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1.
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.  相似文献   

2.
《Planetary and Space Science》2007,55(10):1283-1289
The problem of monoenergetic polarized radiation transfer in a plane-parallel finite atmospheric medium is proposed. Pomraning–Eddington approximation is used to obtain the analytical solution for both the total intensity and the difference function of the polarized radiation. The medium is assumed to have specular reflecting boundaries with angular-dependent externally incident flux. For the sake of comparison, two different forms of the weight function, which introduced to force the boundary conditions to be fulfilled, are used. Numerical results of the reflectivity and transmissivity are obtained for the different degrees of polarization.  相似文献   

3.
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.  相似文献   

4.
The radiative heat flux at the boundary of a sphere containing an internal energy source and subject to general boundary conditions (problem 1) is obtained in terms of the albedo of the corresponding source-free problem with isotropic boundary condition (problem 2). The solution of problem 2 is performed on the basis of the integral Fourier transforms method. Numerical results for the partial heat flux and emissivity for a given internal energy source and inhomogeneous medium, isotropic scattering are obtained.  相似文献   

5.
Radiative transfer equation in a plane-parallel medium with isotropic boundary conditions for linearly anisotropic scattering phase function is considered. Two coupled integral equations for total density of radiation and total radiation flux are obtained. The Galerkin method is used to solve these equations. Numerical results for the radiative fluxes at the boundaries show that the Galerkin method yields accurate results compared well with other exact methods.  相似文献   

6.
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.  相似文献   

7.
The problem of determining the intensity and the degree of polarization of radiation emerging from an inhomogeneous finite plane medium for the case of Rayleigh scattering with internal energy source is considered. A system of coupled integral equations are obtained and solved by the Galerkin method. The degree of polarization for homogeneous and inhomogeneous media are calculated for uniform and nonuniform sources.  相似文献   

8.
The problem of electromagnetic radiation from electric and magnetic line sources interacting with a moving uniaxially anisotropic dielectric or plasma half-space is treated. The anisotropy of the plasma is due to an infinitely strong magnetizing field impressedparallel to the motion of plasma. The line source is oriented normal to the direction of medium motion. TheE and theH modes are excited independently in the medium by the magnetic and the electric line sources, respectively. Invoking the saddle-point method of integration, the far-zone radiation field and the radiation pattern are obtained for both line sources. It is found that the radiation from an electric line source is not affected by the anisotropy of the moving medium and that a magnetic line source invacuum has finite components of radiation in directions which are parallel and antiparallel to the direction of motion, for the case of a uniaxial plasma in contrast to the results for a uniaxial dielectric. Numerical results for the far-zone radiation pattern, referring to a magnetic line source, are presented for several values of parameters characterizing the non-dimensional velocity, the anisotropy of the medium, the electron-plasma density and the location of the line source.  相似文献   

9.
The partial heat fluxes of thermal radiation in an emitting, absorbing, and scattering finite medium bounded by diffusely-reflecting plates is studied, assuming the medium to scatter isotropically. Two algebraic equations connecting the partial heat fluxes relevant to this problem and the corresponding one with simple boundary conditions are obtained. The intergral equation is solved in a semi-analytical from by collection method, using Legendre polynomials as basis functions. Numerical results are presented and compared.  相似文献   

10.
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   

11.
The in fluence of the different reflective boundaries on the polarized radiation field in a conservative homogeneous plane-parallel atmosphere is studied. The equation of transfer for molecular scattering is solved using the method of discrete ordinates and the results are checked by using the invariant imbedding approach. The results of a long series of numerical experiments have shown that in general a reflecting boundary at the bottom depolarizes the radiation field while the depolarizing effect of an isotropic scatterer is much larger than that of a specular reflector or a perfect absorber.  相似文献   

12.
The problem of monoenergetic radiative transfer in a finite planar stochastic atmospheric medium with polarized (vector) Rayleigh scattering is proposed. The solution is presented for an arbitrary absorption and scattering cross sections. The extinction function of the medium is assumed to be a continuous random function of position, with fluctuations about the mean taken as Gaussian distributed. The joint probability distribution function of these Gaussian random variables is used to calculate the ensemble-averaged quantities, such as reflectivity and transmissivity, for an arbitrary correlation function. A modified Gaussian probability distribution function is also used to average the solution in order to exclude the probable negative values of the optical variable. Pomraning-Eddington approximation is used, at first, to obtain the deterministic analytical solution for both the total intensity and the difference function used to describe the polarized radiation. The problem is treated with specular reflecting boundaries and angular-dependent externally incident flux upon the medium from one side and with no flux from the other side. For the sake of comparison, two different forms of the weight function, which introduced to force the boundary conditions to be fulfilled, are used. Numerical results of the average reflectivity and average transmissivity are obtained for both Gaussian and modified Gaussian probability density functions at the different degrees of polarization.  相似文献   

13.
The problem of electromagnetic radiation from electric and magnetic line sources interacting with a moving magnetoplasma slab backed by a finitely conducting medium is treated. The local magnetostatic field is aligned parallel with the line source and is perpendicular to the direction of slab motion. For the configuration, theE andH modes are excited independently by a magnetic and an electric line source respectively. Expressions for the far zone radiation fields and the radiation pattern have been obtained for both the line sources. It is found that the radiation due to an electric line source is not affected by the presence of a static magnetic field and the motion of the slab medium. Numerical results for the radiation pattern referring to both the line sources have been presented for a wide range of parameters characterizing the finite magnetostatic field, the conductivity of the medium backing the plasma, the thickness of the slab and the location of the line source.  相似文献   

14.
A generalized principle of invariance is derived for a plane-parallel atmosphere. On the basis of this principle a method for determining the radiation field in a multilayer atmosphere is proposed. This method, the first part of which is the well-known adding method, permits the application to problems involving optically finite as well as semi-infinite atmospheres. The reflecting boundaries may be incorporated, though in that case it is not possible to use the adding method.Some numerical results are given for the standard and Milne problems and for the problem with internal sources.  相似文献   

15.
Intensities of carbon radio recombination lines are analytically described as function of line number, temperature and medium concentration. Accounting for the process of dielectronic recombination the balance equations for highly excited carbon populations as b n-factors are solved by the diffusional approximation. To determine medium temperature and density with the experimental amplification coefficients the system of boundary condition equations is formulated as . Analytically found in the range of temperatures T e = 25-100, 104 K the line amplification coefficients are compared with the numerical solutions. By the method of radio lines intensity ratio of carbon for the observations at frequencies 34.5–25 MHz the density magnitudes are calculated towards Cassiopeia A as function of temperature. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

16.
This paper studies sonic waves in an optically thick medium under the influence of a magnetic field. The conductivity of the medium has been taken to be infinite. The effects of radiation, radiation energy density, radiative heat transfer and magnetic field have been taken into account. It has been obtained that the magnetic field has significant effect on sonic velocity. The fundamental differential equations governing the growth and decay of sonic waves are determined and solved.  相似文献   

17.
X-ray reflectivity measurements were performed on several thin foil gold mirrors fabricated in TIFR for a Soft X-ray Imaging Telescope. The mirrors were made from thin aluminum foils with a reflecting layer of sputtered gold transferred from a smooth glass mandrel using an epoxy. X-ray reflectivity measurements were performed on a sample of randomly selected mirrors using CuK α (8.05 keV), CrK α (5.41 keV) X-rays and also at several energies in the energy range of 155–300 eV using the synchrotron source Indus-1. It was found that the roughness of the low-density top gold layer as obtained from the fitting of X-ray reflectivity data for CuK α radiation is relatively more as compared to that obtained from the CrK α radiation. This indicates that in the mirrors made by this process, the upper surfaces are smoother as compared to the deeper layers. It was also observed that the critical angle almost vanishes in the very low energy range of 290–300 eV due to strong absorption effects of the low density material sitting on top of these mirrors. Due to this absorption effect, efficiency of these mirrors reduces in this energy range. This is first time that reflectivity measurements are being reported for very soft X-rays (≤ 300 eV) for mirrors made for any X-ray astronomy mission.  相似文献   

18.
T. Takakura 《Solar physics》1984,91(2):311-324
In some gradual hard X-ray bursts with high intensity, hard X-ray source (15–40 keV) is steadily located in the corona along with softer X-ray source (5–10 keV).Two stationary models, high density and high temperature models, are proposed to solve the difficult problem of confinement of hot (or nonthermal) plasma in the direction of the magnetic field along the loops in the corona. In both models, an essential point is that the effective X-ray source is composed of fine dense filamentary loops imbeded in a larger rarefied coronal loop, and the electron number density in the filaments is so high as 1011–1012 cm-3. If the density is so high heat conduction can be as reasonably small as of the order of 1027 erg s -1 for the given emission measures of observed X-rays, since the required cross-sectional area is small and also classical conduction is valid. Collisional confinement of thermal tail, and nonthermal electrons if any, up to 50–60 keV in the filaments is also possible, so that the hard X-ray images can be loop like structure instead of double source (foot points).High density model is applicable to the coronal filamentary loops with temperature T m < 5 × 107 K at the loop summit. The heat flow from the summit downwards is lost almost completely by the radiation from the loop during the conduction to the foot points. A continuous energy release is assumed near the summit to maintain the stationary temperature T m, and pressure balance is maintained along the loop. In this model, the number density at the summit is given by n m - 106 T m 2 /sm, where s m is the length of the loop from the summit to the foot point, and the distribution of temperature and density along the loop are given by T = T m(s/sm)1/3 and n = n m(s/sm)-1/3, respectively.High temperature model is applicable to the filamentary loops with higher temperature up to about 108.5 K and comparatively lower number density as 1011 cm-3 for the requirement of magnetic confinement of the hot plasma in radial direction. The radiation from the loop is negligibly small in this model so that the heat flux is nearly conserved down to the foot points. In this case, temperature gradient is smaller than that of the high density model, depending on the tapering of the magnetic bottle.In both models, the differential emission measure is maximum at the highest temperature T m and the brightness distribution along the loop shows a maximum around the summit of the loop if some magnetic tapering is taken into account.  相似文献   

19.
The aim of the present paper will be to deduce the explicit form of differential equations which govern dynamical tides in close binary systems, with simplifications which are permissible for the mass-point model (Section 2), as well as for one exhibiting finite but high internal density concentration (Section 3). It is pointed out that, whereas the exact formulation of the problem leads to a simultaneous system of equations of sixth order (fourth in the inviscid case), this order reduces to four (or two for inviscid fluids) for the mass-point model; and to five (three for inviscid case) if the density concentration is high but finite.In the last section of this paper the coefficientsC i,j which specify the amplitudes of the individual partial tides are explicitly formulated as functions of the time.  相似文献   

20.
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.  相似文献   

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