Theory of 1D Circular Loop Antenna Arrays in Anisotropic Plasma for VLF Applications

Circular loop antennas, as a typical antenna configuration, can be arranged in a one-dimensional linear array within the ionosphere. Such arrays are expected to be widely employed in future space-borne Very Low Frequency (VLF: 3–30 kHz) transmission systems, promising for space-based underwater navigation. Starting with a single-loop antenna, this paper investigates VLF loop antenna arrays embedded in an anisotropic magnetized plasma using a combined numerical and analytical approach. Fully accounting for the coupling effects between individual antennas, a system of N-coupled integral equations is established. By imposing a fixed phase difference between the currents of adjacent antennas, the N coupled integral equations are reduced to a single independent equation, which is then solved to determine the antenna current distribution and input impedance. Computational results demonstrate that the self-impedance and mutual impedance of the antenna array exhibit oscillatory variations with changing parameters, presenting multiple extrema. The research presented in this paper provides a theoretical foundation for the future design and application of practical space-borne VLF transmission systems.