Algorithm for the real-structure design of neutron supermirrors

The effect of structure imperfections of neutron supermirrors on their performance is well known. Nevertheless, supermirrors are designed with the algorithms based on the theories of reflection from perfect layered structures. In the present paper an approach is suggested, in which the design of a supermirror is made on the basis of its real-structure model (the RSD algorithm) with the use of exact numerical methods. It allows taking the growth laws and the reflectance of real structures into account. The new algorithm was compared with the Gukasov–Ruban–Bedrizova (GRB) algorithm and with the most frequently used algorithm of Hayter and Mook (HM). Calculations showed that, when the parameters of the algorithms are chosen so that the supermirrors designed for a given angular acceptance m have the same number of bilayers, (a) for perfect layers the GRB, HM and RSD algorithms generate sequences of practically the same reflectance; (b) for real structures with rough interfaces and interdiffusion the GRB and HM algorithms generate sequences with insufficient number of thinner layers and the RSD algorithm turns out to be more responsive and efficient. The efficiency of the RSD algorithm increases for larger m. In addition, calculations have been carried out to demonstrate the effect of fabrication errors and absorption on the reflectance of Ni/Ti supermirrors.