A Method of Approximate Greens Function for Solving Reflection of Particles in Plane Geometry

Abstract

A method for approximate analytical solution of transport equation for particles in plane geometry is developed by solving Fredholm integral equations. Kernels of these equations are the Greens functions for infinite media treated approximately. Analytical approximation of Greens function is based on decomposition of the functions into terms that are exactly analytically solved and those which are approximately obtained by usual low order DPN approximation. Transport of particles in half-space is treated, and reflection coefficient is determined in the form of an analytical function. Comparison with the exact numerical solution and other approximate methods justified the proposed analytical technique.