VLF Near-Field Excited by an Arbitrarily Oriented Electric Dipole in a Magnetized Plasma

Since the orientation of a very low frequency (VLF: 3-30 kHz) space-borne antenna relative to the geomagnetic field will change with the satellite orbiting around the earth, precisely computing the near-field excited by an arbitrarily oriented radiator in the ionosphere is of great importance to the antenna analysis in realistic VLF space-borne applications. In this paper, we propose a semi-analytical method for evaluating the near-field of a VLF electric dipole of arbitrary orientation in a magnetized plasma, where the arbitrarily oriented dipole is modeled as the superposition of dipoles parallel and perpendicular to the magnetic field. The near-field in this case consists of the contributions of both the ordinary wave (O-wave) and the extraordinary wave (E-wave). Due to its large attenuation rate, the integral for the O-wave can be directly estimated through numerical integration, while the integral for the E-wave is evaluated with the help of speed-up convergence algorithm and the complex variable theory. Computations show that the O-wave still has comparable amplitudes with the E-wave in the near zone, and the field generated by the dipole perpendicular to the magnetic field is of dominant effects. Moreover, it is found that there exists remarkable “aggregation effect” in the radiation pattern of the E-wave, indicating that the propagable mode in the magnetized plasma propagates mainly along the direction of the magnetic field.