Finite-element modelling of multilayer X-ray optics

Multilayer optical elements for hard X-rays are an attractive alternative to crystals whenever high photon flux and moderate energy resolution are required. Prediction of the temperature, strain and stress distribution in the multilayer optics is essential in designing the cooling scheme and optimizing geometrical parameters for multilayer optics. The finite-element analysis (FEA) model of the multilayer optics is a well established tool for doing so. Multilayers used in X-ray optics typically consist of hundreds of periods of two types of materials. The thickness of one period is a few nanometers. Most multilayers are coated on silicon substrates of typical size 60 mm × 60 mm × 100–300 mm. The high aspect ratio between the size of the optics and the thickness of the multilayer (10⁷) can lead to a huge number of elements for the finite-element model. For instance, meshing by the size of the layers will require more than 10¹⁶ elements, which is an impossible task for present-day computers. Conversely, meshing by the size of the substrate will produce a too high element shape ratio (element geometry width/height > 10⁶), which causes low solution accuracy; and the number of elements is still very large (10⁶). In this work, by use of ANSYS layer-functioned elements, a thermal-structural FEA model has been implemented for multilayer X-ray optics. The possible number of layers that can be computed by presently available computers is increased considerably.