Transient luminous events (TLEs) occasionally observed above a strongthunderstorm system have been the subject of a great deal of research duringrecent years. The main goal of this review is to introduce readers torecent theories of electrodynamics processes associated with TLEs. Weexamine the simplest versions of these theories in order to make theirphysics as transparent as possible. The study is begun with the conventionalmechanism for air breakdown at stratospheric and mesospheric altitudes. Anelectron impact ionization and dissociative attachment to neutrals arediscussed. A streamer size and mobility of electrons as a function ofaltitude in the atmosphere are estimated on the basis of similarity law. Analternative mechanism of air breakdown, runaway electron mechanism,is discussed. In this section we focus on a runaway breakdown field,characteristic length to increase avalanche of runaway electrons and on therole played by fast seed electrons in generation of the runaway breakdown.An effect of thunderclouds charge distribution on initiation of blue jetsand gigantic jets is examined. A model in which the blue jet is treated asupward-propagating positive leader with a streamer zone/corona on the top isdiscussed. Sprite models based on streamer-like mechanism of air breakdownin the presence of atmospheric conductivity are reviewed. To analyzeconditions for sprite generation, thunderstorm electric field arising justafter positive cloud-to-ground stroke is compared with the thresholds forpropagation of positivelyegatively charged streamers and with runwaybreakdown. Our own estimate of tendril's length at the bottom of sprite isobtained to demonstrate that the runaway breakdown can trigger the streamerformation. In conclusion we discuss physical mechanisms of VLF (very lowfrequency) and ELF (extremely low frequency) phenomena associated withsprites.
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