The invention is directed to an arrangement for the generation of short-wavelength radiation based on a hot plasma generated by gas discharge and to a method for the production of coolant-carrying electrode housings. It is the object of the invention to find a novel possibility for gas discharge based short-wavelength radiation sources with high average radiation output in quasi-continuous discharge operation by which efficient cooling principles can be implemented using inexpensive and simple means in order to prevent a temporary melting of the electrode surfaces and, therefore, to ensure a long lifetime of the electrodes. According to the invention, this object is met in that special cooling channels for circulating coolant are integrated in electrode collars of the electrode housings. The cooling channels are advanced radially up to within a few millimeters of the highly thermally stressed surface regions and are connected by necked-down channel portions which are arranged coaxial to the axis of symmetry and which are provided with channel structures for increasing the inner surface and for increasing the flow rate of the coolant.