Fractal dynamics of electric charges in a thunderstorm cloud

A fractal model is suggested for describing the dynamics of electric charge s in a thunderstorm cloud during the preliminary stage of the lightning dis charge. The model is based on the concept of microdischarges (of about 1 to 10 m in size) appearing due to instabilities that are developed in the cen tral part of the cloud and are similar to dissipative beam-plasma instabili ties. The microdischarges are assumed to appear during the nonlinear stage of instability development and represent nonstationary conducting connectio ns whose number increases as the cloud ripens. These connections are essent ially a percolation fractal forming a peculiar kind of a drainage electrica l system for collecting the macroscopic charge in the thunderstorm cloud. T he electric charge runs down by this conducting percolation cluster to the base of the cloud. The use of the fractal dimension of the drainage system makes it possible to determine the electrical characteristics of the system and the characteristic times of charge collection from different regions o f the cloud and to associate them with the observable K- and J-processes. T he mechanism of the electric field enhancement in the region between the bo ttom of the cloud and the ground is assumed to be caused by the transformat ion of the three-dimensional fractal into the two-dimensional one as the el ectric charge is collected at the bottom boundary of the cloud.