  One of the options for increasing longitudinal coherency of X-ray free
electron lasers (XFELs) is their seeding with microbunched electron beam.
Several schemes leading to significant amplitude of the beam bunching at X-ray
wavelengths were recently proposed. All these schemes rely on beam optics
having several magnetic dipoles. While the beam passes through a dipole, its
energy spread increases due to quantum effects of synchrotron radiation. As a
result, the bunching factor at small wavelengths reduces since electrons having
different energies follow different trajectories in the bend. We rigorously
calculate reduction in the bunching factor due to incoherent synchrotron
radiation while the beam travels in arbitrary beamline. We apply general
results to estimate reduction of harmonic current in common schemes proposed
for XFEL seeding.
