Determination of Doped Concentrations in ICF Shells by X-Ray Equivalent Absorption

An X-ray equivalent absorption technique is developed to determine the doped concentrations of the inertial confinement fusion shells. Doped atoms in the shells are used to increase the opacity for radiation, to improve the absorptive capacity of the shell wall for X-ray, and to restrain the growth of hydromechanics instability. The doped concentrations in the shells are difficult to determine for the relatively thick shell wall and the spatial resolution. A novel model is proposed to determine the doped concentrations by a theory of X-ray equivalent absorption. The advantage of this model is that optical density (D) and the exposure curve [D = Φ(I)] of film plates are not necessary to calculate the doped concentrations. The model is validated with a thickness error of 2% by the polypropylene step wedge, the aluminum step wedge, and the polystyrene sphere. The error of results for doped concentration between this method and the energy-dispersive spectroscopy method is less than 0.1 at. %. The uncertainty also is analyzed and the combined expanded uncertainty is better than 0.2 at. % for the Ge-doped glow discharge polymer shell (k = 2).