Solving the Boundary Problem of a Non-Stationary Equation Transfer of Radiation and Particles for a Semi-Infinite Medium

Abstract

The boundary problem of non-stationary radiative and particle transfer equation for a semi-infinite medium with an arbitrary single scattering law is considered. This problem comes to finding of a path length distribution function for particles in a turbid medium. A non-linear integro-differential equation for path length distribution function in the case of non-stationary multiple scattering in a semi-infinite medium with an anisotropic scattering law is found by means of invariant embedding. With the help of the discrete ordinates method, matrix non-linear differential equations are deduced that are solved by formulae of backward differentiation and matrix methods for solution of the Lyapunov equation. The computing results are verified by the Monte Carlo method for the path length distribution function for photons backscattered from a drop WC1 cloud and elastically scattered electrons backscattered from a solid semi-infinite target.