Calculation of thundercloud electric fields for initiating electric discharges between clouds and the upper atmosphere

Nonstationary electric fields of thunderclouds, which are created by these clouds after cloud-to-ground discharges in the atmosphere with exponential electrical conductivity, are calculated in an electrostatic approximation. The asymptotic expressions for the distribution of the vertical component of the electrostatic intensity, depending on time and atmospheric altitude along the axis of symmetry, have been obtained for the point and one-dimensional distributions of the initial cloud charge, as well as for the horizontal distribution of the cloud with a finite cylindrical radius. These results are used to determine the vertical component of the electrostatic intensity and the cloud charges necessary for initiating discharges between clouds and the upper atmosphere.