Thermal optimization of a high-heat-load double-multilayer monochromator

Finite-element analysis is used to study the thermal deformation of a multilayer mirror due to the heat load from the undulator beam at a low-emittance synchrotron source, specifically the ESRF-EBS upgrade beamline EBSL-2. The energy bandwidth of the double-multilayer monochromator is larger than that of the relevant undulator harmonic, such that a considerable portion of the heat load is reflected. Consequently, the absorbed power is non-uniformly distributed on the surface. The geometry of the multilayer substrate is optimized to minimize thermally induced slope errors. We distinguish between thermal bending with constant curvature that leads to astigmatic focusing or defocusing and residual slope errors. For the EBSL-2 system with grazing angles θ between 0.2 and 0.4°, meridional and sagittal focal lengths down to 100 m and 2000 m, respectively, are found. Whereas the thermal bending can be tuned by varying the depth of the `smart cut', it is found that the geometry has little effect on the residual slope errors. In both planes they are 0.1–0.25 µrad. In the sagittal direction, however, the effect on the beam is drastically reduced by the `foregiveness factor', sin(θ). Optimization without considering the reflected heat load yields an incorrect depth of the `smart cut'. The resulting meridional curvature in turn leads to parasitic focal lengths of the order of 100 m.

Modelisation of Thermally Induced Jitter in a Slender Structure

The thermomechanical interactions of onboard space vehicles is an interesting field of research and study. Since the pioneering paper by Bruno Boley, published in 1954, many authors have given their relevant contribution to the comprehension of phenomena not otherwise investigable if not with a cross-sectoral approach and a multidisciplinary methodology. The anomaly that occurred to the spacecraft Alouette 1, in 1962, marked the beginning of a long series of unexpected events due to unconceivable coupling between the mechanical and thermal behaviour of the system. This work aims to emphasise, by means of a simple model, the basic mechanism responsible for elastic vibrations induced by a thermal shock. This is a widespread event experienced by a spacecraft during the transitions shadow-sun and vice-versa or when a flexible appendage, previously shadowed by the spacecraft's main body, comes to the light as a consequence of an attitude manoeuvre [Ulysses, 1990]. For the investigation, a very slender structure has been considered in order to make the thermal and mechanical characteristic times comparable and realise the conditions of strong coupling. The accurate thermal analysis provides an equivalent thermal bending moment, depending on time, which appears as a boundary condition in the subsequent modal analysis of the structural element, where it plays the role of a trigger of elastic transverse vibrations.

Assessment of Flaw Interaction Under Combined Tensile and Bending Stresses: Suitability of ASME Code Case N877-1

In the case of planar flaws detected in pressure components, flaw characterization plays a major role in the flaw acceptability assessment. When the detected flaws are in close proximity, proximity rules given in the Fitness-for-Service (FFS) Codes require to combine the interacting flaws into a single flaw. ASME Code Case N877-1 provides alternative proximity rules for multiple radially oriented planar flaws. These rules are applicable for large thickness components and account for the influence of flaw aspect ratio. They cover the interaction between surface flaws, between subsurface flaws and between a surface flaw and a subsurface flaw. The calculations of flaw interaction have been performed under pure membrane stress. However, actual loading conditions induce non-uniform stresses in the component thickness direction, such as thermal bending or welding residual stresses. Non-uniform stress fields can lead to variations in the Stress Intensity Factors of closely spaced flaws, affecting their mutual interaction. The objective of this paper is to assess the suitability of ASME Code Case N877-1 with regards to the presence of a bending part in the applied stress distribution. For that purpose, various applied stress profiles and flaw configurations are covered. The effect on flaw interaction is assessed through three-dimensional XFEM analyses.