An apparatus for generating electron radiation comprises: an elongated, wire-shaped hot cathode to emit electron radiation having an elongated, line-shaped cross section perpendicular to a direction of propagation of the electron radiation; a cathode electrode; an anode electrode with an opening through which the electron radiation emitted from the hot cathode can pass, wherein a voltage applied between the cathode electrode and the anode electrode accelerates electrons emitted from the hot cathode; and a deflecting unit to deflect the electron radiation downstream of the opening of the anode electrode, wherein a cross section of the electron radiation perpendicular to the direction of propagation is changed by the deflecting unit to decease a longitudinal extent of the electron radiation and to increase a transverse extent of the electron radiation such that longitudinal and transverse extents of the electron radiation perpendicular to the direction of propagation are about the same size.