  In coherent radiation sources (diffraction radiation, Smith-Purcell effect,
etc.) based on relativistic electrons passing by a material radiator, the
electron self-field is partly shadowed after each part of the radiator over a
distance of the order of the formation length g2l. This effect has been
investigated on coherent diffraction radiation (DR) by electron bunches. An
absorbing half-plane screen was placed at various distances L before a standard
DR source (inclined half-plane mirror). The DR intensity was reduced when the
screen was at small L and on the same side as the mirror. No reduction was
observed when the screen was on the opposite side. The shadowing effect can
significantly reduce the total energy radiated in a long radiator.
