On the form invariant volume transformation in phase space by focusing neutron guides: An analytic treatment

Tapered guides with supermirror coating are frequently used to focus neutron beams on specimens. The divergence distribution in the focused beam is of a great importance for the quality of neutron instrumentation. Using an analytic approach we derive the tapering which is needed to achieve a form invariant phase space transformation of a rectangular phase volume. In addition we consider the effect of beam attenuation by the finite reflectivity of supermirrors.