Extinction depth in a smooth X-ray waveguide

An approximate solution to the dispersion equation for the dynamics of an X-ray beam trapped in a plane waveguide with smooth walls is used to study the dependence of extinction depth on the optical density of wall material and X-ray energy. For angles of incidence of the X-ray beam that are no greater than the Fresnel angle, the extinction depth in nonabsorbing medium depends only on difference N e 1 – N e 1 of electron densities in the wall material and waveguide layer as (π r 0 ( N e 1 – N e 2 )) –1/2 , where r 0 ~ 2.81794 × 10 –13 cm is the classical electron radius. The results are in good agreement with the penetration depth of X-ray radiation into surface that is obtained using the Fresnel formulas in the approximation of plane waves at grazing angles that range from zero to one half of the critical angle of total external reflection.