Electromagnetic Field on the Sea Surface Radiated by VLF Spaceborne Antenna Arrays

In this article, we investigate the electromagnetic field radiated by very low-frequency (VLF) spaceborne arrays on the sea surface, where two typical array forms (circular array and curtain array) are under consideration. The closed-form expression for the magnetic field generated on the sea surface is derived through analyzing the wave propagation process via a transmedium (ionosphere-air–sea) path, and the array factors as well as the constraint relations between each element’s current phase and the directed radiation coordinate are given for both array configurations. Computations and analyses show that directed radiation toward sea surface can be effectively realized by adopting array transmitters in VLF spaceborne transmissions. Despite an array with more elements will have greater field strength at the receiving points, the marginal gain of radiation intensity decreases as the element number increases. The results also indicate that a larger geomagnetic dip angle usually leads to a higher excitation efficiency, as long as the dip angle does not exceed the critical angle.