THEORY OF TRANSFER WITH DELAY FOR TRAPPING OF NONSTATIONARY ACOUSTIC RADIATION IN A RESONANT RANDOMLY INHOMOGENEOUS-MEDIUM

The propagation of a quasimonochromatic wave packet of acoustic radiat ion in a discrete randomly-inhomogeneous medium under the condition th at the carrier frequency of the packet is close to the resonance frequ ency of Mie scattering by an isolated scatterer is studied. The two-fr equency Bethe-Salpeter equation in the form of an exact kinetic equati on that takes account of the accumulation of the acoustic energy of th e radiation inside the scatterers is taken as the initial equation. Th is kinetic equation is simplified by using the model of resonant point scatterers, the approximation of low scatterer density, and the Fraun hofer approximation in the theory of multiple scattering of waves. Thi s leads to a new transport equation for nonstationary radiation with t hree Lorentzian delay kernels. In contrast to the well-known Sobolev r adiative transfer equation with one Lorentzian delay kernel, the new t ransfer equation takes account of the accumulation of radiation energy inside the scatterers and is consistent with the Poynting theorem for nonstationary acoustic radiation. The transfer equation obtained with three Lorentzian delay kernels is used to study the Compton-Milne eff ect-trapping of a pulse of acoustic radiation diffusely reflected from a semi-infinite resonant randomly-inhomogeneous medium, when the puls e can spend most of its propagation time in the medium being ''trapped '' inside the scatterers. This specific albedo problem for the transfe r equation obtained is solved by applying a generalized nonstationary invariance principle. As a result, the function describing the scatter ing of a diffusely reflected pulse can be expressed in terms of a gene ralized nonstationary Chandrasekhar H-function, satisfying a nonlinear integral equation. Simple analytical asymptotic expressions are found for the scattering function for the leading and trailing edges of a d iffusely reflected delta-pulse as functions of time, the reflection an gle, the mean scattering time of the radiation, the elementary delay t ime, and the parameter describing the accumulation of radiation energy inside the scatterers. These asymptotic expressions demonstrate quant itatively the retardation of the growth of the leading edge and the re tardation of the decay of the trailing edge of a diffusely reflected d elta-pulse when the conventional radiative transfer regime goes over t o a regime of radiation trapping in a resonant randomly-inhomogeneous medium. (C) 1998 American Institute of Physics.