Electromagnetic scattering field of transmission lines in half-space background

To formulate effective passive interference protection measures, precise quantification of transmission-line scattering fields is essential. In practical engineering, transmission lines are situated above ground, forming a half-space environment. The diffuse reflection of electromagnetic waves from the ground generates an electromagnetic scattering field, which, when vectorially superimposed on the original electromagnetic scattering field of the transmission line, alters the latter’s scattering field. Consequently, using the traditional free-space electric field integral equation (EFIE) cannot accurately solve for the electromagnetic scattering field of the transmission line in a half-space environment. To address this limitation, this study derives a modified EFIE tailored for half-space scenario. Specifically, the half-space Green’s function for electromagnetic scattering and the incident electric field are determined, leading to the reformulation of the EFIE. Numerical analysis demonstrates that the proposed half-space algorithm yields results differing from the traditional (free-space) method by an average relative error of 11.98% and a maximum relative error of 19.75%. Furthermore, parametric studies reveal that the ground’s influence on the scattering field varies with the electromagnetic wave incidence angle relative to vertical: initially decreasing then increasing as this angle grows. Additionally, the effect strengthens with increasing ground relative permittivity. Mechanism analysis of ground-background modulation on transmission-line scattering fields. Derivation of half-space Green’s functions for transmission-line EM scattering. Electric field integral equation (EFIE) formulation for grounded half-space transmission lines.