a discharge chamber which is enclosed by and evacuated in a first and a second coaxial electrode housing and in which a work gas is introduced under a defined pressure and which has an outlet opening for the short-wavelength radiation;

said two electrode housings being electrically insulated from one another so as to resist dielectric breakdown by an insulator layer;

said second electrode housing projecting by a necked-down outlet into the first electrode housing to enable a gas discharge with a region around the outlet opening of the first electrode housing;

said first electrode housing around the outlet opening and the second electrode housing at the necked-down outlet each have an electrode collar so that the gas discharge for generating the radiating plasma is deliberately ignited between these electrode collars inside the discharge chamber of the first electrode housing;

special cooling channels for circulating coolant being integrated in the electrode material in the electrode collars;

said cooling channels being advanced radially up to within a few millimeters of the highly thermally stressed surface regions of the electrode collars and have a necked-down channel portion in the area of the highly stressed surface substantially parallel to the axis of symmetry of the electrode housings in order to increase the flow rate of a circulating coolant; and

said necked-down channel portion being provided with channel structures for increasing the inner surface and for further increasing the flow rate of the circulating coolant, said channel structures being generated by suitable surface working of the necked-down channel portions.