A solution of a time-dependent equation of radiative transfer
Time dependent radiative transfer equation for plane-parallel isotropic scattering medium in first Gaussian approximation
Code, A. D.↗
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Thermal response of the F region ionosphere in artificial modification experiments by HF radio waves
The thermal response of the nighttime F region ionosphere to local heating by HF radio waves has been observed with the incoherent scatter radar at Arecibo, Puerto Rico. The observations consist of high-resolution space and time variation of the electron temperature as a high-power HF transmitter is switched on and off with a period 240 s. As soon as the HF transmitter is turned on, the electron temperature begins to rise rapidly in a narrow altitude region near 300 km, below the F2 layer peak. The electron temperature perturbation subsequently spreads over a broader altitude region. The observations are compared with the anticipated thermal response of the ionosphere based on numerical solutions of the coupled time-dependent heat conduction equations for the electron and composite ion gases and are found to be in good agreement over the entire altitude region covered by the observations.
Mantas, G. P.↗
Quantitative simulation of a magnetospheric substorm. III - Plasmaspheric electric fields and evolution of the plasmapause
Results of a substorm simulation are used to investigate the penetration of substorm-associated electric fields into the plasmasphere. Near 4 earth radii in the equatorial plane, the time-dependent electric field model is characterized by eastward components in the dusk-midnight local time sector and westward components after midnight. With the exception of a small region just before dusk, the model predicts eastward electric field components throughout the daytime sector. The characteristic radial component is directed inward at all local times with the exception of a small region just after dawn. It is noted that these results compare favorably with available whistler and incoherent-scatter radar measurements obtained during magnetically disturbed periods. By assuming an initial plasmapause shape and by following the computed E x B drift trajectories of plasma flux tubes from that initial boundary, the short-term evolution of the plasmapause during the substorm-like event of September 19, 1976, is examined.
Spiro, R. W.↗
Temperature-dependent creep buckling of plates
Time-dependent lateral deflection of flat rectangular plates is predicted by the Norton-Bailey (Norton 1929, Bailey 1935) power law for material creep. The plates have a through-thickness steady-state temperature distribution, and the effects are considered by using Maxwell's law to modify the power creep law. Equations are derived for creep exponents of 3 and 5, using the sandwich plate element to predict creep buckling of plates. Predictions of creep buckling with a temperature variation between the inner and outer plate surfaces are found to be somewhat dependent on the creep buckling relationship assumed. When significant scatter justifies a variation in the creep constants up to an order of magnitude, discrepancies in predictions using the two exponents are reasonable, and for one engineering material, the predictions have the same degree of agreement with experimental data as have the respective creep laws.
Ross, D. A.↗
Atomic collisions in the presence of laser radiation - Time dependence and the asymptotic wave function
A time-dependent, wave-packet description of atomic collisions in the presence of laser radiation is extracted from the more conventional time-independent, stationary-state description. This approach resolves certain difficulties of interpretation in the time-independent approach which arise in the case of asymptotic near resonance. In the two-state model investigated, the approach predicts the existence of three spherically scattered waves in this asymptotically near-resonant case.
Devries, P. L.↗
Physical processes in the strong magnetic fields of accreting neutron stars
Analytical formulae are fitted to observational data on physical processes occurring in strong magnetic fields surrounding accreting neutron stars. The propagation of normal modes in the presence of a quantizing magnetic field is discussed in terms of a wave equation in Fourier space, quantum electrodynamic effects, polarization and mode ellipticity. The results are applied to calculating the Thomson scattering, bremsstrahlung and Compton scattering cross-sections, which are a function of the frequency, angle and polarization of the magnetic field. Numerical procedures are explored for solving the radiative transfer equations. When applied to modeling X ray pulsars, a problem arises in the necessity to couple the magnetic angle and frequency dependence of the cross-sections with the hydrodynamic equations. The use of time-dependent averaging and approximation techniques is indicated.
Meszaros, P.↗
On time-dependent radiative transfer
An integral equation is developed for application to time-dependent laboratory experiments in which partial redistribution effects are important. The equation of transport with the Heasly-Kneer (1976) emission coefficient and the equation of statistical equilibrium lead to a time-dependent redistribution function containing an absorption - reemission term which decays exponentially in time and a scattering term which is instantaneous. This integral equation does not agree with an equation written by Payne et al. (1974) that has been used to compare theory with experiments. The difference between the Payne equation and the equation developed here needs to be examined in detail, since it might under some circumstances be on the same order as the difference between partial and complete redistribution.
Streater, A.↗
Effects of thermospheric motions on the polar wind - A time-dependent numerical study
This paper presents the results of a numerical study investigating the effects of low-altitude short-duration plasma heating episodes (such as horizontal frictional heating) on transient heavy ion outflows from the polar ionosphere using a time-dependent model. In a previous set of calculations, where the effects of high-altitude transient heat sources were investigated, the low-altitude neutral atmosphere (z less than 800 km) acted as a very efficient heat sink, absorbing most of the energy conducted to this region and thus preventing large differences between the ion and neutral temperatures. One purpose of the present study was to investigate whether realistic, specified low-altitude frictional heating rates, based on published experimental data, can result in elevated ion temperatures and lift a part of the heavy ion population over the gravitational barrier before the extra energy is lost to the neutral atmosphere. In these model calculations the specified heating generated an upflowing O(+) disturbance (with a normalized peak flux of about 100 million/sq cm per sec) moving upward along the open magnetic field line with a velocity of about 2 km/s. The spatial extent of the disturbance was approximately equal to the disturbance velocity times the duration of the heat source. The model results provide a possible mechanism to explain recent European Incoherent Scatter observations of high-latitude O(+) upwellings.
Gombosi, T. I.↗
Plume formation in the D-double prime-layer and the roughness of the core-mantle boundary
A series of very-high-resolution finite element calculations of plume formation in the D-double prime-layer has been performed for several plausible rheologies and boundary conditions in order to study both the early and later stages of boundary layer development. The results show that plumes are initiated by coalescence of small-scale convective instabilities within the low-viscosity region immediately above the core-mantle boundary (CMB). These instabilities support topographic roughness on the CMB having horizontal scales of 20-50 km and provide a source for scattered P-waves seen as precursors to the phases PKIKP and PKKP. The calculated structure of fully developed plumes emerging from the D-double prime-layer consists of 5-50 cm/yr flow confined to 50-100 km thick vertical conduits. With strongly temperature-dependent viscosity, plumes exhibit time-dependent behavior, including upward propagating solitary conduit waves, which may contribute to episodicity in hotspot volcanism.
Olson, Peter↗
Solar-cycle modulation of galactic cosmic rays
This paper describes a numerical solution of the spherically-symmetric, time-dependent, cosmic-ray modulation equation, compares it to data taken near the ecliptic, and probes the physical mechanisms responsible for the solar-cycle variations in the cosmic-ray intensity. With a physically defensible diffusion coefficient and other reasonable parameters, the spectra of protons and electrons can be simulated simultaneously over the cycle, the radial intensity gradients for particles greater than about 100 MeV, the overall intensity variation during the cycle, and the time lag in the recovery of low-energy particles behind high-energy ones, known commonly as the 'hysteresis.' The results suggest that cosmic-ray variations near the ecliptic are dominated by turbulent scattering regions in the heliosphere, overwhelming any effects of gradient and curvature drifts.
Perko, John S.↗
Determination of solar flare accelerated ion angular distributions from SMM gamma ray and neutron measurements and determination of the He-3/H ratio in the solar photosphere from SMM gamma ray measurements
Comparisons of Solar Maximum Mission (SMM) observations of gamma-ray line and neutron emission with theoretical calculation of their expected production by flare accelerated ion interactions in the solar atmosphere have led to significant advances in the understanding of solar flare particle acceleration and interaction, as well as the flare process itself. These comparisons have enabled the determination of, not only the total number and energy spectrum of accelerated ions trapped at the sun, but also the ion angular distribution as they interact in the solar atmosphere. The Monte Carlo program was modified to include in the calculations of ion trajectories the effects of both mirroring in converging magnetic fields and of pitch angle scattering. Comparing the results of these calculations with the SMM observations, not only the angular distribution of the interacting ions can be determined, but also the initial angular distribution of the ions at acceleration. The reliable determination of the solar photospheric He-3 abundance is of great importance for understanding nucleosynthesis in the early universe and its implications for cosmology, as well as for the study of the evolution of the sun. It is also essential for the determinations of the spectrum and total number of flare accelerated ions from the SMM/GRS gamma-ray line measurements. Systematic Monte Carlo calculations of the time dependence were made as a function of the He-3 abundance and other variables. A new series of calculations were compared for the time-dependent flux of 2.223 MeV neutron capture line emission and the ratio of the time-integrated flux in the 2.223 MeV line to that in the 4.1 to 6.4 MeV nuclear deexcitation band.
Lingenfelter, Richard E.↗
The wind geometry of the Wolf-Rayet star HD 191765
A time-dependent spectropolarimetric data set of HD 191765 in the wavelength range 3159-7593 A is presented. At all epochs the present observations display a large and strongly wavelength-dependent continuum polarization and reduced levels of polarization across the emission lines. The data imply a significant intrinsic continuum polarization which requires a general deviation of the electron distribution from spherical symmetry. The global shape is quite stable as a function of time; small fluctuations may arise from localized density/temperature changes. The line polarizations are consistent with an axisymmetric wind geometry and ionization stratification. A qualitative model for polarization in a Wolf-Rayet atmosphere is developed. It is argued that the blueward rise of the continuum polarization in HD 191765 can be explained if the density in the wind is high, resulting in a competition of thermal and electron-scattering continuum opacity in the vertical.
Schulte-Ladbeck, R. F.↗
Time-dependent models of magnetized pair plasmas
Attention is given to a numerical code developed to study the time evolution of electron-positron plasmas. The code solves in a self-consistent manner kinetic equations describing the effects of Compton scattering, two-photon pair production, pair annihilation, cooling of pairs via Coulomb scattering, e-e bremsstrahlung, and synchrotron radiation. The kinetic equations are derived under the approximation of homogeneous and isotropic particle distributions on the basis of a study by Coppi and Blandford (1993). Both stationary and time-varying output radiation spectra are computed. Good qualitative agreement with previous calculations is found, except where the differences are attributable to the improved treatment of the microphysics.
Coppi, Paolo S.↗
Finite difference time domain analysis of chirped dielectric gratings
The finite difference time domain (FDTD) method for solving Maxwell's time-dependent curl equations is accurate, computationally efficient, and straight-forward to implement. Since both time and space derivatives are employed, the propagation of an electromagnetic wave can be treated as an initial-value problem. Second-order central-difference approximations are applied to the space and time derivatives of the electric and magnetic fields providing a discretization of the fields in a volume of space, for a period of time. The solution to this system of equations is stepped through time, thus, simulating the propagation of the incident wave. If the simulation is continued until a steady-state is reached, an appropriate far-field transformation can be applied to the time-domain scattered fields to obtain reflected and transmitted powers. From this information diffraction efficiencies can also be determined. In analyzing the chirped structure, a mesh is applied only to the area immediately around the grating. The size of the mesh is then proportional to the electric size of the grating. Doing this, however, imposes an artificial boundary around the area of interest. An absorbing boundary condition must be applied along the artificial boundary so that the outgoing waves are absorbed as if the boundary were absent. Many such boundary conditions have been developed that give near-perfect absorption. In this analysis, the Mur absorbing boundary conditions are employed. Several grating structures were analyzed using the FDTD method.
Hochmuth, Diane H.↗
Minimal microwave anisotrophy from perturbations induced at late times
Aside from primordial gravitational instability of the cosmological fluid, various mechanisms have been proposed to generate large-scale structure at relatively late times, including, e.g., 'late-time' cosmological phase transitions. In these scenarios, it is envisioned that the universe is nearly homogeneous at the times of last scattering and that perturbations grow rapidly sometimes after the primordial plasma recombines. On this basis, it was suggested that large inhomogeneities could be generated while leaving relatively little imprint on the cosmic microwave background (MBR) anisotropy. In this paper, we calculate the minimal anisotropies possible in any 'late-time' scenario for structure formation, given the level of inhomogeneity observed at present. Since the growth of the inhomogeneity involves time-varying gravitational fields, these scenarios inevitably generate significant MBR anisotropy via the Sachs-Wolfe effect. Moreover, we show that the large-angle MBR anisotropy produced by the rapid post-recombination growth of inhomogeneity is generally greater than that produced by the same inhomogeneity growth via gravitational instability. In 'realistic' scenarios one can decrease the anisotropy compared to models with primordial adiabatic fluctuations, but only on very small angular scales. The value of any particular measure of the anisotropy can be made small in late-time models, but only by making the time-dependence of the gravitational field sufficiently 'pathological'.
Jaffe, Andrew H.↗
Variability of accretion disks surrounding black holes: The role of inertial-acoustic mode instabilities
The global nonlinear time-dependent evolution of the inertial-acoustic mode instability in accretion disks surrounding black holes has been investigated. The viscous stress is assumed to be proportional to the gas pressure only, i.e., tau = alphap(sub g). It is found that an oscillatory nonsteady behavior exists in the inner regions of disks (r is less than 10r(sub g) where r(sub g) is the Schwarzschild radius) for sufficiently large alpha(greater than or approximately equal to 0.2) and for mass accretion rates less than about 0.3 times the Eddington value. The variations of the integrated bolometric luminosity from the disk, Delta L/L, are less than 3%. A power spectrum analysis of these variations reveals a power spectrum which can be fitted to a power-law function of the frequency Pis proportional to f(exp -gamma), with index gamma = 1.4-2.3 and a low-frequency feature at about 4 Hz in one case. In addition, a narrow peak centered at a frequency corresponding to the maximum epicyclic frequency of the disk at approximately 100-130 Hz and its first harmonic is also seen. The low-frequency modulations are remarkably similar to those observed in black hole candidate systems. The possible existence of a scattering corona in the inner region of the disk and/or other processes contributing to the power at high frequencies in the inner region of the accretion disk may make the detection of the high-frequency component difficult.
Chen, Xingming↗
The chemical and radiative effects of the Mount Pinatubo eruption
To clarify the mechanisms leading to effects on stratospheric ozone, time-dependent stratospheric aerosol and gas experiment II (SAGE II) and cryogenic limb array elaton spectrometer (CLAES) aerosol optical extinction data and SAGE II surface area density are used as parameters in a two-dimensional (2-D) zonally averaged chemical radiative transport model. The model was integrated with time from before the eruption through December 1993. The modeled impact on global ozone results from increased rates of heterogeneous reactions on sulfate aerosols and from the increased radiative heating and scattering caused by these aerosols. When the aerosol heating is allowed to modify the temperature distribution, the maximum change calculated in equatorial column ozone is -1.6%. The calculated equatorial temperature change and peak local ozone change in October 1991 are +6K and -4%, respectively. When aerosol heating perturbs the circulation in the model, the maximum change in equatorial column ozone is -6%. Increased heterogeneous processing on sulfate aerosols is calculated to have changed equatorial column ozone in late 1991 by -1.5%. Global column ozone in the model in 1992 and 1993 changed by -2.8% and -2.4%, respectively. The relationship of ozone-controlling processes in the lower stratosphere is altered as well; HO(x) becomes the most important catalytic cycle, followed by ClO(x) and NO(x). This is driven by significant changes in trace gas concentrations. In October 1991, lower stratospheric, equatorial NO(x) decreased by 40%, ClO(x) increased by 60%, and HO(x) increased by 25%. When the effect of heterogeneous chemical processing on sulfate aerosols is combined with aerosol heating, modifying either circulation or temperature, dramatically different ozone fingerprints with time and latitude are predicted. Model-derived changes in the equatorial region in column ozone best represented the observed data when perturbed circulation was combined with heterogeneous chemical effects. However, at high latitudes, the increased ozone production from the strengthening of the mean circulation tends to cancel the heterogeneous reduction of ozone. This is not in good agreement with observed data, especially in 1992 and 1993. When the circulation is held fixed and the temperature allowed to change, and heterogeneous chemical effects are included, the equatorial ozone decrease predicted was too small for 1991. However, the mid- to high-latitude decrease in 1992 and 1993 is in better agreement with observed data.
Kinneson, Douglas E.↗
Heating of the solar middle chromosphere by large-scale electric currents
A global resistive, two-dimensional, time-dependent magnetohydrodynamic (MHD) model is used to introduce and support the hypothesis that the quiet solar middle chromosphere is heated by resistive dissipation of large-scale electric currents which fill most of its volume. The scale height and maximum magnitude of the current density are 400 km and 31.3 m/sq m, respectively. The associated magnetic field is almost horizontal, has the same scale height as the current density, and has a maximum magnitude of 153 G. The current is carried by electrons flowing across magnetic field lines at 1 m/s. The resistivity is the electron contribution to the Pedersen resitivity for a weakly ionized, strongly magnetized, hydrogen gas. The model does not include a driving mechanism. Most of the physical quantities in the model decrease exponentially with time on a resistive timescale of 41.3 minutes. However, the initial values and spatial; dependence of these quantities are expected to be essentially the same as they would be if the correct driving mechanism were included in a more general model. The heating rate per unit mass is found to be 4.5 x 10(exp 9) ergs/g/s, independent of height and latitude. The electron density scale height is found to be 800 km. The model predicts that 90% of the thermal energy required to heat the middle chromosphere is deposited in the height range 300-760 km above the temperature minimum. It is shown to be consistent to assume that the radiation rate per unit volume is proportional to the magnetic energy density, and then it follows that the heating rate per unit volume is also proportional to the energy from the photosphere into the overlying chromosphere are briefly discussed as possible driving mechanisms for establishing and maintaining the current system. The case in which part of or all of the current is carried by protons and metal ions, and the contribution of electron-proton scattering to the current are also considered, with the conclusion that these effects do not change the qualitative prediction of the model, but probably change the quantitative predictions slightly, mainly by increasing the maximum magntiude of the current density and magnetic field to at most approximately 100 mA/m and approximately 484 G, respectively. The heating rate per unit mass, current density scale height, magnetic field scale height, temperatures, and pressures are unchanged or are only slightly changed by including these additional effects due to protons and ions.
Goodman, M. L.↗