Analysis and design of multilayer structures for neutron monochromators and supermirrors

• The inequality (not equation) that defines the thicknesses of layers was obtained.
• Ready-to-use formula for the width of the spectral line was found.
• Non-quarter-wave monochromators were suggested.
• We propose a new algorithm for design of a neutron supermirror.
• The problem of minimizing the number of layers in a supermirror is raised.

A relatively simple and accurate analytical model for studying the reflectivity of neutron multilayer monochromators and supermirrors is proposed. Design conditions that must be fulfilled in order to reach the maximum reflectivity are considered. The question of the narrowest bandwidth of a monochromator is discussed and the number of layers required to build such a monochromator is derived. Finally, we propose a new and efficient algorithm for synthesis of a supermirror with specified parameters and discuss some inherent restrictions on an attainable reflectivity.