VLF/ELF input impedance of an arbitrarily oriented loop antenna in a cold collisionless multicomponent magnetoplasma

Abstract
A study is made of the input impedance Z of a small strip-loop antenna with arbitrary orientation in a cold collisionless uniform multicomponent magnetoplasma. Assuming a uniform current distribution, an integral expression for Z is derived which is valid for arbitrary values of driving frequency, plasma composition and density, loop orientation angle \phi_{0} , and static magnetic field strength. The integral expression is evaluated numerically for the VLF/ELF range in a plasma modeled upon the inner magnetosphere. Approximate closed-form expressions for Z are also developed. It is found that the loop VLF/ELF input reactance is essentially identical to its free space self inductance. Also the loop radiation resistance is found to be a strong function of \phi_{0} for frequencies near the lower-hybrid-resonance frequency or below the proton gyrofrequency. In addition it is found that for small loops a second-order quasi-static theory correctly predicts Z over much of the VLF/ELF range.