An Extended Moment Method in Radiative Transfer: The Matrices of Mean Absorption and Scattering Coefficients
✍ Scribed by Henning Struchtrup
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 408 KB
- Volume
- 257
- Category
- Article
- ISSN
- 0003-4916
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✦ Synopsis
In extension of the ideas of Anderson and Spiegel (1972) the radiative transfer equation is replaced by moment equations for the moments
Here p A is the photon 4-momentum, cp 0 RL is the photon energy in the rest Lorentz frame and f is the photon phase density. From these follow moment equations for the projected symmetric trace free moments introduced by Thorne (1981). The required closure of the equations is achieved by use of a series expansion of the phase density which is motivated by the entropy maximum principle. This procedure provides a coupling of the moment equations by means of matrices of mean absorption and scattering coefficients. It is shown that the extension from r=1 (Anderson and Spiegel, 1972;Thorne, 1981;Schweizer, 1988) to r=0, 1, ..., R gives reasonable results: In the limit of local radiative equilibrium (LRE) the well-known Rosseland mean of the absorption coefficient is recovered. For a simple non-LRE experiment, the homogeneous compression and relaxation of radiation, the radiative transfer equation, and the moment equations are solved. The comparison of the results in the case of pure bremsstrahlung (free free) absorption shows an excellent agreement for R 6.
1997 Academic Press
1. Introduction
The goal of radiation thermodynamics is the determination of the transfer of radiative energy and momentum as well as of the interchange of energy and momentum between radiation and matter.
In principle the problem is solved when the radiative transfer equation with all interaction terms is known. Of interest are the thermodynamic quantities energy, momentum, energy and momentum interchange, entropy, etc. They may be calculated from the photon phase density or the intensity of radiation and the spectral absorption and scattering coefficients by integration over all photon frequencies and directions. The photon phase density follows as the solution of the radiative transfer equation which is in general not analytically solvable.