On the phase-space description of synchrotron x-ray beams

Abstract

Simple graphic methods for illustrating the transformation of x-ray beams by optical elements such as mirrors, monochromators, and slits are very helpful tools when optimizing synchrotron radiation experiments. They provide guidelines for matching the optical components to the source and to the experiment, and for checking the physical meaning of the more detailed results obtained by subsequent ray-tracing calculations. Phase-space diagrams have been used extensively to describe synchrotron radiation experiments by plotting an angular variable against a positional one with the possibility to add the energy in a third dimension. For neutron scattering, the traditional method consists in parallel representations, in reciprocal and in real space, that can also be considered as another kind of phase-space diagram. In this paper, we show the specific advantages and the complementary character of the above diagrams. The representation of several optical elements and their effect on beam transformation is given first individually and then for some arrangements of two or more beam-defining devices. Finally, a beamline is described and optimized as a demonstration of the usefulness and the limits of these graphic methods.