共查询到20条相似文献，搜索用时 93 毫秒
1.
E. A. Saad M. A. El Gazzar M. S. Abdel Krim S. A. El Wakil 《Astrophysics and Space Science》1984,107(1):11-18
An asymptotic solution for the equation of radiative transfer in an inhomogeneous medium was obtained on the basis of the corresponding solutions for homogeneous sub-layers in the slowing down region. Function relations between the reflection and transmission coefficients for the whole slab and those of the sublayers are given. The invariant embedding concepts are used to get the reflection and transmission coefficients for the sub-layers. We assumed different models for the slowing-down kernels. Laplace transform was used to transform the Boltzmann equation to one velocity approximation with re-scaled mean-free path and single-scattering albedo. Numerical results are given for energy albedo as a function of the mass number of the host medium. 相似文献
2.
Diffuse reflection and transmission coefficients in a plane parallel medium are calculated for a Rayleigh phase-function averaged over polarization and Rayleigh polarized phase-function. This is calculated by imbedding the finite medium into a semi-infinite scattering and absorbing medium. Numerical calculations for semi-infinite albedo are compared with Pomraning results. The albedos for finite medium are calculated via the imbedding equations which converge for large τ to the value of semi-infinite medium. 相似文献
3.
The interaction of an obliquely incident plane electromagnetic wave with an anisotropic moving conducting medium described by tensor constitutive parameters
is studied. Starting from the Maxwell-Minkowski equations the wave solutions in the laboratory frame, the modified law of refraction and the reflecton and the transmission coefficients are obtained both for incidentE- andH-waves, corresponding to the two specific orientations of the plane of incidence relative to the direction of motion of the medium. The reflection and the transmission coefficients for a moving conducting medium do not, in general, add to unity resulting in the possibility of energy transference between the moving medium and the transmitted wave. Further the various reflection and transmission characteristics are modified in an interesting manner due to the finite conductivity, the anisotropy and the motion of the medium. Numerical results for the reflection and the transmission coefficients are presented for a range of the parameters characterizing the anisotropy and the velocity of the moving medium. 相似文献
4.
A method is presented for solving radiation transfer problems involving space-dependent single-scattering albedoc(x) for a grey plane non-emitting medium with isotropic scattering. Expressions for the exit distributions and the reflection and transmission coefficients, relevant to a medium having a slab geometry, are given. The solution of the linear transport equation is performed on the basis of integral Fourier transforms. Numerical results are obtained in the case of exponentially varying single-scattering albedo and compared with previous results. 相似文献
5.
Tsutomu Takashima 《Astrophysics and Space Science》1974,30(2):309-313
If the atmosphere is simulated by a number of homogeneous sublayers, it was shown (Takashima, 1973a) that the intensity and polarization parameters emerging from any boundary of internal sublayer's field can be determined, provided that the diffuse reflection and transmission matrices of radiation of sublayers are known. Furthermore, if the surface (ground) is assumed to reflect light in accordance with the Lambert law, it is shown in this paper that the internal radiation field at boundary of any sublayer can be also computed in terms of the diffuse radiation matrices of sublayers rather than in terms of that of the entire atmosphere (Sekera, unpublished). The effect of polarization is included. 相似文献
6.
To improve the accuracy of calculations for the reflection and transmission functions, doubling techniques are in use. The central theme of this method is to derive the total reflection function when two portions of a medium are adjoined together. The synthesis is done by the use of star product techniques which require a knowledge of theS andT functions of both parts of the medium. Infinite series expansion is necessary to compute the total reflection. The method developed in this article splits the total reflected beam into two parts, one relating to that flux which suffers no scattering at all in the first portion of the medium and the second portion that undergoes at least one scattering in the first portion. The first part can be evaluated simply by knowing the reflection function of the second portion of the medium. The other part of the total reflection for variations of the thickness of the first portion of the medium is found to obey a simple Riccati type integro-differential equation with zero initial conditions. Knowledge of theT functions is not necessary and integration has to be performed over the interval corresponding to thickness of the first portion of the medium. Order-of-scattering analysis is also carried out. 相似文献
7.
A. G. Nikoghossian 《Astrophysics》2004,47(2):248-259
This paper is a continuation of a study of radiative transfer in one-dimensional inhomogeneous atmospheres. Two of the most important characteristics of multiple scattering in these media are calculated: the photon escape probability and the average number of scattering events. The latter is determined separately for photons leaving the medium and for photons that have undergone thermalization in the medium. The problem of finding the radiation field in an inhomogeneous atmosphere containing energy sources is also examined. It is assumed that the power of these sources, as well as the scattering coefficient, can vary arbitrarily with depth. It is shown that knowledge of the reflection and transmission coefficients of the atmosphere makes it possible to reduce all these problems to solving some first order linear differential equations with specified initial conditions. A series of new analytic results are obtained. Numerical calculations are done for two types of atmosphere with different depth dependences for the scattering coefficient. These are interpreted physically. 相似文献
8.
S. A. El Wakii M. S. Abdel Krim M. T. Attia A. A. El Ghazaly E. A. Saad 《Astrophysics and Space Science》1989,158(1):95-105
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. 相似文献
9.
The interaction of ans-polarized plane electromagnetic wave incident from a dielectric (or vacuum) region on awarm moving magnetized plasma half-space is considered. The external magnetic field is assumed to be normal to the direction of the wave normal and the velocity of the moving medium. Using the first three moment equations, together with Maxwell's electromagnetic equations, we construct the constitutive relations in the rest frame of the moving medium. The constitutive relations are then transformed to the laboratory frame by invokingMinkowski's equations for the moving plasma medium, and the dispersion relation for the propagating ordinary mode in the moving medium is derived. Expressions are obtained for the phase and group velocities and the index of refraction for the ordinary mode, as also for power reflection and transmission coefficients. It is found that in contrast to the case of a cold magnetized plasma, the ordinary electromagnetic mode excited in the warm magnetoplasma medium getsmodified due to the presence of an external magnetic field. In addition, the various reflection and transmission characteristics for a warm magnetoplasma depend on the velocity of the moving plasma as well as on the strength of the applied magnetic field, as against the case for a cold moving magnetized plasma. Numerical results on the reflection coefficient are presented for several values of the parameters characterizing the electron-plasma temperature, the velocity of the moving medium and the strength of the applied magnetic field. 相似文献
10.
In order to facilitate the computations of the intensities of radiation reflected and/or transmitted by plane-parallel, vertically inhomogenous, scattering-absorbing media, we carry out the optical thickness integrations of the Cauchy systems (normally referred to as Invariant Imbedding Equations) for reflection and transmission functions originating from the first three orders of scattering: the medium in question is represented by a stack of a certain number of homogeneous slabs, each of which is characterized by a constant single scattering albedo and a constant phase function together with the optical thickness.The results are a set of recurrence formulae involving only the angular intergrations, a convenient feature for numerical computations, and should prove useful particularly for finding approximate values of the high frequency Fourier coefficients of reflection and transmission functions of inhomogeneous media or efficiently initializing the solution for a thin layer to perform rigorous multiple scattering computations by means of other techniques such as the Doubling-Adding method. 相似文献
11.
A method of computing the diffuse reflection and transmission radiation from an inhomogenous, plane-parallel planetary atmosphere bounded by the hybrid surface of a diffuse and specular reflector is discussed by using the addition method. If the atmosphere is simulated by a number of homogeneous sublayers, the radiation diffusely reflected and transmitted by the atmosphere can be expressed in terms of the diffuse reflection and transmission matrices of radiation of sublayers (Laciset al., 1974; Takashima, 1973, 1975). With this method (Takashima, 1975), the troublesome treatment due to the effect of polarity of radiation is overcome. Moreover, if the surface reflects radiation in accordance with the Lambert law as well as a quite arbitrary phase matrix (Takashima, 1974), the addition method can be easily extended. It is shown in this paper that the addition method is suitable for numerical computation even if the surface reflects light according to the hybrid mode of the diffuse and specular law (Uenoet al., 1974; Mukai, 1976).On leave from the Meterological Research Institute, Tokyo, Japan. 相似文献
12.
A method of full wave analysis with improved stability 总被引：1，自引：0，他引：1
T. Nygrén 《Planetary and Space Science》1982,30(4):427-430
A new version of a previously published method of full wave analysis is presented. The purpose of the procedure is to avoid the numerical instability which in some cases is encountered when the original version is used. In the old method the reflection and inverse transmission coefficient matrices were recursively calculated starting from the top of the layer. It is found that better stability is obtained, if the reflection coefficients are calculated as before, but the transmission coefficients are computed starting from the bottom of the layer and proceeding upwards in the direction of the incident wave. 相似文献
13.
A. G. Nikoghossian 《Astrophysics》2011,54(1):126-138
Group theory is used to describe a procedure for adding inhomogeneous absorbing and scattering atmospheres in a one-dimensional
approximation. The inhomogeneity originates in the variation of the scattering coefficient with depth. Group representations
are derived for the composition of media in three different cases: inhomogeneous atmospheres in which the scattering coefficient
varies continuously with depth, composite or multicomponent atmospheres, and the special case of homogeneous atmospheres.
We extend an earlier proposal to solve problems in radiative transfer theory by first finding global characteristics of a
medium (reflection and transmission coefficients) and then determining the internal radiation field for an entire family of
media without solving any new equations. Semi-infinite atmospheres are examined separately. For some special depth dependences
of the scattering coefficients it is possible to obtain simple analytic solutions expressed in terms of elementary functions.
An algorithm for numerical solution of radiative transfer problems in inhomogeneous atmospheres is described. 相似文献
14.
S. A. El Wakil H. M. Machali M. H. Haggag M. T. Attia 《Astrophysics and Space Science》1987,129(1):95-105
Equations for radiation transfer are obtained for dispersive media with space-dependent albedo. Bivariational bound principle is used to calculate the reflection and transmission coefficients for such media. Numerical results are given and compared. 相似文献
15.
T. Nygrén 《Planetary and Space Science》1981,29(5):521-528
A simple method for obtaining the reflection and transmission coefficients and fields for an electromagnetic wave propagating vertically in a horizontally stratified ionosphere is introduced. The ionosphere is divided into a great number of thin layers, and the boundary conditions of the electric and magnetic fields are applied at all layer interfaces. A recursive formalism is derived, which gives the altitude dependence of the reflection and inverse transmission coefficient matrices starting from the top of the layer. It is then shown how these results can be used in calculating the height dependence of a wave corresponding to any incident polarization. Test results are also presented in order to demonstrate the applicability of the procedure. 相似文献
16.
The coupling of magnetoacoustic waves at a plane interface that separates two semiinfinite collisionless fluids is studied. The fluids are characterized by different temperatures along and transverse to the ambient magnetic field. Continuum equations obtained by Chewet. al. (1956) are used and expressions for the reflection and transmission coefficients are derived. Extensive numerical computations are done to study the variation of the reflection coefficient, with the angle of incidence, for various temperature anisotropies of the media. Relevance of these investigations to the magnetosphere-solar wind boundary is discussed. 相似文献
17.
G. Jovanović 《Solar physics》2014,289(11):4085-4104
We derive the dispersion equation for gravito-magnetohydrodynamical (MHD) waves in an isothermal, gravitationally stratified plasma with a horizontal inhomogeneous magnetic field. Sound and Alfvén speeds are constant. Under these conditions, it is possible to derive analytically the equations for gravito-MHD waves. The high values of the viscous and magnetic Reynolds numbers in the solar atmosphere imply that the dissipative terms in the MHD equations are negligible, except in layers around the positions where the frequency of the MHD wave equals the local Alfvén or slow wave frequency. Outside these layers the MHD waves are accurately described by the equations of ideal MHD. We consider waves that propagate energy upward in the atmosphere. For the plane boundary, z=0, between two isothermal plasma regions with horizontal but different magnetic fields, we discuss the boundary conditions and derive the equations for the reflection and transmission coefficients. In the simpler case of a gravitationally stratified plasma without magnetic field, these coefficients describe the reflection and transmission properties of gravito-acoustic waves. 相似文献
18.
A. G. Nikoghossian 《Astrophysics》2004,47(1):104-116
This series of papers is devoted to multiple scattering of light in plane parallel, inhomogeneous atmospheres. The approach proposed here is based on Ambartsumyan's method of adding layers. The main purpose is to show that one can avoid difficulties with solving various boundary value problems in the theory of radiative transfer, including some standard problems, by reducing them to initial value problems. In this paper the simplest one dimensional problem of diffuse reflection and transmission of radiation in inhomogeneous atmospheres with finite optical thicknesses is considered as an example. This approach essentially involves first determining the reflection and transmission coefficients of the atmosphere, which, as is known, are a solution of the Cauchy problem for a system of nonlinear differential equations. In particular, it is shown that this system can be replaced with a system of linear equations by introducing auxiliary functions P and S. After the reflectivity and transmissivity of the atmosphere are determined, the radiation field in it is found directly without solving any new equations. We note that this approach can be used to obtain the required intensities simultaneously for a family of atmospheres with different optical thicknesses. Two special cases of the functional dependence of the scattering coefficient on the optical thickness, for which the solutions of the corresponding equations can be expressed in terms of elementary functions, are examined in detail. Some numerical calculations are presented and interpreted physically to illustrate specific features of radiative transport in inhomogeneous atmospheres. 相似文献
19.
Equations connecting the transmission and reflection functions of a finite medium to the reflection function of a semi-infinite one are used to get the albedos in the slowing-down region. The transport equation is solved by the modified Eddington method using Fermi's backward-forward scattering model, modulated to allow for different orders of backward-forward and isotropic scattering. Numerical results for the energy albedos are obtained and compared.On leave of absence from Atomic Energy Center, Inchass, Egypt. 相似文献
20.
Tsutomu Takashima 《Astrophysics and Space Science》1973,23(1):201-204
Suppose that the atmosphere consists of homogeneous sublayers whose scattering and transmission matrices are known, then it is shown in this paper how to determine the intensity and polarization parameters of internal radiation field by the matrix method. 相似文献