Theoretical consideration of intensity of an x-ray microbeam formed by a hollow glass pipe

Intensities of x-ray microbeams formed by the 250-mm-long hollow glass pipes of inner diameters of 27.4, 23.0, and 18.8 μm have been theoretically investigated, by taking account of the slope distribution of microprojections (surface roughness) on the pipe inner wall, using the Monte Carlo method. The intensities for all the pipes calculated on the supposition that each pipe inner wall is perfect (i.e., zero rms of the slope distribution) have been much greater than the experimental values in the x-ray energy region from 6.93 to 19.6 keV. Assuming the slope rms from 2.5×10^-4 rad to 3.3×10^-3 rad, the calculated results have agreed with the experimental values. Discussions on the results for all the pipes are given in relation to the x-ray anomalous dispersion, the penetration of x rays, the intensity distribution on the x-ray sources used, undulation of the pipes, and the presence of microdust in the pipes.