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X-ray diffraction and fluorescence of whispering galleries (WGs) which propagate along meniscuses of deionized water or silica hydrosols enriched by CsOH have been analyzed for the first time. The measurements have been performed using the diffractometer with a moving tube-detector system. The X-ray beam rotation angle reached a maximum value of 4° on a silica hydrosol sample. The WG mode propagating near the surface of a concave meniscus as well as the fluorescence intensity have been found from a solution of the respective Helmholtz equations. For analysis of intensities of the X-ray scattering and fluorescence we have used a two-layer model of the liquid with the upper non-uniform corrugated layer in which the concentration of levitating Cs+ ions near the surface has a maximum derived from the experiment in the hydrosol depth of ~ 15 nm for SiO2 particle sizes of ~ 5÷7 nm. In order to determine the fluorescence intensity we have used the approach based on a method of fundamental parameters using the reciprocity theorem.
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