The paper presents the results of our theoretical investigations of fast electron beam generation in high-temperature plasma of a laser plume and further acceleration of electrons in atmosphere. The discharge formation in these inhomogeneous media was also investigated. Results of calculations have shown an opportunity of generation of fast beam with a current in a range ≈ 10^2 - 10^3 A from the laser plume with the length of 5 mm and the area of 0.1 mm^2. The main reason of limitation of fast electrons current pulse was the breakdown of the discharge gap. The preliminary experiments carried out by us have shown the correctness of chosen direction.
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