On the use of acceptance diagrams to calculate the performance of multiple-section straight-sided neutron guide systems

The author describes a method to calculate the performance of multiple section systems of straight-sided guides and collimators. The approach is based on the concept of acceptance diagrams, previously described by J.M. Carpenter and D.F.R. Mildner, which display the transverse spatial and angular coordinates of the neutrons in the system. For a given section of guide the construction of the exit diagram, from the entrance diagram, is shown to be accomplished using a shear transformation followed by translational and rotational operations applied to polygons representing respectively even and odd numbers of reflections within the section. The reflected neutron polygons are then truncated leaving only the neutrons that never strike a surface at an angle greater than the critical angle for total reflection. 4 refs., 4 figs