The Quality of the Illumination for a Spherical Capsule Enclosed in a Radiating Cavity

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Abstract
The implosion of spherical capsules by the incoherent X-rays emitted from surrounding hot high-Z walls seems to be a scheme relevant to inertial confinement fusion. In this paper the quality of the illumination for a spherical capsule enclosed in an axisymmetric radiating cavity is considered for the two extreme cases of given, (optically) thick or thin, non-uniform, emitting cavity surface layer. If the specific intensity on the radiating surface is represented by an expansion in Legendre polynomials, it is found, for spherical radiating cavities, that the n-term contribution to the power density upon the capsule factorizes as the product of a function of the position on the capsule surface, times a function f(n, x) of its radius x. Furthermore, it is found that values of x may exist for which f(n, x)=0, this being true both for thick and thin modeling with values of x almost the same. Simple criteria to get a given degree of uniformity are suggested. The effects of the cavity shape on the illumination quality have been also studied as a function of the cavity aspect ratio for spherical capsules enclosed in ellipsoidal cavities (oblate or prolate).

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