate the effects of surface shadowing and multiple surface reflections, thereby bypassing the time-consuming ray tracing inside the medium and providing a great savings of CPU time.

Mishchenko, Michael I.↗