Radiation Patterns of an Arbitrarily Oriented VLF Curtain Array in an Anisotropic Magnetoplasma

In this article, we propose a theoretical method for calculating the radiation patterns of a very low-frequency (VLF: 3–30 kHz) curtain array immersed in an anisotropic magnetoplasma. As the arrays formed by multiple VLF linear antennas may become a potential scheme for VLF space-borne transmissions, figuring out the radiation pattern of such arrays is essential to the performance evaluation or efficiency improvement of practical VLF space-borne transmitting systems. The analytical expression for the VLF field excited by an electric dipole is first given at arbitrary orientations. By considering the influence of current nonuniformity and mutual coupling, the total radiation field of the array is obtained for both near- and far-zone cases, and the array factor is derived under the far-zone condition. Computations and analyses show that variations in the current phase difference or electrical separation will cause certain changes to the directivity of the array in the near zone, while the radiation pattern in the far zone mainly follows the direction of the geomagnetic field. It is also found that despite the total field of an array can be enhanced by increasing the number of elements, the marginal gain on the field amplitude is descendant as the element number keeps increasing. Moreover, due to the larger wave attenuation in the propagation direction vertical to the magnetic field, the radiation ability of the array will gradually decrease when the geomagnetic inclination angle becomes larger.