The TEM wave characteristic impedance of lightning return stroke by multi-fractal theory

The TEM wave characteristic impedance of lightning return stroke is investigated by considering the channel of Cloud-to-Ground(CG) flash as a coaxial transmission line(TL) with both the good conductor quality factor theory and the multi-fractal theory. It takes the lightning return stroke channel (RSC) and outer corona sheath as a coaxial wave guide. The relationships among the 2D-Hausdroff dimension, the RSC radius and the corona sheath radius are calculated by utilizing the fractal dimension definitions both under the low and high frequency condition with the skin-depth as the characteristic length at the TM01 wave cut-off frequency, respectively.