A method and a device for generating extreme ultraviolet (EUV) and soft x-ray radiation from a gas discharge. The device has at least two electrodes each having a flush opening by which an axis of symmetry is defined, in which an intermediate space with a wide spatial homogenous gas filling between anode and cathode is provided. The electrodes are formed in such a way, that the gas discharge is formed exclusively in the volume defined by the flush openings. The current pulses with respect to amplitude and period duration are selected in such a way that a dense hot plasma channel is formed on the axis of symmetry, the plasma being the source of EUV and/or soft x-ray radiation. The preferred area of application is the EUV projection lithography in the spectral range around 13 nm.