Analysis and design of multilayer structures for neutron monochromators and supermirrors

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.