Acceptance diagram calculations of the performance of neutron removal mirrors

We have used the method of acceptance diagrams to compute the performance of low energy neutron removal mirrors, or “deflectors”, placed within a parallel neutron guide. Such devices are typically used to remove long wavelength neutrons from cold neutron beams. With appropriate coatings they may also be used as low energy neutron polarizers, ideally transmitting one spin state and reflecting the other spin state out of the beam. Within the small angle approximation, ignoring absorption, and representing reflectivities using unit step functions (either 0% or 100%, depending on the angle of incidence and the critical angle), the transmission probability reduces to a function of 3 ratios among 4 angles: the inclination angle of the deflector and the critical angles (which are proportional to neutron wavelength) of the upstream entrance guide, the deflector, and the guide within which the deflector is placed. The results of the acceptance diagram calculations, and of complementary ray-tracing calculations using realistic reflectivity profiles for the deflector, should benefit scientists and engineers involved in the design of neutron scattering instruments that potentially incorporate neutron deflectors.