FINITE ELEMENT ANALYSIS OF HIGH HEAT LOAD DEFORMATION AND MECHANICAL BENDING CORRECTION OF A BEAMLINE MIRROR FOR THE APS UPGRADE
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The impending Advanced Photon Source Upgrade (APS-U) will introduce a hard x-ray source that is set to surpass the current APS in brightness and coherence by two to three orders of magnitude. To achieve this, the storage ring light source will be equipped with a multi-bend achromat (MBA) lattice . In order to fully exploit and preserve the integrity of new beams actualized by upgraded storage ring components, improved beamline optics must also be introduced. The design process of new optics for the APS-U and other fourth generation synchrotrons involves the challenge of accommodating unprecedented heat loads. This dissertation presents an ex-situ analysis of heat load deformation and the subsequent mechanical bending correction of a 400 mm long, grazing-incidence, H2O side-cooled, reflecting mirror subjected to x-ray beams produced by the APS-U undulator source. Bending correction is measured as the smallest rms slope error, σrms, that can be resolved over a given length of the heat deformed geometry due to mechanical bending. Values of σrms in the <0.1 µrad regime represent a given mirror length over which incident x-ray beams from modern sources can be reflected without significant loss of quality [2, 3]. This study assumes a perfectly flat mirror surface and does not account for finish errors or other contributions to σrms beyond the scope of thermal deformation and elastic bending. The methodology of this research includes finite element analysis (FEA) employed conjointly with an analytical solution for mechanical bending deflection by means of an end couple. Additionally, the study will focus on two beam power density profiles predicted by the APS-U which were created using the software SRCalc . The profiles account for a 6 GeV electron beam with second moment widths of 0.058 and 0.011 mm in the x- and y- directions respectively; the electron beam is passed through a 4.8 m long, 28 mm period APS-U undulator which produces the x-ray beam incident at a 3 mrad grazing angle on the flat mirror surface for both cases. The first power density profile is the most extreme case created by the undulator at it’s closest gap with a critical energy of 3 keV (ky=2.459); the second profile is generated for the case in which the undulator is tuned to emit at 8 keV (ky=1.026). The 3 keV case is of particular interest as it represents one of the most intense peak heat loads predicted to be incident on first optics at the APS-U. The FEA results revealed that the deflection due to the 3 keV heat load yields a 10.9 µrad rms slope error over the full mirror length. The projected correction via the elastic bending of the substrate yields a 0.10 µrad σrms within the center longitudinal 300 mm. The FEA also predicts that the 8 keV heat load deflection can be corrected to a σrms of 0.11 µrad within the center 300 mm from 1.50 µrad over the entire length. Attempts to optimize the end couple to correct over the entire 400 mm mirror length were unable to resolve the heat load deflection rms slope error to within a < 0.1 µrad value for either case. However, if a larger corrected surface is required, a longer mirror can be implemented so as to absorb the heat load of a larger beam than necessary which can then be cut by an aperture to the desired size and energy range.