The physical design of a cylindrical x‐ray source, producing Al Karadiation (1486.6 eV) for use with a spherical photoelectron spectrometer, is presented. Design requirements, such as maximum efficiency and maximum intensity of characteristic radiation for minimum bremsstrahlung, are included in the presentation. The electron trajectories from filament to anode are calculated for various geometries. A brief description of the calculations, involving a numerical solution of Laplace's equation in cylindrical coordinates is given. Experimental evidence is presented to confirm the adaptation of these calculations in the design of the source.