VLF input impedance of a loop antenna embedded in the magnetosphere

An analysis is made to calculate input impedance of a loop antenna for radiation of the VLF whistler mode in the magnetosphere. The magnetosphere is assumed to be represented by a cold, uniform and collisionless magnetoplasma medium. Assuming a uniform current distribution of a circular loop, oriented at an arbitrary angle with respect to the Earth's magnetic field line, several closed-form expressions for the loop impedance have been derived. It is found that the loop input reactance is in substantial agreement with the self-inductance of a loop in free space and that the radiation resistance for a small loop can be as large as ～10 ² Ω. It is also found that a second order quasi-static theory is quite valid for determining the input impedance for small loops radiating VLF whistlers in the magnetosphere.