Geometrical description of the X-ray capillaries with assumed reflection features

• Published in: Journal of alloys and compounds 2004-11, Vol.382 (1-2), p.311-319
• Main Authors: Mroczka, Robert, Żukociński, Grzegorz, Kuczumow, Andrzej
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Instruments, apparatus, components and techniques common to several branches of physics and astronomy; Light absorption and reflection; Physics; Synchrotron radiation; Total reflection; X- and γ-ray instruments and techniques; X-ray capillary optics; X-ray spectroscopy
• ISSN: 0925-8388; 1873-4669
• DOI: 10.1016/j.jallcom.2004.06.007

The geometrical description of the capillary systems adjusted for controlled guiding of X-rays is presented. Simple relationships between the reflection angle ϑ, the angle α of the capillary wall inclination with respect to the capillary main axis and the angle γ of the ray inclination in relation to the main axis are proved. Once established, the relationships help in the small angle approximation to derive differential equations describing the constant reflection profile of the capillary wall. Alternatively, the system of algebraic relationships is established. The systems of equations correspond either to the control over reflection angle or to the control over the shape of the wall. The way for calculation of the forces to draw capillaries of desired shape is then demonstrated. Finally, complete relationship between capillary shape and variability of the reflection coefficient is suggested.