An Extended Moment Method in Radiative Transfer: The Matrices of Mean Absorption and Scattering Coefficients

Abstract In extension of the ideas of Anderson and Spiegel (1972) the radiative transfer equation is replaced by moment equations for the moments A A 1 A 2 …A N r =∫: (p 0 RL ) r+1−N p A 1 p A 2 …p A N f dP, r=0, 1, …, R. HerepAis the photon 4-momentum,cp0RLis the photon energy in the rest Lorentz frame andfis 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 ofmatricesof mean absorption and scattering coefficients. It is shown that the extension fromr=1 (Anderson and Spiegel, 1972; Thorne, 1981; Schweizer, 1988) tor=0, 1, …, Rgives 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 forR⩾6.