The process of scattering of coherent diffraction radiation (CDR) generated
by short electron bunch on one of the subsequent bunches of the accelerato
r is considered. CDR spectrum from bunch passing through circular aperture
in an ideally conducting disc have been calculated. It is shown that the CD
R yield is suppressed significantly in the soft part of the spectrum due to
finite outer radius of the disc. The use of the concave mirror with centra
l hole instead of the flat disc with aperture is proposed. The focusing of
the backward diffraction radiation onto following bunch may be possible in
this case. The estimation of the yield of scattered hard photons has been o
btained, that is proportional to N-e(3), where N-e is the number of electro
n per bunch. (C) 2000 Elsevier Science B.V. All rights reserved.