Novel numerical analysis of electric fields in the near field of very-low-frequency antennas based on the charge simulation method

Very-low-frequency (VLF) transmitting antennas have a crucial influence on the nearby electromagnetic environment. Commercial software packages, such as CST Studio Suite (CST) or Altair FEKO (FEKO), are always utilised to calculate the electric fields of VLF antennas, which consume considerable computing resources and time. The classical method of electric field calculation, the charge simulation method (CSM), is first applied to the calculation of electric field near the VLF transmitting antenna. The distribution characteristics of three-dimensional electric fields were analysed. The electric field surrounding the antenna exhibited axial symmetry. The highest electric field strength was at the top of the antenna, and as the distance from the antenna increased, the electric field strength exponentially decreased. The comparisons are performed between the results of the CSM and those of commercial software, the average relative errors of CSM on two observation paths are very small, 2.20% and 2.21%, respectively. Meanwhile, the CSM shows considerable advantages in saving calculation resources and improving efficiency. Additionally, the comparison between CSM calculation and the measured data is carried out. The results show that this method can accurately calculate the electric field near VLF transmitting antenna and offer valuable insights and a new solution.