RADIATIVE-TRANSFER THEORY WITH TIME-DELAY FOR THE EFFECT OF PULSE ENTRAPPING IN A RESONANT RANDOM MEDIUM - GENERAL TRANSFER EQUATION AND POINT-LIKE SCATTERER MODEL

A pulse propagation of a vector electromagnetic wave field in a discre te random medium under the condition of Mie resonant scattering is con sidered on the basis of the Bethe-Salpeter equation in the two-frequen cy domain in the form of an exact kinetic equation which takes into ac count the energy accumulation inside scatterers. The kinetic equation is simplified using the transverse field and far wave zone approximati ons which give a new general tensor radiative transfer equation with s trong time delay by resonant scattering. This new general radiative tr ansfer equation, being specified in terms of the low-density limit and the resonant point-like scatterer model, takes the form of a new tens or radiative transfer equation with three Lorentzian time-delay kernel s by resonant scattering. In contrast to the known phenomenological sc alar Sobolev equation with one Lorentzian time-delay kernel, the deriv ed radiative transfer equation does take into account effects of (i) t he radiation polarization, (ii) the energy accumulation inside scatter ers, (iii) the time delay in three terms, namely in terms with the Ray leigh phase tensor, the extinction coefficient and a coefficient of th e energy accumulation inside scatterers, respectively (i.e. not only i n a term with the Rayleigh phase tensor). It is worth noting that the derived radiative transfer equation is coordinated with Poynting's the orem for non-stationary radiation, unlike the Sobolev equation. The de rived radiative transfer equation is applied to study the Compton-Miln e effect of a pulse entrapping by its diffuse reflection from the semi -infinite random medium when the pulse, while propagating in the mediu m, spends most of its time inside scatterers. This specific albedo pro blem for the derived radiative transfer equation is resolved in scalar approximation using a version of the time-dependent invariance princi ple. In fact, the scattering function of the diffusely reflected pulse is expressed in terms of a generalized time-dependent Chandrasekhar H -function which satisfies a governing nonlinear integral equation. Sim ple analytic asymptotics are obtained for the scattering function of t he front and the back parts of the diffusely reflected Dirac delta fun ction incident pulse, depending on time, the angle of reflection, the mean free time, the microscopic time delay and a parameter of the ener gy accumulation inside scatterers. These asymptotics show quantitative ly how the rate of increase of the front part and the rate of decrease of the rear part of the diffusely reflected pulse become slower with transition from the regime of conventional radiative transfer to that of pulse entrapping in the resonant random medium.