On compensation of Coulomb interaction of charges by beam's self-consistent field (model of isothermal equilibrium with homogeneous temperature)

Abstract

the transportation of intensive cylindrical beams of charged particles in vacuum demands solution of problem of space charge. The paradox of experimental electrostatic is that similar charges donated to conductor of cylindrical shape have formed the cluster of terminal thickness near the conductor's surface.It is founded in report that Coulomb interaction of charges is compensated by its electric macroscopic selfconsistent field. The equilibrium equations are written and the mechanism of charges' confinement is suggested in the frame of reference with beam's magnetic field absence. The essence of mechanism is determined by that pressure gradients of field and charges are equal with each other at arbitrarily unit of volume.The model for cylindrical symmetry is considered. The exact solutions of equilibrium equation with homogeneous temperature are found. They permit to calculate diameters of intensive beams, radial distributions of potential, field strength, pressure and density of charges. The numerical estimates of beams' diameters for various cathodes are made.Index Terms -intensive cylindrical beam, charge cluster, self-consistent field, collective interaction, equilibrium equation, Coulomb interaction compensation.

Ball lightning and unidentified flying objects (UFOs)

“…To explain the structure of such objects, various models have been proposed, among which the most reasonable is the Sapogin's model. 37 According to this model, the spherical layer of like charges has a configuration that promotes the appearance of a hypothetical self-consistent electric field in it. The presence of this field leads to a non-uniform distribution of charges and the appearance of a gradient force that prevents Coulomb repulsion of charges.…”