The neutron transmission through a cylindrical guide tube

The transmission of neutrons or X-rays through a straight cylindrical channel can be determined for an input beam for which the beam divergence has azimuthal symmetry. For polar angles greater than the critical angle, the acceptance of trajectories is restricted and allowable trajectories are close to the perimeter of the channel. The distribution of available polar angles has been calculated, from which both the transmission and the beam profile as a function of distance from the end of the channel can be calculated as a function of polar angle. Since the distance between successive reflections can be determined, the number of reflections per unit length can be calculated as a function of polar angle. Hence, the distribution of the beam profile for nonperfect reflectivity can be determined.