An EUV light source and method of operating same is disclosed which may comprise: an EUV plasma production chamber comprising a chamber wall comprising an exit opening for the passage of produced EUV light focused to a focus point; a first EUV exit sleeve comprising a terminal end comprising an opening facing the exit opening; a first exit sleeve chamber housing the first exit sleeve and having an EUV light exit opening; a gas supply mechanism supplying gas under a pressure higher than the pressure within the plasma production chamber to the first exit sleeve chamber. The first exit sleeve may be tapered toward the terminal end opening, and may, e.g., be conical in shape comprising a narrowed end at the terminal end.