Fluorescence analysis of x-ray whispering gallery waves propagating along liquid meniscuses

X-ray fluorescence of whispering gallery (WG) waves, which propagate along meniscuses of silica hydrosols enriched by CsOH, has been detected and analyzed. The measurements were performed using the diffractometer with a laboratory x-ray tube at a radiation energy of 8048.05 eV, the x-ray fluorescence detector and a trough-motor system which rotates liquid samples. 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 equation. In order to determine the fluorescence scattering intensity, we have used the approach based on a method of fundamental parameters using the reciprocity theorem. In the analysis we used a two-layer model of the liquid surface with the upper non-uniform corrugated layer in which the concentration of levitating Cs
⁺
ions has a maximum near the surface, derived from the experiment, while the concentration maximum for SiO
₂
particles with sizes of ~ 10 nm is positioned at the depth of ~ 15 nm from the hydrosol surface.