In the present study, it was examined generation of nanosecond-duration electron-beam (EB) pulses by a wide-aperture open discharge burning in helium or in a mixture of helium with nitrogen and water vapor. In the experiments, a discharge cell with coaxial electrode geometry, permitting radial injection of the electron beam into operating lasing medium, was used, with the cathode having radius 2.5 cm and length 12 cm. It was shown possible to achieve an efficient generation of a high-intensity electron beam (EB pulse power ∼250 MW and EB pulse energy up to 4 J) in the kiloampere range of discharge currents (up to 26 kA at ∼12 kV discharge voltage). The current-voltage characteristics of the discharge proved to be independent of the working-gas pressure. The existence of an unstable dynamic state of EB, conditioned by the presence of an uncompensated space charge accumulated in the discharge cell due to the exponential growth of the current in time during discharge initiation and the hyperbolic growth of current density in the direction towards the tube axis, was revealed. The obtained pulsed electron beam was used to excite the self-terminated laser on He 21P10-21S0 transition. The oscillations developing in the discharge cell at high discharge currents put limit to the pumping energy and emissive power of the laser excited with the radially converging electron beam.