An apparatus is provided for impinging fluids and inner walls of hollow bodies with accelerated electrons, comprising a cylindrical electron exit window as a component of a cylindrical housing having a cylinder axis and enclosing an evacuable space; a wire-shaped, strand-shaped, rod-shaped, annular, helical, or cylindrical cathode which is arranged within the evacuable space and is enclosed by the cylindrical electron exit window and by a cylindrical control grid, wherein the cylindrical control grid has a diameter that is smaller than the diameter of the cylindrical electron exit window and a first power supply unit is connected between the wire-shaped, strand-shaped, rod-shaped, annular, helical, or cylindrical cathode and the cylindrical electron exit window, so that electrons can be emitted from the wire-shaped, strand-shaped, rod-shaped, annular, helical, or cylindrical cathode and accelerated radially away from the cylinder axis of the cylindrical housing in the direction of the cylindrical electron exit window.