On asymptotic light regime in an infinite medium far from a linear source of energy

Abstract

Stationary and nonstationary monochromatic radiative transfer in an infinite medium with cylindrical symmetry is considered. It is supposed that the medium is illuminated by a stationary or momentary linear source of energy. The medium is assumed to be homogeneous. Its optical properties are characterized by the volume absorption coefficient α, the single-scattering albedo λ and the anisotropic phase function, which is represented by a finite sum of Legendre polynomials. The finite speed of light and the duration of the light scattering process are taken into account. The radiation field at large optical distances τ from the source of radiation (τ ≫ 1) is investigated. The true absoption of light in the medium is assumed to be small (1 − λ ≪ 1). The partial-differentialintegral equations of radiative transfer in the medium illuminated by a stationary linear energy source are solved by means of the Case method. Asymptotic formulae for the mean intensity and the radiation flux is derived. Transition from a stationary to a non-stationary radiation field is realized by the technique proposed by I. N. Minin [3]. In this way the asymptotic expressions for the above-mentioned values are reduced for the case of a momentary linear source of energy. Refs 22.

Keywords:

radiative transfer, linear energy source, momentary energy source, radiation field, asymptotic expressions