Stationary transport with partially reflecting boundary conditions

The stationary monoenergetic transport equation (the Lorentz model) is considered in a semiinfinite geometry with partially reflecting boundary conditions at x=0. The extrapolation length, the density, and the space-dependent diffusion coefficient are studied as functions of the accommodation coefficient α, both for constant and renormalized current. The hydrodynamical description at the level of the evolution equation is practically unaffected by α and is still valid at distances of several mean free paths (mfp) from the boundary. Yet, when consistently applying the boundary condition, the boundary layer has to be considered in terms of the Milne extrapolation length, which varies like (1-α)^-1. The case α=1 is a singular limit in the sense that the boundary layer solution disappears completely.