Neutron Transmission Through Tapered Channels

The transmission of neutrons through a tapered channel is analyzed and the relationships among various parameters such as the distance between reflections and the polar and grazing angles of a trajectory at each reflection are established. These relationships are used in a simulation to study the transmission characteristics of a cylindrical tapered channel. The transmission, the transmitted beam angular divergence and the number of reflections are determined for different values of the taper angle and the incident beam divergence. The simulation results for the straight channel agree exactly with the derived analytical expressions. Those for the tapered channels can be described using the same expressions but with a lower effective critical angle. This reduced critical angle depends on the length of the taper and on the taper angle. For long gentle tapers, the reduction in critical angle is equal to the reduction in channel diameter.