A gas discharge source, in particular, for generating extreme ultraviolet and/or soft X-radiation, has a gas-filled intermediate electrode space located between two electrodes, devices for the admission and evacuation of gas, and one electrode that has an opening that defines an axis of symmetry and is provided for the discharge of radiation. A diaphragm exhibits at least one opening on the axis of symmetry and operates as a differential pump stage, between the two electrodes.