Abstract: The invention relates to a device to irradiate surfaces with electrons, especially to harden surface layers. The device includes a vacuum chamber that has an electron beam window; an electron beam-permeable film that closes off the vacuum chamber from the ambient medium; and an electron beam generating system, consisting of a cathode and a forming electrode which are connected to a high-voltage and beam current feed line. In order to achieve an increase of the electron beam power and to reduce the energy losses during the transfer out of the electron beam window in such a device, according to the invention, the forming electrode is designed as a tubular hollow body with inner hollow space lengthwise dividers and with a lengthwise slit that is open towards the electron beam window. A wire-shaped cathode is arranged in each hollow space segment divided off by the hollow space lengthwise divider.