In an X-ray tube having a glow cathode for emitting an electron beam, an anode, focusing and deflecting coils and a target in an evacuated envelope, the cathode is a U-bent filament the dimensions of which are large in relation to the electron emitting area. The cathode is heated by passing electric current through it and is differentially cooled so that a small surface area at the site of electron emission is at a substantially higher temperature than remaining surface areas of the cathode. Cooling is effected by a thick-walled cylindrical grid which surrounds the cathode and has at its outer end an annular inward projection which absorbs heat rays from the cathode. The grid has a funnel-shaped outer end surface having an included angle of about 100 DEG to 140 DEG . The electron emitting surface of the cathode lies approximately in a plane defined by the inner peripheral edge of the funnel-shaped end surface of the grid. The electric field applied to the cathode has its highest value at the small electron emitting surface of the cathode.
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