Electron beams of relatively high currents (0.5 &mgr;A) and 50‐keV energy with observable modulability at optical frequencies can be produced without violating the Langmuir brightness relationship by shaping the beam in a ``filamentary'' structure, whereby each single‐beam ``filament'' fulfills the recently reported monochromaticity requirement (energy spread better than 10 meV). The monochromator and the electron‐optical‐beam ``shaper'' have to be made adjustable for accurate spatial coherence between the electron‐beam ``filaments''.