A cathode sheath for a thermionic electron-gun cathode. The sheath is substantially in the form of a hollow cylinder and has an outer surface and an inner surface, a central axis, a closed end and an axially-opposite open end, and a side wall extending between the closed end and the open end. The sheath is a continuous bimetallic laminate having a first layer of material forming the inner surface and a second layer of electron-emissive material overlying substantially the entirety of the first layer and forming the outer surface. The laminate has a preselected thickness at the closed end and has a thickness at the side wall which varies along the central axis.