This invention relates to a triode type cathode structure comprising a cathode conductor (22), an electrical insulation layer (24) and a grid electrode (25), superposed on a support (21), the electrical insulation layer and the grid electrode comprising openings exposing at least one electron emitting element, electrically connected to the cathode conductor (22) and comprising nanotubes (28) made of an electron emitting material. The cathode structure comprises protective means preventing the longest nanotubes from coming into contact with the grid electrode (25).