Useful identities for half-space problems in linear transport theory

Abstract

A typical translationally invariant linear transport problem for a half-space is solved by the eigenfunction method. Using some derived identities for the solution of the associated homogeneous Hilbert problem it is shown that the usual cumbersome integrals occurring in half-space problems can be reduced to a simple form. The usefulness of the identities is illustrated by solving the problem of a plasma confined to a half-space by a diffuse reflecting wall.