Lightning return stroke electromagnetic field generated by tortuous channel under different observation scales

Due to the tortuosity of real cloud-to-ground lightning channel, a 3D model of lightning electromagnetic field generated by a section of sloped lightning channel in the space is proposed according to the dipole method, and the analytic expressions for lightning electromagnetic field in the cylindrical coordinate system are presented. On this basis, the influence of observation scale for the channel on the calculation of lightning electromagnetic field generated by the first return stroke and subsequent return stroke is analyzed. The results show that the tortuosity of lightning channel is the direct reason of oscillation in the electromagnetic field waveform. There is nearly no oscillation in both first and subsequent return stroke electric field waveform in near-zone even for tortuous lightning channel. The channel tortuosity also has no influence on the rise time of electromagnetic field waveform. However, the initial peak value (or the initial knee point for the electric field waveform in near-zone and intermediate-zone), the degree of oscillation, and the frequency spectral energy distribution of lightning electromagnetic field waveform are all seriously influenced by the channel tortuosity and the channel observation scale. The oscillation in lightning electromagnetic field waveform becomes visible under the situation of small observation scale, far observation distance, and short rise time of the return stroke current.