[en] Considered is the effect of shielding of electron ring self-fields with chamber conducting walls close to it, on the ring electron coherent and incoherent motion. It is shown that for ultrarelativistic electron energies the intensity limitation, imposed by the requirement of ring stability as a whole in the chamber mid-plane, is the most stringent. The more is the shift between the chamber and external magnetic field mid-planes, the less is acceptable number of electrons in the ring. A method of passive stabilizing the ring axial coherent motion with the system of opposing coils is proposed. The coils compensate partially electrostatical ring attraction to chamber walls and diminish tha asymmetry of external magnetic field. It is demonstrated that such a system permits to increase twofold a number of electrons in the ring compressed