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The propagation of an annular intense relativistic electron beam inside a cylindrical drift tube is affected by many factors such as external magnetic field, drift tube geometry, the beam self electric and magnetic fields, etc. It is shown, experimentally and theoretically, that the deleterious influence of the self‐fields on the electron flow can be reduced when part of the beam return current is allowed to flow on a grounded conductor that is inserted coaxially within the beam. The improvement manifested itself by reducing the axial magnetic field needed to confine the electron beam or alternately by lowering the electron transverse velocities.