Abstract
A Si(111) winged crystal has been designed to minimize anticlastic bending and improve sagittal focusing efficiency. The crystal was thin with wide stiffening wings. The length-to-width ratio of the crystal was optimized by finite element analysis, and the optimal value was larger than the `golden value'. The analysis showed that the slope error owing to anticlastic bending is less than the Darwin width. The X-rays were focused two-dimensionally using the crystal and a tangentially bent mirror. The observed profiles of the focal spot agreed well with the results of a ray-tracing calculation in the energy range from 8 to 17.5 keV. X-ray diffraction measurements with a high signal-to-noise ratio using this focusing system were demonstrated for a small protein crystal.
Highlights
Two-dimensional focusing by combining a bent second crystal in a double-crystal monochromator (Sparks et al, 1980, 1982) and a tangential-focusing mirror is an efficient method of increasing the flux density at bending-magnet and wiggler beamlines (e.g. Borsboom et al, 1998; Bilsborrow et al, 2006; Koshelev et al, 2009; Nomura & Koyama, 1999; Yoneda et al, 2005)
In this method the beam size in two-dimensional focusing is sensitive to the shape error of the second crystal from the ideal cylindrical shape owing to anticlastic bending
Nisawa et al Sagittal focusing of X-rays using a winged crystal tion in a four-point bender (Quintana et al, 1995; Kushnir et al, 1993)
Summary
Two-dimensional focusing by combining a bent second crystal in a double-crystal monochromator (Sparks et al, 1980, 1982) and a tangential-focusing mirror is an efficient method of increasing the flux density at bending-magnet and wiggler beamlines (e.g. Borsboom et al, 1998; Bilsborrow et al, 2006; Koshelev et al, 2009; Nomura & Koyama, 1999; Yoneda et al, 2005). Under clamped crystal with a tangential-focusing mirror was carried out using edge boundary conditions [z(x, y) = 0 and @z=@x = ‘constant’ at the optical geometry of beamlines BL26B1 and BL26B2 x = Æ X] the golden value decreases to 1.42. The optimized width obtained by the analysis is 30 mm (Fig. 5), corresponding to a ratio of = 3 and an acceptance angle of ’H = 0.9 mrad This is larger than the optimum value for two-dimensional focusing of ’H = 0.7 mrad. The applied uniform displacement UZ values for the crystals were À40 mm, À30 mm, À20 mm and À17 mm, respectively From these results it was clarified that the anticlastic bending effect decreases with increasing aspect ratio .
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