Ellipsoidal concentrators for laboratory X-ray sources: Analytical approach for optimization

Extremely low intensity of most existing laboratory X-ray sources (λ ∼ 0.01–10 nm) calls for the development of collimating and concentrating optics, which allow to increase significantly the radiation power on the sample surface. The problem of optimizing concentrator parameters is analytically solved in this study. This solution allows one to determine (without any auxiliary calculations) the maximum possible efficiency of a concentrator at any wavelength and analyze the dependence of its efficiency on the source size, wavelength, the source-sample distance, etc.