Applicability of the Gauss´ law on Lightning channel corona sheath modeling

Generalized lightning traveling current source return stroke model (GTCS) has been used to calculate the dynamics of lightning channel corona sheath surrounding thin channel core during the return stroke stage. Using measured electric field waveforms of Miki et al., 2002 in the immediate vicinity of the lightning channel, the channel discharge function vs. time is calculated. The applicability of the simple form of the Gauss´ law on lightning channel corona sheath modeling is examined. The conditions for the validity of the expressions of the electric field inside and outside the corona sheath are derived. It is concluded that the simple form of the Gauss´ law can be successfully used for the corona sheath modeling if the radial distance of the measuring point from the channel core is small compared to its vertical position.