Electron-ionic model of ball lightning
The electron-ionic model of ball lightning was represented by Sergey G. Fedosin , a physicist and the philosopher from Perm, Russia, and Sergey A. Kim, from Perm state university, in a number of works.  
In this model, ball lightning is a cluster of the very hot ionized air with the positive charge in general, whose shell consists of the rapidly revolving electrons with the total current up to 1,4•105 A. Ball lightning as whole is supported by the balance of the electromagnetic forces, which act between the charges. Positive ions inside the lightning are distributed freely as a result of the spherical symmetry, and attract to themselves the electrons of shell, retaining them from the dispersion. According to the model the ball lightning is formed from two close branches of a linear lightning at the time of termination of current in the main channel with the subsequent closure of branches in a current ring.
Electronic currents in the shell create strong magnetic field inside the lightning. These currents are perpendicular to rotational axis, the diameter of rotation decreases to the poles, where magnetic field grows. This retains positive ions from the dispersion along the rotational axis due to the effect of magnetic bottle. Basic magnetic field inside the lightning is directed along the rotational axis. I.e., ions can move along the axis along the lines of magnetic field. From other side, the ions revolve in the circle perpendicularly to axis under the action of Lorentz force with respect to their thermal velocity. As a result at a certain distance from the axis of lightning appears the intersection of two ion flows, which is observed as the luminous shells inside the lightning. Emission from the shells appears from friction and recombination of the being intersected ion flows.
Theory predicts from the first principles the maximum diameter of ball lightning 34 cm.  With the larger size the summary charge of lightning, which has positive sign, grows to the value of 10 –5 C and appears the electrical breakdown of air near the lightning. The energy of the lightning in this case reaches 10.6 kJ, the current in the shell 1.4∙10 5 A, the internal magnetic field of 0.5 Tesla. Because of its charge ball lightning does not simply float under the action of the force of Archimedes, but it is retained by electric force from clouds and the induced charge on the Earth. The formula for the maximum radius of ball lightning has the form:
Where m, q are the electron mass and charge, E0=30 kV/cm is the greatest possible electric field of ball lightning, leading to the electric air discharge, c - the speed of light. In moist air maximum field strength becomes smaller, which allows ball lightning have the sizes more than 34 cm.
According to the model under different sizes of ball lightning its parameters are as follows: 1) radius of 7 cm, the current in the shell 2.9 • 10 3 A, the internal magnetic field of 0.026 T, the energy of 503 J. 2) the radius of 1 cm, the current in the shell 20 A, the internal magnetic field of 0.0013 T, the energy of 2.2 J.
It was confirmed by investigations in the St. Petersburg Institute of Nuclear Physics, that the ball lightning actually consists of positively charged ions and negatively charged shell.  It was confirmed also the presence of uncompensated electric charge at a ball lightning. 
Bead lightning is also explained on the basis of electron-ionic model of ball lightning. 
- Fedosin S.G. Sovremennye problemy fiziki: v poiskakh novykh printsipov. – Moskva.: Editorial URSS, 2002, 192 pp.
- Fedosin S.G., Kim A.S. The Physical Theory of Ball Lightning. Applied Physics (Russian Journal) , No. 1, 2001, P. 69 – 87.
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- Sergey Fedosin, The physical theories and infinite hierarchical nesting of matter, Volume 1, LAP LAMBERT Academic Publishing, pages: 580, ISBN-13: 978-3-659-57301-9.
- Kim A.S. and Fedosin S.G. Method of production of ball lightning // Patent of the Russian Federation No. 2210195, class 7H05H1/00, G09B23/18, bulletin No. 22, 2003.
- Sergey G. Fedosin, Anatolii S. Kim. Electron-Ionic Model of Ball Lightening. Journal of new energy, V. 6, No. 1, 2001, P. 11 - 18.
- Electron-ionic model of ball lightning in Russian
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