An EUV radiation source device with a chamber that is divided into a discharge space and a collector mirror space provided with EUV collector optics. Between them, an aperture component with an opening which is cooled is provided. First and second discharge electrodes are rotated. Sn or Li is irradiated with a laser. Pulsed power is applied between the first and second discharge electrodes to form a high density and high temperature plasma between the two electrodes so that EUV radiation with a wavelength of 13.5 nm is emitted, is focused by the EUV collector optics and is guided into the irradiation optical system of an exposure tool. There are a first pumping device and a second pumping device for pumping the discharge space and the collector mirror space. The discharge space is kept at a few Pa, and the collector mirror space is kept at a few 100 Pa.