X-ray beam propagation in an inhomogeneous plasma with a continuously varied refractive index

From Maxwell's equation a diffraction-integral-like solution of X-ray propagation is derived. The paper puts emphasis, theoretically and numerically, on the analysis of the effect of refractive index gradient on the beam parameters. The results show that the higher is electron density, the effect is more evident. It has a direct impact on the distribution of the beam intensity, the diffraction and the deflection of the X-ray beam.