The “infinity catastrophe” associated with radiation in magnetoionic media

In recent years many papers have appeared in the technical literature dealing with the question of radiation from sources imbedded in magnetoionic media. Most of these papers, which have restricted their consideration to media described by the Appleton-Hartree dielectric tensor, have come to the conclusion that the radiation resistance of a point dipole may be infinite in some regime of magnetoionic parameters even if the medium itself is lossless. Recently, two authors have purported to show, by introducing arguments of time reversibility, that the “infinity catastrophe” that appeared in the earlier papers is due to an incorrect formulation of the problem and that if the correct formulation were used the infinity would disappear. This paper reexamines the fundamental formulas for radiation in magnetoplasmas and concludes that the formulas used by earlier authors are valid and that the “infinity catastrophe” arises not from the method of calculation but rather from a physical inconsistency in the Appleton-Hartree dielectric tensor.