  A new method for investigation of x-ray propagation in a rough narrow
dielectric waveguide is proposed on the basis of the numerical integration of
the quazioptical equation. In calculations a model rough surface was used with
the given statistical properties. It was shown that the losses in the narrow
waveguides strongly depend on the wall roughness and on the input angle. The
losses are not zero even at zero input angle if the width of the waveguide is
smaller or about 1 mkm. The effect is accounted for as the influence of
diffraction. The angular spread of the transmitted X-ray radiation is much more
narrow than the Fresnel angle of the total external reflection.
