Showing papers on "Radiative transfer published in 1979"

Radiative processes in astrophysics

Abstract: Chapter 1 Fundamentals of Radiative Transfer 1.1 The Electromagnetic Spectrum Elementary Properties of Radiation 1.2 Radiative Flux Macroscopic Description of the Propagation of Radiation Flux from an Isotropic Source-The Inverse Square Law 1.3 The Specific Intensity and Its Moments Definition of Specific Intensity or Brightness Net Flux and Momentum Flux Radiative Energy Density Radiation Pressure in an Enclosure Containing an Isotropic Radiation Field Constancy of Specific Intensity Along Rays in Free Space Proof of the Inverse Square Law for a Uniformly Bright Sphere 1.4 Radiative Transfer Emission Absorption The Radiative Transfer Equation Optical Depth and Source Function Mean Free Path Radiation Force 1.5 Thermal Radiation Blackbody Radiation Kirchhoff's Law for Thermal Emission Thermodynamics of Blackbody Radiation The Planck Spectrum Properties of the Planck Law Characteristic Temperatures Related to Planck Spectrum 1.6 The Einstein Coefficients Definition of Coefficients Relations between Einstein Coefficients Absorption and Emission Coefficients in Terms of Einstein Coefficients 1.7 Scattering Effects Random Walks Pure Scattering Combined Scattering and Absorption 1.8 Radiative Diffusion The Rosseland Approximation The Eddington Approximation Two-Stream Approximation Problems References Chapter 2 Basic Theory of Radiation Fields 2.1 Review of Maxwell's Equations 2.2 Plane Electromagnetic Waves 2.3 The Radiation Spectrum 2.4 Polarization and Stokes Parameters 62 Monochromatic Waves Quasi-monochromatic Waves 2.5 Electromagnetic Potentials 2.6 Applicability of Transfer Theory and the Geometrical Optics Limit Problems References Chapter 3 Radiation from Moving Charges 3.1 Retarded Potentials of Single Moving Charges: The Lienard-Wiechart Potentials 3.2 The Velocity and Radiation Fields 3.3 Radiation from Nonrelativistic Systems of Particles Larmor's Formula The Dipole Approximation The General Multipole Expansion 3.4 Thomson Scattering (Electron Scattering) 3.5 Radiation Reaction 3.6 Radiation from Harmonically Bound Particles Undriven Harmonically Bound Particles Driven Harmonically Bound Particles Problems Reference Chapter 4 Relativistic Covariance and Kinematics 4.1 Review of Lorentz Transformations 4.2 Four-Vectors 4.3 Tensor Analysis 4.4 Covariance of Electromagnetic Phenomena 4.5 A Physical Understanding of Field Transformations 129 4.6 Fields of a Uniformly Moving Charge 4.7 Relativistic Mechanics and the Lorentz Four-Force 4.8 Emission from Relativistic Particles Total Emission Angular Distribution of Emitted and Received Power 4.9 Invariant Phase Volumes and Specific Intensity Problems References Chapter 5 Bremsstrahlung 5.1 Emission from Single-Speed Electrons 5.2 Thermal Bremsstrahlung Emission 5.3 Thermal Bremsstrahlung (Free-Free) Absorption 5.4 Relativistic Bremsstrahlung Problems References Chapter 6 Synchrotron Radiation 6.1 Total Emitted Power 6.2 Spectrum of Synchrotron Radiation: A Qualitative Discussion 6.3 Spectral Index for Power-Law Electron Distribution 6.4 Spectrum and Polarization of Synchrotron Radiation: A Detailed Discussion 6.5 Polarization of Synchrotron Radiation 6.6 Transition from Cyclotron to Synchrotron Emission 6.7 Distinction between Received and Emitted Power 6.8 Synchrotron Self-Absorption 6.9 The Impossibility of a Synchrotron Maser in Vacuum Problems References Chapter 7 Compton Scattering 7.1 Cross Section and Energy Transfer for the Fundamental Process Scattering from Electrons at Rest Scattering from Electrons in Motion: Energy Transfer 7.2 Inverse Compton Power for Single Scattering 7.3 Inverse Compton Spectra for Single Scattering 7.4 Energy Transfer for Repeated Scatterings in a Finite, Thermal Medium: The Compton Y Parameter 7.5 Inverse Compton Spectra and Power for Repeated Scatterings by Relativistic Electrons of Small Optical Depth 7.6 Repeated Scatterings by Nonrelativistic Electrons: The Kompaneets Equation 7.7 Spectral Regimes for Repeated Scattering by Nonrelativistic Electrons Modified Blackbody Spectra y"1 Wien Spectra y"1 Unsaturated Comptonization with Soft Photon Input Problems References Chapter 8 Plasma Effects 8.1 Dispersion in Cold, Isotropic Plasma The Plasma Frequency Group and Phase Velocity and the Index of Refraction 8.2 Propagation Along a Magnetic Field Faraday Rotation 8.3 Plasma Effects in High-Energy Emission Processes Cherenkov Radiation Razin Effect Problems References Chapter 9 Atomic Structure 9.1 A Review of the Schrodinger Equation 9.2 One Electron in a Central Field Wave Functions Spin 9.3 Many-Electron Systems Statistics: The Pauli Principle Hartree-Fock Approximation: Configurations The Electrostatic Interaction LS Coupling and Terms 9.4 Perturbations, Level Splittings, and Term Diagrams Equivalent and Nonequivalent Electrons and Their Spectroscopic Terms Parity Spin-Orbit Coupling Zeeman Effect Role of the Nucleus Hyperfine Structure 9.5 Thermal Distribution of Energy Levels and Ionization Thermal Equilibrium: Boltzmann Population of Levels The Saha Equation Problems References Chapter 10 Radiative Transitions 10.1 Semi-Classical Theory of Radiative Transitions The Electromagnetic Hamiltonian The Transition Probability 10.2 The Dipole Approximation 10.3 Einstein Coefficients and Oscillator Strengths 10.4 Selection Rules 10.5 Transition Rates Bound-Bound Transitions for Hydrogen Bound-Free Transitions (Continuous Absorption) for Hydrogen Radiative Recombination - Milne Relations The Role of Coupling Schemes in the Determination of f Values 10.6 Line Broadening Mechanisms Doppler Broadening Natural Broadening Collisional Broadening Combined Doppler and Lorentz Profiles Problems References Chapter 11 Molecular Structure 11.1 The Born-Oppenheimer Approximation: An Order of Magnitude Estimate of Energy Levels 11.2 Electronic Binding of Nuclei The H2+ Ion The H2 Molecule 11.3 Pure Rotation Spectra Energy Levels Selection Rules and Emission Frequencies 11.4 Rotation-Vibration Spectra Energy Levels and the Morse Potential Selection Rules and Emission Frequencies 11.5 Electronic-Rotational-Vibrational Spectra Energy Levels Selection Rules and Emission Frequencies Problems References Solutions Index

Atomic radiative and radiationless yields for K and L shells

Abstract: The available body of information on (a) fluorescence, Auger, and Coster‐Kronig yields, (b) radiative and radiationless transition rates, (c) level widths, (d) x‐ray and Auger line widths, (e) x‐ray and Auger spectra, and (f) Coster‐Kronig energies has been used to generate an internally consistent set of values of atomic radiative and radiationless yields for the K shell (5 ?Z?110) and the L subshells (12 ?Z?110). Values of fluorescence yields ωk, ω1, ω2, ω3, Coster‐Kronig yields F1, F1.2, F1.3, F1.3, F2.3. Auger yields ak, a1, a2, a3, and effective fluorescence yields ν1 and ν2 are presented in tables and graphs. Estimates of uncertainties are given. Updated and expanded graphs of partial and total widths of K, L1, L2, and L3 levels are presented as well as a reference list of papers published since about 1972.

Effect of surface roughness on the microwave emission from soils

Abstract: The effect of surface roughness on the brightness temperature of a moist terrain was studied through the modification of Fresnel reflection coefficient and using the radiative transfer equation. The modification involves introduction of a single parameter to characterize the roughness. It is shown that this parameter depends on both the surface height variance and the horizontal scale of the roughness. Model calculations are in good quantitative agreement with the observed dependence of the brightness temperature on the moisture content in the surface layer. Data from truck mounted and airborne radiometers are presented for comparison. The results indicate that the roughness effects are greatest for wet soils where the difference between smooth and rough surfaces can be as great as 50K.

Theoretical models of interstellar shocks. I - Radiative transfer and UV precursors

Abstract: Theoretical models of interstellar radiative shocks are constructed, with special attention to the transfer of ionizing radiation. These models are 'self-consistent' in the sense that the emergent ionizing radiation (the UV precursor) is coupled with the ionization state of H, He, and the metals in the preshock gas. For shock velocities of at least 110 km/s the shocks generate sufficient UV radiation for complete preionization of H and He, the latter to He(+). At lower velocities the preionization can be much smaller, with important consequences for the cooling function, the shock structure, and the emission. For models with shock velocities of 40 to 130 km/s the intensities of the strongest emission lines in the UV, optical, and infrared are tabulated, as well as postshock column densities of metal ions potentially observable by UV absorption spectroscopy. Possible applications to supernova remnants and high-velocity interstellar gas are assessed.

Identification of gaseous SO2 and new upper limits for other gases on Io

Abstract: The identification of gaseous sulfur dioxide on Io by Voyager 1 is reported, and preliminary upper limits for other atmospheric gases are presented. Averaged spectra taken by the Voyager IRIS experiment in the range of 1,000 to 1,200/cm are interpreted as containing three fundamental sulfur dioxide bands, with intensities most nearly corresponding to an atmospheric model with a sulfur dioxide abundance of 0.2 cm atm. Upper limits for COS, CS2, SO3, H2S, CO2, O3, N2O, H2O, CH4, NH3 and HC1, not detected in the spectra, were calculated on the basis of the radiative transfer equation for temperatures of 130 and 250 K; a depletion of hydrogen, carbon and nitrogen is noted. It is suggested that a SO2 outgassing from a cooling sulfur extrusion is the major source of the observed atmospheric SO2.

Theoretical studies of atmospheric tides

Abstract: Advances in the theory of atmospheric tides since the monograph by Chapman and Lindzen (1970) are comprehensively reviewed. Major developments include investigations of the effects of mean zonal winds and meridional temperature gradients, molecular viscosity and thermal conductivity, radiative damping, composition variations, and hydromagnetic coupling, including seasonal and solar cycle effects. Linearized inviscid and viscid equations of general applicability are documented in this review, and a number of quantitative studies of atmospheric tides are considered as simplifications or modifications of these equations. Recent calculations of thermal excitation due to insolation absorption by H2O and O3 below 80 km, UV and EUV absorption in the lower thermosphere, and latent heat release in the tropical troposphere are presented. Although no attempt is made to exhaustively review incoherent scatter, meteor radar, and satellite mass spectrometer contributions to the study of atmospheric tides, representative wind, temperature, and composition data from these sources are interpreted within the framework of the most recent quantitative models, and the current status of our understanding of atmospheric tides is assessed. Some potentially fruitful areas of future research are also presented.

The Role of Stratospheric Ozone in the Zonal and Seasonal Radiative Energy Balance of the Earth-Troposphere System

Abstract: The role of ozone in the tropospheric-surface energy balance is discussed in the context of its latitudinally and seasonally varying modulation of solar and longwave energy fluxes. We analyze in detail the various radiative energy inputs to the stratosphere and the radiative fluxes from the stratosphere to the troposphere. To a very close approximation, on an annual and hemispherical mean, longwave emission from the stratosphere balances the absorbed radiant energy. The stratosphere absorbs about twice as much longwave radiation from the troposphere as it does solar radiation. About 20% of the longwave flux from the stratosphere to the troposphere is directly due to O2. A change in O3 concentrations perturbs the stratospheric and tropospheric-surface energy balances through a number of distinct mechanisms involving changes in solar and longwave fluxes and which are separated into direct effects due to the change of O3 and indirect effects due to the accompanying change of stratospheric temperatur...

Diffuse reflectance of the ocean: the theory of its augmentation by chlorophyll a fluorescence at 685 nm

Abstract: The radiative transfer equation is modified to include the effect of fluorescent substances and solved in the quasi-single scattering approximation for a homogeneous ocean containing fluorescent particles with wavelength independent quantum efficiency and a Gaussian shaped emission line. The results are applied to the in vivo fluorescence of chlorophyll a (in phytoplankton) in the ocean to determine if the observed quantum efficiencies are large enough to explain the enhancement of the ocean's diffuse reflectance near 685 nm in chlorophyll rich waters without resorting to anomalous dispersion. The computations indicate that the required efficiencies are sufficiently low to account completely for the enhanced reflectance. The validity of the theory is further demonstrated by deriving values for the upwelling irradiance attenuation coefficient at 685 nm which are in close agreement with the observations.

Atomic to molecular hydrogen transition in interstellar clouds

Abstract: The photodestruction of molecular hydrogen is reexamined in the context of recent observational data. Improvements in the theory of radiation transfer are made by using a more accurate self-shielding integral, treating anisotropic scattering by dust grains, and including photodissociation from excited rotational states. The total column density of hydrogen required to obtain 10% conversion decreases with a parameter, epsilon, the ratio of the formation rate to the destruction rate, as epsilon to the -m power, with m in the range 1.4-1.6. Satisfactory agreement with the data for thicker diffuse clouds is obtained for epsilon of about 0.00006.

Radiative lifetimes of OH(A2Σ) and Einstein coefficients for the A-X system of OH and OD

Abstract: Radiative lifetimes of individual rotational states of OH(A2Σ) were observed using a delayed coincidence technique. The values obtained were scaled to a theoretical functional form to give τrad(A2Σ, v = 0, N = 1, J = 32 = 686 ± 14 ns. Einstein A and B coefficients for the A-X system of OH and OD were computed, using numerical integrals of a transition moment of the form Re(r) = 3.75 × 10-30 (1-0.75 r) C … m and vibrational wavefunctions obtained from numerical solutions of the radial Schrodinger equations (including centrifugal terms) for RKR potentials for the two electronic states. Matrix elements in Hund's case b were transformed to intermediate coupling for the X state to yield proper oscillator strengths for computation of the Einstein coefficients. Tables of the A and B coefficients for the 0-0 vibrational transitions are included. Extended tables are available on microfiche or microfilm from the authors.

The effects of terrain shape on nonlinear hydrostatic mountain waves

Abstract: Solutions to Long's equation for a stably stratified incompressible fluid traversing a mountain range are obtained for various terrain shapes and amplitudes when the horizontal scale is large compared to the vertical wavelength. Nonlinear lower and upper (radiative) boundary conditions are utilized and found to have a strong influence on the wave structure at large amplitudes. The results for symmetric and asymmetric mountain profiles reveal that the wave amplitude and wave drag are significantly enhanced for mountains with gentle windward and steep leeward slopes. These results confirm and explain those obtained by Raymond (1972) using a different solution method. Several results obtained by Smith (1977) from perturbation analysis are also confirmed and extended to large amplitudes. The methods are also applied to investigate the nonlinear nature of the singularity predicted by linear theory for flow over a step.

Geometrical vector flux and some new nonimaging concentrators

Abstract: The geometrical vector flux, a quantity related to measures of illumination, is defined; some of its properties are explained and used to develop new forms of nonimaging concentrators.

Optical absorption and radiative heat transport in olivine at high temperature

Abstract: Results are presented of measurements of the optical absorption spectra (300-8000 nm) of olivine as a function of temperature (300-1700 K) under conditions of controlled and known oxygen fugacity within the stability field of the samples. The absorption spectra are used to calculate the temperature-dependent radiative transfer coefficient of olivine and to numerically study the accuracy of the method. The present absorption measurements in olivine under oxidizing conditions known to be within the olivine stability field indicate that the effective radiative conductivity K(R) is lower than that obtained in previous studies under different experimental conditions. The lower value of K(R) makes it more likely that some of the earth's internal heat is removed by convection and less likely that thermal models involving conduction and radiation alone will satisfactorily explain thermal conditions in the earth's mantle.

Determination of the Ground Albedo and the Index of Absorption of Atmospheric Particulates by Remote Sensing. Part I : Theory'

Abstract: A statistical technique is developed for inferring the optimum values of the ground albedo and the effective imaginary term of the complex refractive index of atmospheric particulates. The procedure compares measurements of the ratio of the hemispheric diffuse to directly transmitted solar flux density at the earth’s surface with radiative transfer computations of the same as suggested by Herman el al. (1975). A detailed study is presented which shows the extent to which the ratio of diffuse to direct solar radiation is sensitive to many of the radiative transfer parameters. Results indicate that the optical depth and size distribution of atmospheric aerosol particles are the two parameters which uniquely specify the radiation field to the point where ground albedo and index of absorption can be inferred. Varying the real part of the complex refractive index of atmospheric particulates as well as their vertical distribution is found to have a negligible effect on the diffuse-direct ratio. The statistical procedure utilizes a semi-analytic gradient search method from least-squares theory and includes a detailed error analysis.

Radiative decay and radiationless deactivation in selectively excited CN

Abstract: Individual vibrational levels (v=3–9) of the A 2Π state of the CN radical are excited by a tunable dye laser The time and wavelength resolved fluorescence of the selectively excited levels is then recorded as a function of the Ar carrier gas pressure It is found that the decay of many levels is, particularly at lower pressures, strongly double exponential, with the longer component time constant considerably in excess of the CN A 2Π radiative lifetime The short time constant portion of this exponential is interpreted in terms of a model which includes fast collisional equilibration between the excited v′A 2Π level and a nearby v″, X 2Σ level The slower part of the decay consists of quenching and radiative decay from the coupled levels Approximate values for the rate constants governing these processes are derived

Line Broadening and Radiative Recombination Background Interferences in Inductively Coupled Plasma-Atomic Emission Spectroscopy

Abstract: Spectral line broadening and radiative electron-ion recombination processes may make significant contributions to the total spectral background level when inductively coupled plasma excitation sources are observed with spectrometers having low stray light levels. These background contributions are more easily identified in inductively coupled plasma discharges because of their stable background level and by the fact that net analyte line intensities are affected to such a small degree by changes in the concentration of concomitants. The wings of collisionally broadened lines may produce significant background changes at wavelengths removed 10 nm from the parent line center. For some elements such as Mg, linear Stark-broadened lines produced spectral background at unexpectedly large displacements from the line center. The radiative Al ion-electron recombination continuum produces a greater than tenfold increase in the background from ~210 down to 193 nm at Al solution concentration of 2500 μg/ml. Thus, a solution containing only 250 μg/ml of Al will cause an ~100% increase in the background level below 210 nm over that measured when deionized water is nebulized into the plasma.

Reflected irradiance indicatrices of natural surfaces and their effect on albedo

Abstract: The indicatrices of solar radiation reflected from characteristic natural surfaces were measured with a Nimbus Medium Resolution Radiometer (MRIR) 3 m above the ground. Results indicated that areas such as salt and alkali flats had only small deviations from isotropic reflections, while others such as sparsely vegetated areas had substantial deviations. The indicatrices were strongly dependent on the sun angle; thus a daily variation was found for most features. Typical indicatrices, normalized to nadir angle of zero degrees, are presented along with their impacts on measured albedo, which varies with solar angle. Our results can (1) improve surface albedo considerations using space-generated data, and (2) serve as a more realistic lower boundary condition for atmospheric transfer determinations based on space data.

Mid-ocean observations of atmospheric radiation

Abstract: Mid-ocean (35°N 155°W) observations of the various components of radiative flux were made from the R/P FLIP during the period 2 through 13 February 1974. Cloud cover ranged from clear skies to overcast, and water vapour pressure varied between 9 and 18 mb, with sea surface temperature near 15.0°C. The net longwave radiative fluxes reported here were obtained: (1) by taking the difference between simultaneous measurements of net all-wave and net solar fluxes; and (2) by direct measurements with a net longwave radiometer designed by G. W. Paltridge. When observations during rain and fog are excluded, the difference between night-time 15-minute averages by the two methods is generally less than lmWcm−2. During day-time, indirect measurements are often larger than direct by about 5mWcm−2; from internal evidence we prefer the direct values. The albedo of the sea surface was calculated from simultaneous measurements of downward and upward solar fluxes. The observations were analysed to represent albedo as a function of solar altitude and atmospheric transmittance, following the work of R. E. Payne; our results suggest that Payne's smoothed representation is suitable for use over the open ocean. Albedo was observed to decrease with increasing wind speed for clear skies with solar altitude between 15 and 30 degrees but no variation was discernible at higher solar altitudes. Empirical formulae for calculating both shortwave and net longwave components of the radiative flux were compared with measurements. A formula due to F. E. Lumb for determining the incident solar flux given solar altitude, cloud amount and cloud type, consistently yields good agreement with the measurements, within about lmWcm−2. Daily averages of net longwave flux calculated from several empirical formulae using a linear correction for clouds are within 2mWcm−2 of the observations reported in this paper. Since daily radiation balance values were measured as only 5mWcm−2, the limitations of the best current empirical formulae are evident.

Radiative power loss from laboratory and astrophysical plasmas. I. Power loss from plasmas in steady-state ionisation balance

Abstract: Described a calculation of the power radiated by an optically thin low-density plasma in steady-state ionisation balance taking account of spectral lines, recombination continuum and bremsstrahlung. The calculations have been done in the temperature range 104-1010K for all ions of the elements carbon, oxygen, silicon and argon and for all ions of iron and molybdenum of charge greater than 7 and 23 respectively. Collision strength data of good accuracy have been used where they are available and extrapolation methods developed where they are not. The bremsstrahlung power loss is considered in detail in the appendix. Results are presented in tabular form for each of the ions treated. These are combined with steady-state ionisation balance data in a further table to give the radiated power-loss functions for each element in turn. The role of impurity radiation loss for a deuterium-tritium power-producing plasma is investigated. A composite calculation of the radiated power loss from the solar atmosphere is also presented.

Radiative amplification of sound waves in the winds of O and B stars

Abstract: The velocity perturbation associated with an outwardly propagating sound wave in a radiation-driven stellar wind gives rise to a periodic Doppler shifting of absorption lines formed in the flow. A linearized theory applicable to optically thin waves is used to show that the resulting fluctuation in the absorption-line force can cause the wave amplitude to grow. Detailed calculations of the acceleration due to a large number of lines indicate that significant amplification can occur throughout the high-velocity portion of winds in which the dominant force-producing lines have appreciable optical depths. In the particular case of the wind of Zeta Pup (O4f), it is found that the e-folding distance for wave growth is considerably shorter than the scale lengths over which the physical properties of the flow vary. A qualitative estimate of the rate at which mechanical energy due to nonlinear waves can be dissipated suggests that this mechanism may be important in heating the supersonic portion of winds of early-type stars.

Parameterization of the Radiative Properties of Clouds

Abstract: Reflection, transmission and absorption of solar radiation by four cloud types (low cloud, middle cloud, high cloud and stratus) are computed as functions of the solar zenith angle and cloud liquid water/ice content. The reflection, transmission and emission of infrared radiation by cirrus clouds are calculated as functions of the cloud ice content. The plane-parallel radiative transfer program employed is based on the discrete-ordinate method with applications to inhomogeneous atmospheres covering the entire solar and infrared spectra and taking into account the gaseous absorption in scattering atmospheres. The resulting values of the solar radiative properties of clouds are fitted with known mathematical functions involving the solar zenith angle and cloud liquid water/ice content as variables. Effects of the atmospheric profile are discussed and the effects of surface reflectivity on the solar radiative properties of clouds are parameterized in terms of the water vapor absorbtivity below the c...

The effects of ice thickness on the exchange of solar radiation over the polar oceans

Abstract: Total transmission, absorption, and reflection of solar radiation have been determined for bare blue and white ice between 0.02 and 0.8 m in thickness as well as for blue ice covered with 0.01 to 0.4 m of dry packed snow. The calculations were performed at 45 wavelengths between 400 nm and 2150 nm using a two-stream model to account for the finite thickness of the ice and snow layers. Total radiative energies were found by numerical integration over wavelength. The results were compared with corresponding calculations for optically thick ice of the same types. Albedos increase from about 0.05 for open water to a maximum of 0.9 for thick snow. For 0.8 m blue and white ice, predicted albedos on cloudy days are 0.28 and 0.67 respectively. Under clear skies these albedos decrease by 10 to 30%. Total transmission through thin ice (less than 0.8 m) is from 50% to 300% greater than is predicted by Beer’s law depending on ice type and cloud cover. Radiative energy absorption at the surface is independent of thickness, but significant departures from Beer’s law of as much as 200% are evident in all cases below a depth of 2.5 mm. A parameterization scheme is presented for incorporating these results into heat- and mass- balance studies.