Radiation resistance of a small filamentary loop antenna in a cold multicomponent magnetoplasma

A study is made of the radiation resistance of a small filamentary loop antenna immersed in a cold collisionless uniform multicomponent magnetoplasma. Assuming that the current distribution along the loop is uniform and that the loop axis is parallel to the static magnetic field, an integral expression is derived for which is valid for arbitrary values of driving frequency, plasma composition and density, and static magnetic field strength. The mathematical properties of this integral are such that is finite for all values of the driving frequency, including the upper and lower hybrid frequencies as well as the multiple-ion hybrid-resonance frequencies. Application of the integral expression is made to the case of the inner magnetospheric plasma and approximate closed-form expressions are developed for for the very low-frequency/extremely low-frequency (VLF/ELF) range in the magnetosphere. Numerical results in the VLF/ELF range are also presented. It is found that the inclusion of multiple ions introduces interesting effects: sharp maxima appear at the gyrofrequency and the multipleion hybrid-resonance frequency associated with each ion, while sharp minima occur at the "crossover" frequencies. It is concluded that the presence of these relative extrema in the radiation resistance presents interesting possibilities for the use of a small loop as a diagnostic tool in a multicomponent plasma.