To describe diffraction by a thick mosaic crystal, it is usually assumed that the constituent crystallites are so thin that each of them reflects at most a small fraction of the incident beam. Primary extinction and other dynamical diffraction effects can then be neglected. Reflections by different crystallites add incoherently, and can therefore be treated by classical transport theory. When only beams within the scattering plane are considered, then they obey the Darwin–Hamilton equations (Darwin 1922, Hamilton 1957),
where  are the directions of the incident and diffracted beam,  are the corresponding currents, &mu; is the Bragg reflectivity, and &sigma; accounts for losses by absorption and by thermal and elastic diffuse scattering. A generic analytical solution has been obtained remarkably late (Sears 1997; for the case &sigma;=0 Bacon/Lowde 1948). An exact treatment must allow for three-dimensional trajectories of multiply reflected radiation. The Darwin–Hamilton equations are then replaced by a Boltzmann equation with a very special transport kernel. In most cases, resulting corrections to the Darwin–Hamilton–Sears solutions are rather small (Wuttke 2014).