Coherent radiation recoil effect for the optical diffraction radiation beam size monitor at SLAC FFTB

A short electron bunch with length (T passing through a slit in the diffraction radiation (DR) target generates radiation with a broad spectrum. Optical part of the spectrum (incoherent radiation) may be used for beam size measurements, but in the wavelength range lambda greater than or equal to sigma a radiation becomes coherent. The coherent DR spectrum per each electron in a bunch is equal to single electron spectrum times by the number of electrons in a bunch N-c and bunch form factor. For SLAC FFTB conditions (N-c similar to 10(,)(10) sigma = 0.7 mm, outer target size R similar to 10 mm, slit width h similar to 0.1 mm) we approximated coherent DR (CDR) spectrum by coherent transition radiation JR) one because in the wavelength region lambda similar to sigma much greater than h TR and DR spectra coincide with high accuracy. Changing the DR target by a TR target with projection on the plane perpendicular to electron beam as a circle with radius R less than or equal to 20 mm we calculated CDR spectra using simple model. \ Knowing the CDR spectrum we estimated the energy CDR emitting by each electron in the perpendicular direction (due to target inclination angle 45degrees). It means an electron receives the radiation recoil in this direction. In other words, electron has a transverse kick about 1 murad that may be considered as permissible. Published by Elsevier B.V.