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

A short electron bunch with length σ 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 λ ≥ σ 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 _e and bunch form factor. For SLAC FFTB conditions (N_e ∼ 10¹⁰, σ = 0.7 mm, outer target size R ∼ 10 mm, slit width h ∼ 0.1 mm) we approximated coherent DR (CDR) spectrum by coherent transition radiation (TR) one because in the wavelength region λ ∼ σ ≫ 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 ≤ 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 45°). It means an electron receives the radiation recoil in this direction. In other words, electron has a transverse kick about 1 μrad that may be considered as permissible. Published by Elsevier B.V.