Simple analytic solutions for uniform irradiation of spherical targets

For directly driven Inertial Confinement Fusion targets, it is crucial to maximize the smoothness of the intensity incident on the target's initially spherical surface. It is possible to irradiate spherical targets with perfect uniformity from a finite number of finite aperture beams, provided that the intensity profile of each beam is a square-root function of its radius in the target plane. The consequences of this observation are described, some simple examples of geometries that realize perfect uniformity are presented, and heuristic rules for arranging beams with the appropriate symmetry are defined