The criteria of the laminated electron-ion beam electrostatic equilibr
ium are found, the modulated beams with the modulation frequency lower
than the Langmuir plasma frequency being treated. A self-focusing mec
hanism is shown to exist for both electron and ion bunches. The phenom
enon also occurs in the external longitudinal magnetic field In an ext
ernal transverse magnetic field the action of the Lorenz force onto el
ectrons and ions results in the particle escaping from the potential w
ells, in the edge regions of the beam cross-section. However, the pola
rization electric field, originating from the beam charge lamination,
partially compensates the Lorenz force. This, in rum, results in the e
nhanced transport conditions of the layered beams trough a dense plasm
a as compared to the case of bunched electron beams.