An apparatus and method comprising a cathode structure which can be a cylindrical filament coiled in a helix or which can be constructed of a ribbon or other suitable shape. The cathode structure can be heated by passage of an electrical current, or by other means such as bombardment with energetic electrons. Selected portions of the surface of the cathode structure have an altered property with respect to the non-selected portions of the surface. In one embodiment, the altered property is a curvature. In another embodiment, the altered property is a work function. By altering the property of the selected portions of the surface, the electron beam intensity is increased, and the width is decreased.