Effect of aberration of light in X-ray free electron lasers

We discuss the physics of a microbunched electron beam kicked by the dipole field of a corrector magnet by describing the kinematics of coherent undulator radiation after the kick. Particle tracking shows that the electron beam direction changes after the kick, while the orientation of the microbunching wavefront stays unvaried. Therefore, electrons motion and wavefront normal have different directions. Coherent radiation emission in a downstream undulator is expected to be dramatically suppressed as soon as the kick angle becomes larger than the divergence of the output radiation. In fact, according to conventional treatments, coherent radiation is emitted along the normal to the microbunching wavefront. Here we show that kinematics predicts a surprising effect. Namely, a description of coherent undulator radiation in the laboratory frame yields the radical notion that, due light aberration, strong coherent radiation is produced along the direction of the kick. We hold a recent FEL study made at the LCLS as a direct experimental evidence that coherent undulator radiation can be kicked by an angle of about five times the rms radiation divergence without suppression. We put forward our kinematical description of this experiment.