A Symmetry Criterion for Arrangements of Energy Sources in Spherical Target Excitation

A symmetry-based criterion is developed for arranging source locations to produce a nearly spherically uniform, volumetric deformation of a spherical target. The criterion requires that the source coordinates be combined in a certain manner to form an isotropic second-rank tensor. This criterion, combined with a method for maximizing the symmetry, produces a sequence of preferred configurations given by4T, 6C, 121, 201, 301, 321, 421, 501, 601, and 621,where the integer is the number of sources and where T, C, and I refer, respectively, to specific tetrahedral, cubic, and icosahedral symmetry arrangements. The results are of interest for a generic class of problems involving the excitation of a spherical medium through mechanical, thermal, or electromagnetic energy deposition by discrete sources.