According to one embodiment, an X-ray tube includes an anode target, a cathode including a filament and a convergence electrode which includes a groove portion, and an envelope. The groove portion includes a pair of first bottom surfaces which are located in the same plane as the filament and between which the filament is interposed in a width direction of the groove portion, and a pair of second bottom surfaces between which the filament and the pair of first bottom surfaces are interposed in a length direction of the groove portion and which are located closer to an opening of the groove portion than the pair of first bottom surfaces.

An extreme-ultraviolet light source device comprises: a discharge chamber of which the inside is maintained in a vacuum; an electron beam-emitting unit which is located inside the discharge chamber and produces electron beams; and a metal radiator which is located inside the discharge chamber and is ionized by the electron beams. Extreme-ultraviolet radiation occurs in plasma generated from the metal radiator. The electron beam-emitting unit comprises: a cathode electrode; a plurality of emitters located on the cathode electrode and including a carbon-based material; and a gate electrode which is located on the plurality of emitters at a distance therefrom and to which a pulse voltage is applied.