Treated is the steady state of a beam interacting with the plasma which it produces in a low‐density gas and in which magnetic self‐focusing must be considered. Self‐focusing is assumed to exist when the second time derivative of the moment of inertia of the beam electrons is negative and when that of the ions is neglected. Predictions are related to experiments with 10–15‐keV beam electron energies, beam currents of several hundred milliamps, and system pressures of 10−4Torr. Simultaneous pinching is observed with approximately equal radial forces on the beam electrons due to overneutralization and due to magnetic self‐focusing.