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We review the basic issues of the initiation and development of the lightning discharge, which top the list of the most important and yet unsolved problems of atmospheric electricity. The main challenges of creating theoretical models are due to the fact that the value of the electric strength of atmospheric air exceeds the peak electric fields measured in thunderstorm clouds by approximately an order of magnitude. Among several concepts proposed to explain the process of initiation of a lightning discharge at different times, two ideas stand apart, namely, the hypothesis of the lightning birth caused by the initiation of a positive streamer from the surface of a hydrometeor and the hypothesis of lightning initiation due to the development of a runaway electron breakdown. However, none of these approaches has become universally recognized or dominant due to various difficulties. A fundamentally new mechanism of lightning discharge initiation, which has been proposed recently, is based on the noise-induced kinetic transition occurring in the stochastic field of charged hydrometeors. The proposed approach looks like a sequence of discharge activity transitions from small spatial scales to increasingly larger ones. One of the main features of the proposed hypothesis is that the generation of streamers is determined by the level of small- and mesoscale fluctuations of the electric field in the thunderstorm and is essentially independent of the large-scale field. In this case, the role of the large-scale field is to ensure interaction of the initiated streamers, when they start developing mainly in the direction specified by this field. In the final section of the review, we discuss the fundamental role of the polarity asymmetry in the processes of the initiation and further development of lightning discharges. [ABSTRACT FROM AUTHOR]

We propose a small-scale transport model of the electric-discharge tree formation and analyze its implementation for a characteristic case of the thundercloud conditions. The following innovative features of the model can be emphasized: no connection to the spatial grid, high spatiotemporal resolution, and allowance for the asymmetry of the development of the positive and negative streamers and the time evolution of the discharge-channel parameters. The criterion of the streamer-to-leader transition, which is used in this work, is formulated in terms of the channel temperature and is based on the well-known mechanism of ionization-overheating instability, which is universal for the spark discharge. Within the framework of the described approach, a heated well-conducting leader channel is formed by combining the currents of tens of thousands of streamers, so that each of them initially has f negligible conductivity and a temperature that does not differ from the ambient temperature. The model bileader tree has electrodynamic characteristics that are intermediate between those known for the laboratory long spark and the developed lightning, which is expected for an "immature" lightning leader. The morphology and electrical parameters of the calculated discharge tree of the incipient model lightning leader agree with the modern data on the lightning-discharge development. [ABSTRACT FROM AUTHOR]

Electrodynamics of a thunderstorm cloud is considered with allowance for recirculation and multiflow motion of charged intracloud particles. In this simulation, the large-scale electric-field emerges due to the charge separation at the process of air convection and develops through the oscillation regime in the initial and final stages of the thunderstorm evolution. These oscillations qualitatively explain the observed behavior of the electric field of a thunderstorm. On the other hand, the multiflow convection is unstable and leads to generation of small-scale electrostatic waves (wavelength from 1 to 100 m) with amplitude reaching the conventional breakdown value. Such an instability can initiate microdischarge intracloud activity at the preliminary stage of the lightning discharge and between individual return strokes. We propose a three-dimensional cellular automata model which describes the main features of the preliminary stage of the lightning. [ABSTRACT FROM AUTHOR]