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

The transportation of intensive cylindrical beams of charged particles in vacuum demands the solution of space charge problems. The paradox of experimental electrostatics is that similar charges donated to conductors of cylindrical shape have formed a cluster of terminal thickness near the conductor´s surface. It is reported that Coulomb interaction of charges is compensated by its electric macroscopic self-consistent field. The equilibrium equations are written and the mechanism of charges´ confinement is suggested in a frame of reference with the beam´s magnetic field absent. The essence of the mechanism is determined by the fact that pressure gradients of field and charges are equal to each other at arbitrary units of volume. The model for cylindrical symmetry is considered. The exact solutions of equilibrium equations with homogeneous temperature are found. They permit the calculation of 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.