Radiative transfer in an infinite cylinder

The problem of radiation transfer in a cylinder with diffuse reflectivity and containing an energy source is connected with the source-free radiation transfer problem with isotropic boundary condition. Equation for the radiation heat flux is obtained for a polynomial source. In the special case of isotropic scattering, the radiation heat flux is given in terms of the albedo of the second problem. An expression is also given for the net radiation heat flux.     

Anisotropic radiation transfer in a sphere with internal source

In this work we connect the problem of anisotropic radiation transfer in a sphere with diffuse reflectivity and containing an energy source with the problem of source free amisotropic radiation transfer with isotropic boundary condition. Exact equation for radiation heat flux for the first problem is obtained in terms of the source, the flux and the albedo of the second problem. Modeled kernel is used to represent the anisotropy of the phase function. Numerical results are given.     

Padé approximant calculations for dispersive,isotropic scattering,homogeneous media

Exact relations for radiation heat flux at the boundaries of a slab with diffusely reflecting boundary conditions and internal source are obtained in terms of the reflection and transmission coefficients of a source free slab with isotropic boundary conditions. The integral equation defining the radiation heat flux contains explicitly the internal source. So, the particular solution for radiative transfer equation is not required. Available exact values for albedos give exact values of radiation heat flux. Padé approximant technique is used to obtain numerical values for homogenous media.     

The energy-dependent radiation transfer in a homogeneous finite cylinder

Radiation transfer problem in the slowing-down region for cylindrical geometry with diffuse reflectivity and internal source is connected with source-free problem with isotropic boundary condition. Modelled kernels are used to represent the slowing-down kernel. Calculations are performed for the radiation flux at the boundary of the cylinder. Numerical results are obtained using the bi-variation technique.     

The heat flux calculation for the laser-fusion problem

The problem of heat flux at the critical surfaces and the surfaces of a pellet of deuterium and tritium (conduction zone) heated by laser have been considered. Ion-electron collisions are only allowed for: i.e., the linear transport equation is used to describe the problem with boundary conditions consists of isotropic and diffuse boundary conditions. The bi-variational technique has been used to calculate the electron density and temperature across the conduction zone as well as the heat flux. Numerical results are given and compared with those of Rouse and Williams (1981) results.     

Energy-dependent transport problem with generalized boundary conditions

The slowing-down Boltzmann equation for generalized boundary conditions is considered and transformed to one-speed equation in Laplace space. Exact relations between energy reflection and transmission coefficients for a problem with diffuse reflecting boundary conditions and the albedos for the problem with isotropic boundary conditions are obtained. The Galerkin method is used to calculate the energy reflection coefficient for a finite slab for different thicknesses at different mass ratiosA, target to projectile mass, at different synthetic-scattering kernels. The results for partial heat fluxes for isotropic and anisotropic-scattering dispersive medium are given. The results obtained for isotropic boundary conditions are compared well with the exact results.     

Radiation transfer in a diffuse and specular reflecting slab with Rayleigh scattering

A method of analysis is presented for solving the radiative transfer problem in an absorbing, emitting, inhomogeneous, and anisotropically scattering plane-parallel medium with specular and diffuse reflecting boundaries and internal source (problem 1). Exact relations for the radiation heat flux at the boundaries of problem 1 are obtained in terms of the radiation density and albedos of the corresponding source-free medium with specular reflecting boundaries (problem 2). Two coupled integral equations for the radiation density and the second moment of the radiation intensity for problem 2 with Rayleigh phase functions are obtained. The Galerkin method is used to solve these equations. Albedos of problem 2 are compared with theF _n method. Numerical results for radiation heat fluxes at the boundaries of problem 1 are tabulated for different forms of the internal source.     

The energy-dependent radiation transfer in a homogeneous finite sphere

Radiation transfer problem in the slowing-down region is solved for a spherical geometry. Modelled kernels are used to represent the slowing-down kernel. Calculations are performed for the radiation flux at the boundary of the sphere for two cases: (i) in the presence of internal source, (ii) if the radiation is incident on the sphere. Numerical results are obtained by using the Padé approximant technique.     

Observations of energetic ions in inverted V events

Simultaneous measurements of keV ions and electrons with the ESRO 1A satellite have shown the following ion characteristics among others. Ions of about 6 keV energy are strongly field-aligned on the flanks of the inverted V events (mainly through the disappearance of the ion flux near 90° pitch angle). Field-aligned electron fluxes are often found in the same regions of the inverted V events where the ions are field-aligned. At the centre of inverted V events isotropization occurs (except in some small events). The 1 keV ion flux at large pitch angles (80°) is generally not reduced very much when the 6 keV, 80° ion flux shows strongly decreased values. The ratio of the 1 to 6 keV ion flux has a maximum near the centre of an inverted V event where the electron spectrum is hardest and the 6 keV ions are isotropic (or nearly isotropic).The observations are interpreted in terms of a model with two oppositely directed field-aligned electrostatic potential drops: one upper accelerating electrons downward and one lower, produced by the electron influx, which accelerates ions downward. Ion scattering in turbulent wave fields is proposed to be responsible for the observation that the 1 keV ion flux at large pitch angles does not decrease strongly where the 6 keV ion flux does and as an explanation of the isotropization at the centre of the event. The source problem for the ions is eliminated by the precipitating electrons ionizing continuously the thin neutral atmosphere even at altitudes of a few thousand kilometers.     

Effects of electromagnetic field on shearfree spherical collapse

This paper is devoted to study spherically symmetric shearfree charged gravitational collapse with radial heat flux and isotropic pressure. For the matching of the interior spacetime, we take Vaidya-Reissner-Nordström metric outside the spherical system. We solve the field equations numerically by taking ansatz on the metric functions and using Darmois junction conditions. The behavior of density, pressure, radial heat flux, luminosity and the mass function is analyzed. Finally, we check validity of the energy conditions through plots.     

Radiation transfer through atmospheric aerosol media with anisotropic scattering

Radiation transfer in atmospheric aerosol media with general boundary conditions has been studied for anisotropic scattering. The considered aerosol medium assumed to have specular and diffused reflecting boundary surfaces and in the presence of internal source. The radiation transfer scattering parameters as single scattering albedo, asymmetry factor, scattering, absorption, extinction efficiencies and anisotropic scattering coefficient have been calculated using the Mie theory. The problem with general boundary conditions is solved in terms of the solution of source-free problem with simply boundary conditions. Pomraning-Eddington approximation is used to solve the source-free problem. For the sake of comparison, a weight function is introduced and used in two special forms. The calculated partial heat fluxes with the two methods are compared and showed good agreement. Some of our results are found in a good agreement with published data.     

Combined-Operations method for diffuse reflection by an isotropic,non-coherent scattering homogeneous sphere

Combined-Operations method has been utilised to solve the problem of diffuse reflection by a homogeneous, isotropic, non-coherent scattering spherical medium. The source function is considered to be frequency independent. The auxiliary equation has been formulated, the scattering function defined, and the integro-differential equation for this function deduced. A method for obtaining the emergent intensity and the internal source function for non-zero internal source distribution has been suggested for a given line profile.     

Surface heat current in an inhomogeneous slab with reflecting walls

The problem of radiative transfer in an inhomogeneous finite medium with boundary surfaces which reflects both diffusely and specularly is connected with a source-free specular boundary condition radiation tramsfer. Numerical results are obtained for the partial heat flux using the bi-variational technique.     

Pitch-angle scattering of energetic protons in the magnetotail current sheet as the dominant source of their isotropic precipitation into the nightside ionosphere

Characteristics of the nightside isotropic precipitation of energetic protons during a period of 4 quiet days has been studied using data from the ESRO 1A satellite. The observed features of the equatorward precipitation boundary (its thickness, energy dependence, dynamics, dependence of its latitudinal position on the magnetic field at the geosynchronous orbit, etc.) were found to be in good agreement with calculations based on recent magnetospheric magnetic field models. We argue that the mechanism of non-adiabatic pitchangle scattering in the equatorial current sheet is a dominant source of isotropic precipitation of energetic protons observed in the nightside auroral zone. Observations of the isotropic precipitation boundary can be used for monitoring the changes in the magnetotail current intensity.     

Simulation of the Magnetothermal Instability

In many magnetized, dilute astrophysical plasmas, thermal conduction occurs almost exclusively parallel to magnetic field lines. In this case, the usual stability criterion for convective stability, the Schwarzschild criterion, which depends on entropy gradients, is modified. In the magnetized long mean free path regime, instability occurs for small wavenumbers when (∂ P/∂z) (∂ ln T/∂ z) > 0, which we refer to as the Balbus criterion. We refer to the convective-type instability that results as the magnetothermal instability (MTI). We use the equations of MHD with anisotropic electron heat conduction to numerically simulate the linear growth and nonlinear saturation of the MTI in plane-parallel atmospheres that are unstable according to the Balbus criterion. The linear growth rates measured from the simulations are in excellent agreement with the weak field dispersion relation. The addition of isotropic conduction, e.g. radiation, or strong magnetic fields can damp the growth of the MTI and affect the nonlinear regime. The instability saturates when the atmosphere becomes isothermal as the source of free energy is exhausted. By maintaining a fixed temperature difference between the top and bottom boundaries of the simulation domain, sustained convective turbulence can be driven. MTI-stable layers introduced by isotropic conduction are used to prevent the formation of unresolved, thermal boundary layers. We find that the largest component of the time-averaged heat flux is due to advective motions as opposed to the actual thermal conduction itself. Finally, we explore the implications of this instability for a variety of astrophysical systems, such as neutron stars, the hot intracluster medium of galaxy clusters, and the structure of radiatively inefficient accretion flows. J. M. Stone: Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544     

Hydrodynamic response of the solar chromosphere to an elementary flare burst

Impulsive heating of the upper chromosphere by a very powerful thermal flux is studied as the cause of hard X-rays during a solar flare. The electron temperature at the boundary between the corona and chromosphere is assumed to change in accordance with the hard X-ray intensity in an elementary flare burst (EFB). A maximum value of about 10⁸ K is reached after 5 s, after which the boundary temperature decreases. These high-temperature changes lead to fast propagation of heat into the chromosphere. Numerical solution of the hydrodynamic equations, which take into account all essential dissipative processes, shows that classical heat conduction is not valid due to heat flux saturation in the case of impulsive heating from a high-temperature source. The saturation effect and hydrodynamic flow along a magnetic field lead to electron temperature and density distributions such that the thermal X-ray spectrum of a high-temperature plasma can be well enough approximated by an exponential law or by two power-law spectra. According to this dissipative thermal model for the source of hard X-rays, the emission measure of the high-temperature plasma increases monotonously during the whole EFB even after the temperature maximum. Some results for the low-temperature region are discussed in connection with short-lived chromospheric bright points.     

The diurnal heat budget of the thermosphere

Detailed numerical calculations of thermospheric heat sources and sinks are presented and their relative importance is discussed in reference to the energy balance phenomena of the neutral atmosphere. It is shown that the thermal energy available from the absorption in the Schumann-Runge continuum leading to photo-dissociation of O₂ is by far the largest energy source in the lower thermosphere. Other sources of varying importance in different altitude ranges are: (1) energy from photoelectrons; (2) energy exchange from thermal plasma; (3) chemical reaction (ion-electron dissociative recombination) energy gain; (4) kinetic and dissipative energy associated with the neutral wind. The energy sinks of importance are (1) thermal conduction at the lower boundary (120km); and (2) radiative cooling of atomic oxygen.It is shown that the combined energy from processes 2–4 constitutes only a small fraction of the total energy available from photoelectrons and is in phase with the latter. These secondary sources (processes 2–4), therefore, do not constitute a significant energy source and their contribution can be simply incorporated into photoelectron energy (process 1) by defining an effective photo-ionization heating efficiency. The heating efficiencies for photo-ionization (including processes 2–4) and photo-dissociation are estimated to be 0.5 and 0.3, respectively.As the important heat input (photo-dissociation) and loss (conduction and radiation) rates are basically governed by the O₂ and O densities, any diurnal or seasonal variation in these constituents at the lower boundary would have profound effects on the thermal structure of the overlying atmosphere. For this and other reasons, it is suggested that a choice of lower boundary much below 120km, e.g. near the mesopause level (90 km), should be more appropriate for general thermospheric studies.     

γ-ray observations from the OSO-3 satellite

The result on λ-rays obtained from the analysis of 5800 orbits of data from the University of Rochester telescope on board the OSO-3 satellite are presented. For γ-rays of energy greater than 100 MeV, an upper limit of 2.3×10^?4 cm^?2 s^?1 std has been placed on the diffuse (assumed isotropic) flux. An upper limit to the flux from the Sun is set at 3.2×10^?5 and 2.4×10^?5 cm^?2 s^?1 for energies greater than 50 MeV and 100 MeV, respectively. All flux values are calculated assuming a π⁰-decay source of γ-rays.     

On the clouds of uranus

Several models for the atmosphere of Uranus are considered. If the H₂ abundance is less than 250 km-am and the internal heat source is only a few percent of the total emitted energy then the cloud at the base of the atmosphere may be composed of solid CH₄ particles, while if the H₂ abundance is greater than 250 km-am or if the internal heat source is near the current upper limit of 35% of the total emitted energy the cloud at the base of the atmosphere may be composed of either solid NH₃ or H₂S particles.     

Magnetized centrifugal winds

It is argued that for steady, axisymmetric, non-relativistic magneto-centrifugal winds, not only the boundary and criticality conditions but also the current-closure condition are of crucial significance as global conditions in resolving the acceleration-collimation problem. In Sakurai's numerical models, the split-monopole field adopted at the surface of the source provided the most favourable condition for global collimation of the flow, by making the domain of anti -collimating flow with outgoing electric current degenerate into an infinitely thin boundary layer at the equator, and hence suppressing the explicit appearance of the current-closure condition.
For more general or realistic boundary conditions at the source, it is shown that the current-closure condition yields a two-component structure (with the return current at least in part in a volume current, not totally a sheet current) as a natural consequence of the transfield equation in the asymptotic domain. This equation, combined with the Bernoulli (and other) integrals, requires the wind to tend asymptotically to a 'quasi-conical' structure, as a natural consequence of the flow particles' becoming more and more ballistic as a result of the magnetohydrodynamic (MHD) acceleration. This is a result that the Poynting energy flux diminishes to zero along each field line. The criticality problem is solved for magneto-centrifugal winds, to give the eigenvalues of the Alfvénic distance and other quantities at the fast magnetosonic surface, situated somewhere between the subasymptotic and asymptotic domains.