An electron gun includes a sealed chamber under vacuum. A cathode having an emitting face is placed inside the chamber. An anode forms a sealed window, formed facing the emitting face in one of the walls of the chamber. The anode is capable of allowing electrons emitted by the emitting face to pass through. A biasing apparatus sets up a voltage between the anode and the cathode, capable of accelerating these electrons towards the anode, the electrons thus accelerated forming a beam that passes through the anode. The anode and the emitting face each have a curvature, the curvature of the anode making it capable of resisting a pressure difference between the inside and the outside of the chamber and being designed to cooperate with the curvature of the emitting face to focus the electron beam outside the chamber.